A combined inverse design method and system for reinforcement and thickness of a shield tunnel segment

Abstract

The present application relates to the technical field of civil engineering, in particular to a kind of shield tunnel segment reinforcement and thickness combined counter-design calculation method and system, method includes: determining the internal force of any position of shield tunnel segment ring, and setting steel force area;Concrete and steel consumption target function is built, and setting test thickness;According to the current test thickness, determine effective height, and based on the height of compression zone of shield tunnel segment, combined with internal force, strain compatibility equation, constitutive equation and section balance equation are established in turn, and the height of compression zone and steel force area corresponding position are obtained by solving;Determine the optimal steel area of each position;Optimal steel area is screened to unify the ring steel, the optimal thickness of each position is re-determined, and the optimal thickness is smoothed to obtain smooth thickness distribution, determine the ring thickness and corresponding steel area of shield tunnel segment;Through counter-design calculation, the structure requirement of each position is determined.

Description

Technical Field

[0001] This invention relates to the field of civil engineering technology, specifically to a method and