Structural Design Method of Prestressed Shield Tunnel

Abstract

A method for designing a prestressed shield tunnel structure comprises the following steps: S1, determining basic design parameters of a prestressed shield tunnel; S2, designing a plurality of prestressing schemes; S3, determining the overall effective axial force distribution under the plurality of prestressing schemes; S4, establishing a homogeneous circular ring model of a tunnel structure according to a newly revised conventional method; S5, using a load structure method to calculate the internal force distribution of water and soil loads of a tunnel structure of a most unfavorable section; S6, calculating the overall internal force distribution of the tunnel structure after taking into account the effect of prestressing; S7, optimizing the reinforcement scheme and prestressing scheme of the tunnel structure in consideration of cost; through the above method, the present invention creatively proposes a method for designing a prestressed shield tunnel structure that takes into account the loss of prestressing and the reinforcing effect of prestressing on the segment structure, and effectively reduces the amount of steel bars used and reduces the production cost by being able to characterize the performance advantages of the prestressed shield tunnel structure; at the same time, the design method has a clear concept, is simple to calculate, and conforms to the usage habits of designers.

Description

Technical Field

[0001] The present invention relates to the technical field of shield tunnel structures, and in particular to a design method for a prestressed shield tunnel structure. Background Art

[0002] Prestressed concrete, created by applying a certain amount of precompressive stress to concrete, can offset or partially offset the tensile stress generated by the structure's load-bearing behavior, thereby improving mechanical properties such as crack resistance, stiffness, and bearing capacity, while also reducing the amount of steel required. Introducing prestressing technology into existing shield tunnel structures can create a prestressed shield tunnel structure.

[0003] Prestressed shield tunnel structures apply prestressing force to provide additional axial force to the tunnel structure, forming a self-stabilizing structural system. This reduces structural deformation with virtually no increase in bending moment, resulting in a more balanced load distribution. Compared to existing shield tunnel structures, prestressed shield tunnel structures achieve stiffness approaching that of cast-in-place concrete, significantly improving mechanical properties such as structural toughness, ductility, cracking load, and ultimate bearing capacity. This effectively mitigates defects such as large deformation, water leakage, and settlement, reduces the use of steel and concrete, and extends the service life.

[0004] To this end, in view of the above-mentioned defects, the designers of the present invention have conducted intensive research and design, and integrated the experience and achievements of many years of working in related industries to research and design a prestressed shield tunnel structure design method that can reflect the working mechanism of the prestressed shield tunnel structure, while conforming to the usage habits of designers and being simple and easy to use, in order to overcome the above-mentioned defects. Summary of the Invention

[0005] The purpose of the present invention is to provide a prestressed shield tunnel structure design method. The method proposes a prestressed shield tunnel structure design method that takes into account prestress loss and the reinforcing effect of prestress on the segment structure. The method can demonstrate the performance advantages of the prestressed shield tunnel structure, reduce the amount of steel bars used, and lower production costs. At the same time, the design method has a clear concept, simple calculations, and conforms to the usage habits of designers.

[0006] To achieve the above object, the present invention discloses a prestressed shield tunnel structure design method, which is characterized by comprising the following steps:

[0007] S1. Determine the basic design parameters of prestressed shield tunnel;

[0008] S2. Design various prestressing schemes;

[0009] S3. Determine the overall effective axial force distribution under various prestressing schemes;

[0010] S4. Establish a homogeneous circular ring model of the tunnel structure according to the new modified conventional method;

[0011] S5. Use the load structure method to calculate the internal force distribution of water and soil loads in the most unfavorable section of the tunnel structure;

[0012] S6. Calculate the overall internal force distribution of the tunnel structure after taking into account the effect of prestressing;

[0013] S7. Consider the cost and optimize the tunnel structure reinforcement scheme and prestressing scheme.

[0014] The steps include:

[0015] S1. Determine the basic design parameters of prestressed shield tunnels based on tunnel type, function, ground conditions, and shield parameters;

[0016] S2. Design various prestressing schemes based on the bonded or non-bonded tensioning scheme and the number of prestressing strands in a single bundle;

[0017] S3. Calculate the long-term prestress loss of a single prestressed strand and determine the overall effective axial force distribution under various prestressing schemes;

[0018] S4. Establish a homogeneous circular ring model of the tunnel structure and use the new correction method to correct the tunnel structure stiffness;

[0019] S5. Use the load structure model to calculate the internal force distribution of water and soil loads on the tunnel structure at unfavorable sections along the shield tunnel, and calculate and determine the internal force distribution of water and soil loads on the tunnel structure at the most unfavorable section;

[0020] S6. Determine the overall internal force distribution of the tunnel structure based on the water and soil load internal force distribution and the overall effective axial force distribution of the tunnel structure at the most unfavorable section;

[0021] S7. Comprehensively consider the main reinforcement scheme and prestressing scheme of the prestressed shield tunnel structure, and select the scheme with the lowest cost as the reinforcement scheme of the prestressed shield tunnel structure.

[0022] Among them, the prestressed shield tunnel includes multiple prestressed blocks arranged in a ring, which are divided into prestressed anchor blocks, prestressed capping blocks, prestressed standard blocks and prestressed adjacent blocks. The prestressed standard blocks are located at the bottom of the tunnel structure, and their two ends are connected to the prestressed anchor blocks. The other end of the prestressed anchor block is connected to the prestressed adjacent blocks. The prestressed capping blocks are located at the top of the tunnel structure, and their two ends are connected to the prestressed adjacent blocks. Prestressed channels that are interconnected are embedded in each prestressed block. Each prestressed block is connected in an annular direction by a longitudinal seam connector and connected longitudinally by an annular seam connector.

[0023] Wherein, the S3 specifically includes:

[0024] S31. Calculate the long-term prestress loss and overall effective axial force of a single prestressed strand under various prestressing schemes;

[0025] S32. Calculate the angle between the prestressed anchor blocks;

[0026] S33. Calculate the overall effective axial force of the prestressed shield tunnel structure under various prestressing schemes based on the angles between the prestressed anchor blocks.

[0027] Wherein, the S4 specifically includes:

[0028] S41. A homogeneous circular ring model of a prestressed shield tunnel is established using beam elements of uniform cross-section and stiffness, and the interaction between the model and the stratum is modeled using a foundation spring model.

[0029] S42. Set the overall stiffness of the homogeneous ring model according to the stiffness adjustment coefficient of the new modified convention.

[0030] Among them, S5 specifically includes: selecting unfavorable sections such as the thickest and thinnest tunnel cover, the highest and lowest groundwater levels, the presence of overload or bias, and the tunnel passing through a sudden change in stratum conditions, and using the load structure model to calculate the water and soil load internal force distribution of the tunnel structure at each unfavorable section in turn, and determining the most unfavorable section and the corresponding water and soil load internal force distribution.

[0031] Among them, the S6 specifically includes: the overall bending moment of the prestressed shield tunnel structure is the water and soil load bending moment after the ordinary shield tunnel structure adopts the new revised conventional method; the overall axial force is the sum of the water and soil load axial force after the ordinary shield tunnel structure adopts the new revised conventional method and the overall effective axial force of the tunnel structure.

[0032] Among them, S7 specifically includes: calculating the reinforcement schemes in sequence according to the overall internal force distribution of the prestressed shield tunnel structure under various prestressing schemes, and then calculating the total cost of steel bars and prestressed strands under various prestressing schemes in sequence, and selecting the main reinforcement scheme and prestressing scheme with the lowest total cost.

[0033] From the above content, it can be seen that the prestressed shield tunnel structure design method of the present invention has the following effects:

[0034] 1. The modified method proposed in this paper takes into account prestress loss and the reinforcing effect of prestress on the segment structure, building on the traditional modified method. The introduced stiffness adjustment factor adjusts the stiffness of the prestressed shield tunnel structure. The adjusted stiffness of the prestressed shield tunnel structure is between the stiffness reduction factor of the traditional modified method and 1, better demonstrating the performance advantages of the prestressed shield tunnel structure.

[0035] 2. The present invention simplifies the calculation of the overall internal force of the prestressed shield tunnel structure. That is, the overall bending moment is the bending moment of the water and soil load after the new revised conventional method is adopted for the ordinary shield tunnel structure; the overall axial force is the sum of the axial force of the water and soil load after the new revised conventional method is adopted for the ordinary shield tunnel structure and the overall effective axial force of the tunnel structure. The concept is clear, the calculation method is simple, and it conforms to the usage habits of designers.

[0036] 3. The present invention designs multiple prestressing schemes and determines the main reinforcement scheme and prestressing scheme with the lowest total cost through calculation. Compared with traditional shield tunnel design schemes, the present invention uses less steel bars and has lower production costs.

[0037] The details of the present invention can be found in the following description and the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 A schematic diagram showing the prestressed shield tunnel structure design method of the present invention.

[0039] Figure 2 A schematic diagram of a prestressed shield tunnel structure according to the present invention is shown.

[0040] Figure 3 A schematic diagram of the prestressed anchor blocks of the prestressed shield tunnel structure of the present invention is shown.

[0041] Figure 4 A schematic diagram showing the effective axial force of a single prestressed strand after considering the prestress loss in the present invention.

[0042] Figure 5 A schematic diagram showing the effective axial force of a single prestressed strand at different anchor end positions and the overall effective axial force of the tunnel structure after considering prestress loss in the present invention.

[0043] Figure 6 Schematic diagram showing the load-deformation curves of the elastic stage during full-scale full-ring loading tests of the prestressed segment structure and the ordinary segment structure in the present invention.

[0044] Figure 7 A schematic diagram showing the effect of the improved tunnel structure stiffness on the internal forces of the structure according to the present invention.

[0045] Figure 8 A schematic diagram showing the new modified method of using the prestressed shield tunnel structure of the present invention.

[0046] Figure 9 A schematic diagram showing the axial force monitoring results of full-scale full-ring loading tests of the prestressed segment structure of the present invention and a conventional segment structure.

[0047] Figure 10A schematic diagram showing the bending moment monitoring results of full-scale full-ring loading tests of the prestressed segment structure of the present invention and a conventional segment structure.

[0048] Figure 11 A schematic diagram showing the difference in axial force between the full-scale full-ring loading test of the prestressed segment structure of the present invention and the conventional segment structure, and the axial force provided by the prestressed strands.

[0049] Figure 12 The figure shows a schematic diagram of calculating the loss of prestressing of steel bars after considering reverse friction in the present invention.

[0050] Reference numerals:

[0051] 100: Prestressed anchor block; 101: Prestressed capping block; 102: Prestressed standard block; 103: Prestressed duct; 104: Longitudinal seam connector; 105: Circumferential seam connector. DETAILED DESCRIPTION

[0052] See also Figures 1 to 12 , showing the prestressed shield tunnel structure design method of the present invention.

[0053] like Figure 1 As shown, the present invention discloses a prestressed shield tunnel structure design method, which may include the following steps:

[0054] S1. The basic design parameters of prestressed shield tunnels can be determined based on tunnel type, function, ground conditions, shield parameters, etc.

[0055] S2. Design various prestressing schemes based on the bonded or non-bonded tensioning scheme, the number of prestressed strands per bundle, etc.

[0056] S3. Calculate the long-term prestress loss of a single prestressed strand and determine the overall effective axial force distribution under various prestressing schemes;

[0057] S4. Establish a homogeneous circular ring model of the tunnel structure and use the new correction method to correct the tunnel structure stiffness;

[0058] S5. Use the load structure model to calculate the internal force distribution of water and soil loads on the tunnel structure at unfavorable sections along the shield tunnel, and calculate and determine the internal force distribution of water and soil loads on the tunnel structure at the most unfavorable section;

[0059] S6. Determine the overall internal force distribution of the tunnel structure based on the water and soil load internal force distribution and the overall effective axial force distribution of the tunnel structure at the most unfavorable section;

[0060] S7. Comprehensively consider the main reinforcement scheme and prestressing scheme of the prestressed shield tunnel structure, and select the scheme with the lowest cost as the reinforcement scheme of the prestressed shield tunnel structure.

[0061] Figures 2 to 3 The schematic diagram of the prestressed shield tunnel structure design is shown. Figure 2 In the prestressed shield tunnel, there are multiple prestressed blocks arranged in a ring, which can be divided into prestressed anchor blocks 100, prestressed capping blocks 101, prestressed standard blocks 102 and prestressed adjacent blocks. The prestressed standard blocks 102 are located at the bottom of the tunnel structure, with both ends connected to the prestressed anchor blocks 100. The other end of the prestressed anchor blocks 100 is connected to the prestressed adjacent blocks. The prestressed capping blocks 101 are located at the top of the tunnel structure, with both ends connected to the prestressed adjacent blocks. Each prestressed block is embedded with interconnected prestressed channels 103, such as Figure 3 Each prestressed block is connected in the annular direction by a longitudinal seam connector 104 and in the longitudinal direction by an annular seam connector 105.

[0062] The prestressed shield tunnel structure design method of the present invention is carried out according to the following principles: first, the outer diameter, ring width, assembly machine hoisting scheme, etc. of the prestressed shield tunnel structure should meet the performance requirements of the shield machine equipment; the prestressed anchor blocks 100 should be arranged near the shield machine pedestrian passage and should be symmetrically arranged on both sides of the tunnel structure to ensure that the prestressed tensioning can be made with the help of the shield machine pedestrian passage to ensure that the circumferential prestress distribution of the entire tunnel is more uniform; the block scheme of the prestressed shield tunnel structure can adopt a prestressed capping block 101 with a larger central angle according to the assembly capacity of the assembly machine to improve the top stiffness of the tunnel structure. Reduce damage to the prestressed capping block 101; the prestressed shield tunnel structure should adopt a through-seam assembly scheme to ensure that the position of the prestressed anchor block 100 remains unchanged and reduce the cost of the reserved pre-buried system; the prestressed shield tunnel structure should be arranged with at least two prestressed channels 103, and each prestressed channel 103 should ensure 360° circumferential coverage of the tunnel structure; the prestressed shield tunnel structure recommends that bolts be eliminated as longitudinal seam connectors 104 and circumferential seam connectors 105, and the longitudinal seam connectors 104 are recommended to be connected with positioning rods, mortise and tenon or flat joints, and the circumferential seam connectors 105 are recommended to be connected with socket joints.

[0063] Preferably, in the present invention, the design of multiple prestressing schemes in step S2 may include the following steps:

[0064] S21. Prestressed strands can be tensioned with a bonded or unbonded method. When the bonded method is used, prestressed strands are selected, but grouting is required in the prestressed duct 103 after the strands are tensioned. The advantage is that the bonding performance between the prestressed strands and the tunnel structure is guaranteed, and even if the tensioning anchor fails, the structural safety can be guaranteed. However, the prestress loss of this method is large, and the uniformity of the circumferential prestress distribution is poor. When the unbonded method is used, PE sheathed steel strands are required (a type of prestressed strand specially used for the unbonded method, that is, the prestressed strand is wrapped with a layer of PE material outer shell, and the inner shell is filled with grease). Grease is filled between the prestressed strands and the PE. The advantage is that the prestress loss is small, the circumferential axial force of the tunnel structure is increased more, and the force is more uniform, but the cost is high, and the reliability requirements of the anchoring system are also high.

[0065] S22. The tension control stress of a single prestressed strand is generally 0.75 of the ultimate tensile strength. After accounting for prestress loss, the effective axial force of the prestressed shield tunnel structure remains essentially constant. Increasing the number of prestressed strands in a single bundle can effectively increase the effective axial force of the prestressed shield tunnel structure, allowing the main reinforcement ratio to be reduced during subsequent reinforcement. However, there is a minimum main reinforcement ratio requirement of 0.2%, and the cost of prestressed strands is higher than that of ordinary steel bars. In other words, there is an optimal value between the number of prestressed strands in a single bundle and the main reinforcement ratio. Due to significant variations in tunnel structure design parameters and ground conditions across projects, the number of prestressed strands in a single bundle cannot be determined, necessitating the design of multiple prestressing schemes. To facilitate the design of the number of prestressed strands in a single bundle, the following case study can be used to estimate the effective axial force and select the number of prestressed strands in a single bundle. For example, the tension control stress of a single 15.2mm diameter prestressed strand with an area of approximately 140mm is 1320MPa. 2 , the prestress loss is calculated as 45%, then the effective axial force of a single prestressed strand is about 1320 MPa * 140 mm 2 * (1-45%) = 101.64 kN. Generally speaking, for a prestressed shield tunnel structure with an outer diameter of 6 m, when two prestressed ducts 103 are tensioned, the recommended number of single-bundle prestressed strands is 4, and the effective axial force that can be provided is approximately 813.12 kN. For a prestressed shield tunnel structure with an outer diameter of 10 m, when two prestressed ducts 103 are tensioned, the recommended number of single-bundle prestressed strands is 6, and the effective axial force that can be provided is approximately 1219.68 kN. However, as the number of single-bundle prestressed strands increases, the inner diameter of the prestressed duct 103 also needs to be increased accordingly. Therefore, those skilled in the art will know that the number of single-bundle prestressed strands is related to the tunnel structure design parameters, stratum conditions, etc., and the prestressing scheme design can be based on the above number of strands and the corresponding axial force values.

[0066] Among them, preferably in the present invention, the calculation method of the long-term prestress loss of a single prestressed strand and the overall effective axial force distribution of the prestressed shield tunnel structure in step S3 is as follows:

[0067] S31. Refer to Section 6.2 of the current industry standard "Design Specifications for Highway Reinforced Concrete and Prestressed Concrete Bridges and Culverts" JTG3362 to calculate the long-term prestress loss of a single prestressed strand. The main factors affecting prestress loss include:

[0068] : Friction between the prestressed strands and the prestressed duct wall;

[0069] : deformation of the tensioning end anchor and shrinkage of the prestressed strands;

[0070] : Temperature difference between the prestressed strand and the pedestal (not included in post-tensioning method);

[0071] : elastic compression of concrete;

[0072] : stress relaxation of prestressed strands;

[0073] : Shrinkage and creep of concrete.

[0074] in to is the short-term prestress loss, and The long-term prestress loss item is a prestressed shield tunnel structure that is constructed using the post-tensioning method. The tunnel structure is designed to have a service life of more than 100 years, so long-term prestress loss needs to be considered. 、 、 、 、 、 .

[0075] The various parameters that need to be considered in the above-mentioned prestress loss calculation can be determined according to the current national standards. Specifically, the calculation method for prestress loss in prestressed shield tunnels is as follows:

[0076] The calculation method is as follows:

[0077] (1)

[0078] In the formula ——tension control stress value of prestressed strands;

[0079] — Friction coefficient between prestressed strands and prestressed duct wall;

[0080] ——The sum of the angles between the tensioning end and the tangent line of the calculated cross-section curve;

[0081] ——The influence coefficient of local deviation per meter of prestressed duct on friction;

[0082] ——The length of the channel from the tensioning end to the calculated section.

[0083] The prestressed shield tunnel structure is symmetrically tensioned at both ends. Since the prestress loss is symmetrical, The value range can be half of the total length of the prestressed channel 103.

[0084] The calculation method is as follows:

[0085] Prestressed shield tunnels are curved prestressed strands. It is usually assumed that the reverse friction coefficient caused by anchor deformation and retraction is the same as the forward friction coefficient, and the direction of prestress loss is opposite, e.g. Figure 12 As shown, The reverse friction influence length can be determined according to the following formulas 2 and 3:

[0086] (2)

[0087] (3)

[0088] In the formula ——Prestress loss per unit length caused by pipeline friction;

[0089] - loss of prestress caused by pipe friction;

[0090] —Deformation of the anchorage at the tensioning end and shrinkage of the prestressed strand;

[0091] - the distance between the tensioning end and the anchoring end;

[0092] ——Elastic modulus of prestressed strands.

[0093] The prestressed shield tunnel structure is symmetrically tensioned at both ends. When the prestressed strand is away from the tensioning end The prestress loss after considering reverse friction can be calculated according to the following formulas 4 and 5:

[0094] (4)

[0095] (5)

[0096] The calculation method is as follows:

[0097] (6)

[0098] In the formula - The normal stress in the concrete generated by the subsequent batch of prestressed strands at the center of gravity of the prestressed strands in the calculated section;

[0099] ——The ratio of the elastic modulus of prestressed strands to the elastic modulus of concrete.

[0100] In a prestressed shield tunnel structure, the influence of a prestressed strand on other surrounding prestressed strands is limited. Therefore, it is assumed that each prestressed strand is only affected by the half-bundle prestressed strands on both sides of it. Since the annular prestressed strands are located on the neutral plane, the increase in normal positive pressure due to eccentricity is not considered. The above formula is:

[0101] (7)

[0102] In the formula — area of a single prestressed strand;

[0103] —segment thickness;

[0104] ——Prestressed hole spacing;

[0105] ——The effective stress value after deducting the prestress losses of the first two items.

[0106] The calculation method is as shown in formula 8:

[0107] (8)

[0108] In the formula ——Standard value of tensile strength of prestressed stranded wire.

[0109] The prestressed shield tunnel structure uses low relaxation prestressed strands. After deducting the friction loss of the anchor, the tension control stress does not exceed 0.7 .

[0110] The calculation method is as shown in formulas 9 and 10:

[0111] (9)

[0112] (10)

[0113] In the formula - The normal compressive stress of concrete generated by the prestressing strands and their own weight (vertical prestressing strands need to be considered), and the prestressing loss at the corresponding stage is deducted during the calculation;

[0114] ——elastic modulus of prestressed strands;

[0115] —Reinforcement ratio of main reinforcement and prestressed strands;

[0116] ——net cross-sectional area, i.e. the area after deducting the hole and reinforcement;

[0117] ——area of a single prestressed strand;

[0118] ——Number of prestressed strands;

[0119] ——Main reinforcement area, take 0.002A n ;

[0120] ——Ultimate value of shrinkage strain;

[0121] ——Ultimate value of creep coefficient.

[0122] Then the effective prestress of a single prestressed strand at each section after considering the long-term prestress loss is expressed as Equation 11:

[0123] (11)

[0124] In the formula ——effective prestress;

[0125] ——Prestressing control stress value of prestressed strands.

[0126] The effective axial force of each section of the prestressed shield tunnel structure is expressed as Equation 12:

[0127] (12)

[0128] In the formula ——effective axial force;

[0129] ——area of a single prestressed strand;

[0130] ——Number of prestressed strands.

[0131] Example 1: Calculation of the effective axial force of a single prestressed strand and the overall effective axial force of the tunnel structure:

[0132] The prestressed segment structure has an outer diameter of 6000mm, a thickness of 300mm, a ring width of 1200mm, and a concrete grade of C50. Two prestressed channels are set up with a spacing of 600mm. Each bundle of prestressed strands uses four 15.2mm steel strands, and the cross-sectional area of a single bundle of prestressed strands is 560mm. 2 The tension control stress is 1320MPa, and the bonding tension scheme is adopted. The friction coefficient between the prestressed steel bar and the prestressed duct wall is The influence coefficient of local deviation of prestressed duct per meter on friction is 0.2. is 0.0015, the deformation of the tensioning end anchor and the shrinkage value of the prestressed tendon 6mm, prestressed strand elastic modulus The ultimate value of shrinkage strain is 195GPa. The ultimate value of creep coefficient is 0.000277 It is 1.73.

[0133] Substituting the relevant data of the prestressed segment structure in Example 1 into equations (1) to (12), the effective axial force of each section of a single bundle of prestressed strands within 360° of the circumferential direction can be calculated, as follows: Figure 4 As shown in the figure, the top of the prestressed segment structure is 0°, the angle increases as it rotates clockwise, and 180° is the anchor end.

[0134] Depend on Figure 4 As can be seen, due to the varying distances between each section of the prestressed segment and the anchorage, the prestress loss varies across each section, resulting in a non-uniform distribution of the effective axial force along the 360° circumferential range. The bottom section, where the anchorage is located and anchorage retraction must be considered, is the farthest from the anchorage, resulting in relatively low effective axial forces. The maximum and minimum effective axial forces are 478 kN and 298 kN, respectively, with a difference of 195 kN, or 39.5% of the maximum value.

[0135] S32, by Figure 4 It can be seen that the effective axial force of a single bundle of prestressed strands within the 360° circumferential direction is significantly different. For prestressed shield tunnel structures, if the anchoring positions of multiple bundles of prestressed strands are different, the overall effective axial force of the tunnel structure will be different. That is, the position of the prestressed anchor blocks 100 and the angle between them have a greater impact on the overall effective axial force. Generally speaking, the anchor end of the prestressed strand is located in the middle of the prestressed anchor blocks 100, and there is a gap between the prestressed anchor blocks 100. n prestressed standard block 102, if the central angle of the prestressed anchor block 100 is α1. The central angle of the prestressed standard block 102 is α 2. Angle between prestressed anchor blocks 100 α ( Figure 1 )for: α=α 1+ nα 2.

[0136] Figure 5 The figure shows the effective axial force of a single prestressed strand at different anchorage positions after considering prestress loss and the effective axial force of the entire tunnel structure. The anchorage ends of the two prestressed channels are located on both sides of the tunnel structure, the central angle of the prestressed anchor block 100 is 67.5°, the central angle of the prestressed standard block 102 is 67.5°, and the angle between the prestressed anchor blocks 100 is 135°. The effective axial force of the entire tunnel structure is Figure 4 The effective axial force curve of a single prestressed strand in the figure is obtained by superimposing the data after rotating 67.5° clockwise and 67.5° counterclockwise. Figure 4 The effective axial force curve for a single prestressed strand is anchored at 180°, i.e., the bottom of the tunnel structure. Therefore, the data rotated 67.5° clockwise represents the effective axial force for prestressed duct 103 corresponding to prestressed anchor block 100 on the left, and the data rotated 67.5° counterclockwise represents the effective axial force for prestressed duct 103 corresponding to prestressed anchor block 100 on the right. The overall effective axial force is more evenly distributed than that of a single prestressed strand. The maximum and minimum effective axial forces are 928 kN and 753 kN, respectively, with a difference of 175 kN, representing 18.9% of the minimum value.

[0137] Wherein, preferably in the present invention, the process of establishing the homogeneous ring model of the prestressed shield tunnel structure in step S4 is as follows:

[0138] S41. A homogeneous circular ring model of a prestressed shield tunnel is established using beam elements of uniform cross-section and stiffness, and the interaction between the model and the stratum is modeled using a foundation spring model.

[0139] Preferably, the beam unit, uniform cross-section, uniform stiffness, and homogeneous circular ring models can refer to Article 7.2.2 of the current national standard "Shield Tunnel Engineering Design Standard" GB / T 51438; the foundation spring model can refer to Article 7.2.7 of the current national standard "Shield Tunnel Engineering Design Standard" GB / T 51438.

[0140] 1. Based on the design parameters of the prestressed shield tunnel structure, including the outer diameter, inner diameter, ring width, thickness, and concrete strength grade of the segments, a homogeneous ring model is established for the beam element without considering the joint surface. The cross-sections of the ring model are equal in size (equal cross-section) and the elastic modulus of each section is EI (equal stiffness).

[0141] 2. The surrounding rock will exert load on the prestressed shield tunnel. The surrounding rock can be equivalent to a foundation spring that only bears pressure in the normal direction and does not bear tension. The stiffness of the foundation spring is calculated using the following formulas 13 and 14:

[0142] (13)

[0143] (14)

[0144] In the formula ——normal spring stiffness of foundation (kN / m);

[0145] ——Normal bed coefficient of the formation (kN / m 3 );

[0146] ——Calculation unit width (m);

[0147] ——average length of adjacent calculation units (m);

[0148] ——average bed coefficient of the stratum (kN / m 3 );

[0149] ——Average vertical bed coefficient of the stratum (kN / m 3 );

[0150] ——The angle between the center line of action of the spring and the horizontal line.

[0151] S42. Since the shield tunnel structure is not a monolithic structure, the segments are connected by bolts and other connectors. Due to the low strength of bolts and other connectors and the small preload they provide, the stiffness of the segment joints is less than that of the segment body, making the overall stiffness of the shield tunnel structure lower than that of the homogeneous ring model. The traditional correction method uses the stiffness reduction factor η The stiffness of the homogeneous ring model is reduced, and the stiffness of the homogeneous ring model after reduction is ηEI However, after the prestress is applied to the prestressed shield tunnel structure, the prestressed strands can provide a joint load far greater than that of bolts and other connectors, greatly improving the stiffness of the segment joints and the tunnel structure. If the stiffness reduction factor of the traditional modified method is used η , which will cause the numerical simulation stiffness of the prestressed shield tunnel structure to be lower than the actual stiffness, thereby causing an increase in structural deformation.

[0152] Example 2: Analysis of the stiffness difference between the full-scale full-ring loading test of the prestressed segment structure and the ordinary segment structure:

[0153] Figure 6 The load-deformation curves of the elastic stage of the full-scale full-ring loading test of the prestressed segment structure and the ordinary segment structure are shown in Figure 2. The dimensions of the prestressed segment structure and the ordinary segment structure are the same, with an outer diameter of 6000mm, a thickness of 300mm, and a ring width of 1200mm. The prestressed shield tunnel structure is equipped with two prestressed channels. Each prestressed strand uses four 15.2mm steel strands with an area of 560mm. 2 The tensioning control stress was 1320 MPa, using a bonded tensioning scheme. The load applied to the tunnel structure's perimeter was identical. Calculations show that the elastic stiffnesses of conventional and prestressed segments are 11.6 kN / mm and 20.1 kN / mm, respectively, with the prestressed segment structure showing a 73% increase in stiffness.

[0154] Figure 7 The effect of tunnel structural stiffness improvement on structural internal force is shown. The percentage of structural stiffness improvement is 0.8. EI As a benchmark, the internal force improvement percentage is 0.8 EI As shown in the figure, the increase in structural stiffness has little effect on the axial force, but has a certain effect on the maximum and minimum bending moments. That is, for every 10% increase in stiffness, the maximum positive and negative bending moments increase by approximately 5.2% and 3.7%, respectively.

[0155] Based on the test results of the full-scale ring test, the stiffness of the prestressed shield tunnel structure is about 1.73 ηEI , the stiffness reduction factor of the traditional modified method η Generally, the value is 0.7 or 0.8, then the stiffness of the prestressed shield tunnel structure will be greater than EI Considering that a certain amount of safety reserve should be reserved in actual design work, the parameter values should be appropriately conservative. At the same time, the stiffness increase of the prestressed shield tunnel structure is not easy to accurately define during the design process. Taking all factors into consideration, the stiffness is increased based on the traditional correction method, but the increase should not exceed the cross-sectional stiffness of the homogeneous ring model. EI , forming a new modified method applicable to prestressed shield tunnels, the stiffness of the ordinary segment structure is ηEI , Formula (15) takes into account the stiffness of the section after the prestressed segment structure is enhanced by the prestressed stress, and Formula (16) constrains the maximum stiffness of the prestressed segment structure, that is, k p ≤EI.

[0156] k p = ληEI (15)

[0157] λη ≤1 (16)

[0158] Where:

[0159] k p —The stiffness of the prestressed segment structure after cross-section adjustment;

[0160] λ——stiffness adjustment coefficient;

[0161] η——Stiffness reduction coefficient of traditional modified method;

[0162] EI - the section stiffness of ordinary segment structure before reduction.

[0163] The new revised practice for prestressed shield tunnel structures is shown in Figure 8 The new modified conventional method is used to calculate the internal forces of the tunnel structure. Due to the increase in stiffness, the axial force of the tunnel structure remains unchanged, but the bending moment increases slightly.

[0164] Preferably, in step S5, the stratum conditions, tunnel burial depth, groundwater level, surrounding environment, etc. along the shield tunnel are constantly changing, resulting in large differences in the water and soil loads of the shield tunnel structure at various sections along the tunnel, resulting in different distributions of its water and soil load internal forces. When performing water and soil load analysis on the shield tunnel structure, unfavorable locations such as the thickest and thinnest tunnel cover, the highest and lowest groundwater levels, the locations where overload or bias exists, and the locations where the tunnel passes through sudden changes in stratum conditions should be selected to calculate the distribution of water and soil load internal forces of the tunnel structure in sequence. Then, the most unfavorable sections in each calculated section are selected in sequence for reinforcement calculation, and then the most unfavorable sections among the most unfavorable sections along the entire tunnel are determined. Generally speaking, in the distribution of water and soil load internal forces at different sections, the top, bottom and both sides of the tunnel structure are unfavorable sections, and their bending moments are large and the axial forces are small.

[0165] Optionally, the internal force calculation can refer to Chapter 7 of the current national standard "Shield Tunnel Engineering Design Standard" GB / T 51438, and the reinforcement calculation can refer to Section 6.2 of the current national standard "Concrete Structure Design Standard" GB / T50010-2010 (2024 edition).

[0166] Example 3: The internal force distribution difference between the prestressed segment structure and the ordinary segment structure, a full-scale full-ring loading comparison test of the prestressed segment structure and the ordinary segment structure under the same conditions is carried out. The loading conditions include construction, operation, earthquake, overload, unloading, close construction, eccentric load, destruction and other conditions. The test parameters are as follows: The dimensions of the prestressed segment structure and the ordinary segment structure are both 6000mm in outer diameter, 300mm in thickness and 1200mm in ring width. The prestressed segment structure is provided with 2 prestressed channels, and each bundle of prestressed strands uses 4 15.2mm steel strands with an area of 560mm 2The anchorage ends of the two prestressed ducts are located on either side of the tunnel structure. The central angle of the prestressed anchor block 100 is 67.5°, the central angle of the prestressed standard block 102 is also 67.5°, and the angle between the prestressed anchor blocks 100 is 135°. Under various loading conditions, the internal force differences between the prestressed segment structure and the conventional segment structure exhibit the same trend.

[0167] Taking the operating conditions of a tunnel with a depth of 34m and a water level of -14.6m as an example, the difference in internal force distribution between the prestressed segment structure and the ordinary segment structure is explained. The bending moment and axial force are converted from the strain gauge monitoring data during the test. Figure 9 and Figure 10 The bending moment difference between the prestressed segment structure and the conventional segment structure is small, with the maximum bending moment being 107 kN·m and 101 kN·m, respectively, a difference of 6 kN·m. The axial force difference is large, with the maximum axial force being 2606 kN and 1830 kN, respectively, a difference of 776 kN.

[0168] Figure 11 The relationship between the difference in axial force between the two types of segment structures and the axial force provided by the prestressed strands is given by: Figure 5 The overall effective axial force of the tunnel structure, area 560mm 2 . Figure 10 The changing trends of the two curves are basically consistent and the values are close, indicating that the difference in axial force between the prestressed segment structure and the ordinary segment structure is caused by the circumferential prestress applied by the prestressed segment structure.

[0169] Based on the above analysis, the bending moment of the prestressed segment structure is slightly greater than that of the conventional segment structure under the same operating conditions. Considering that the new modified conventional method for calculating the internal forces of prestressed shield tunnel structures during the design process results in a slight increase in bending moment due to the higher stiffness, the result after this increase in bending moment is essentially the same as the bending moment of the conventional method for conventional shield tunnel structures. The axial force of the prestressed segment structure is approximately equal to the sum of the axial force of the conventional segment structure under the same operating conditions and the axial force provided by the prestressed strands. Since the increased stiffness has no effect on the axial force, the axial force of the conventional segment structure is essentially the same as the axial force of the conventional segment structure using the new modified conventional method.

[0170] Therefore, in step S6, the overall bending moment distribution of the prestressed shield tunnel structure can be characterized by the bending moment distribution of the water and soil loads of the ordinary shield tunnel structure after the new modified conventional method is adopted, and the overall axial force distribution of the prestressed shield tunnel structure can be characterized by the sum of the axial force distribution of the water and soil loads of the ordinary shield tunnel structure after the new modified conventional method is adopted and the overall effective axial force distribution of the tunnel structure.

[0171] In step S7, due to the different numbers of prestressing strands in a single bundle under various prestressing schemes, the overall axial force increases while the bending moment remains unchanged for the prestressed shield tunnel structure. According to the current national standard "Code for Design of Concrete Structures" (GB50010), the axial force-bending moment combinations under various prestressing schemes are reinforced to determine the main reinforcement area and reinforcement quantity for the segment cross section. The total reinforcement cost under different prestressing schemes is calculated as Equation 17:

[0172] C = W mr · C 1+ W hr · C 1+ W ps · C 2+ W pp · C 1 (17)

[0173] Where:

[0174] C — total cost of prestressed shield tunnel structural reinforcement;

[0175] Wmr is the weight of the main reinforcement, which is related to the prestressing scheme. Generally speaking, as the number of strands in a single prestressing bundle increases, the amount of main reinforcement decreases and the weight decreases, but it cannot be lower than the minimum reinforcement ratio;

[0176] C1 — price of steel bars;

[0177] Whr - stirrup weight, independent of prestressing scheme;

[0178] Wps is the weight of prestressed strands, which is proportional to the number of prestressed strands in a single bundle;

[0179] C2 — price of prestressed stranded wire;

[0180] Wpp - weight of prestressed protective reinforcement.

[0181] Since the weight of stirrups and prestressed protective steel bars remain unchanged under different schemes. W hr · C 1=0, W pp · C 1=0. The total cost of steel bars can be simplified to:

[0182] C = W mr · C 1+ Wps · C 2 (18)

[0183] W mr = A s *π D ( DH c / 2) (19)

[0184] W ps = A p *π( DH c / 2) (20)

[0185] Where A s ——main reinforcement area;

[0186] A p ——area of a single prestressed strand;

[0187] n——number of prestressed strands;

[0188] D——segment outer diameter;

[0189] H c ——Segment thickness.

[0190] By calculating the different prestressing design schemes C Value, select C The smallest solution.

[0191] It is obvious that the above description and record are only examples and are not intended to limit the disclosure, application or use of the present invention. Although the embodiments have been described in the embodiments and described in the drawings, the present invention is not limited to the specific examples illustrated in the drawings and described in the embodiments as the best mode currently believed to implement the teachings of the present invention, and the scope of the present invention will include any embodiment that falls within the previous description and the appended claims. The description of the present invention contains multiple inventive concepts, such as "preferably" or "according to a preferred embodiment" means that the corresponding paragraph discloses an independent concept, and the applicant reserves the right to file a divisional application based on each inventive concept. Throughout the text, the features guided by "preferably" are only an optional method and should not be understood as having to be set, so the applicant reserves the right to abandon or delete the relevant preferred features at any time.

Claims

1. A prestressed shield tunnel structure design method, characterized in that The following steps are involved: S1. Determine the basic design parameters of prestressed shield tunnels based on tunnel type, function, ground conditions, and shield parameters; S2. Design various prestressing schemes based on the bonded or non-bonded tensioning scheme and the number of prestressing strands in a single bundle; S3. Calculate the long-term prestress loss of a single prestressed strand and determine the overall effective axial force distribution under various prestressing schemes; S4. Establish a homogeneous circular ring model of the tunnel structure and use the new correction method to correct the tunnel structure stiffness; Wherein said S4 specifically includes: S41. A homogeneous circular ring model of a prestressed shield tunnel is established using beam elements of uniform cross-section and stiffness, and the interaction between the model and the stratum is modeled using a foundation spring model. S42. Setting the overall stiffness of the homogeneous ring model according to the stiffness adjustment coefficient of the new modified conventional method; S5. Use the load structure model to calculate the internal force distribution of water and soil loads on the tunnel structure at unfavorable sections along the shield tunnel, and calculate and determine the internal force distribution of water and soil loads on the tunnel structure at the most unfavorable section; S6. Determine the overall internal force distribution of the tunnel structure based on the water and soil load internal force distribution and the overall effective axial force distribution of the tunnel structure at the most unfavorable section; S7. Comprehensively consider the main reinforcement scheme and prestressing scheme of the prestressed shield tunnel structure, and select the scheme with the lowest cost as the reinforcement scheme of the prestressed shield tunnel structure.

2. The prestressed shield tunnel structure design method according to claim 1, characterized in that: The prestressed shield tunnel includes multiple prestressed blocks arranged in a ring, which are divided into prestressed anchor blocks, prestressed capping blocks, prestressed standard blocks and prestressed adjacent blocks. The prestressed standard blocks are located at the bottom of the tunnel structure, and their two ends are connected to the prestressed anchor blocks. The other end of the prestressed anchor block is connected to the prestressed adjacent block. The prestressed capping block is located at the top of the tunnel structure, and its two ends are connected to the prestressed adjacent blocks. Prestressed channels that are interconnected are pre-buried in each prestressed block. The prestressed blocks are connected in the ring direction by longitudinal seam connectors and in the longitudinal direction by annular seam connectors.

3. The prestressed shield tunnel structure design method according to claim 1, characterized in that: The S3 specifically includes: S31. Calculate the long-term prestress loss and overall effective axial force of a single prestressed strand under various prestressing schemes; S32. Calculate the angle between the prestressed anchor blocks; S33. Calculate the overall effective axial force distribution of the prestressed shield tunnel structure under various prestressing schemes based on the angles between the prestressed anchor blocks.

4. The prestressed shield tunnel structure design method according to claim 1, characterized in that: The S5 specifically includes: selecting unfavorable sections where the tunnel cover is the thickest and thinnest, the groundwater level is the highest and lowest, there is overload or bias, and the tunnel passes through a sudden change in stratum conditions, and using the load structure model to calculate the water and soil load internal force distribution of the tunnel structure at each unfavorable section in turn, and determining the most unfavorable section and the corresponding water and soil load internal force distribution.

5. The prestressed shield tunnel structure design method according to claim 1, characterized in that: The S6 specifically includes: the overall bending moment of the prestressed shield tunnel structure is the water and soil load bending moment of the ordinary shield tunnel structure after the new revised conventional method is adopted; the overall axial force is the sum of the water and soil load axial force of the ordinary shield tunnel structure after the new revised conventional method is adopted and the overall effective axial force of the tunnel structure.

6. The prestressed shield tunnel structure design method according to claim 1, characterized in that: The S7 specifically includes: calculating the reinforcement schemes in sequence according to the overall internal force distribution of the prestressed shield tunnel structure under various prestressing schemes, and then calculating the total cost of steel bars and prestressed strands under various prestressing schemes in sequence, and selecting the main reinforcement scheme and prestressing scheme with the lowest total cost.

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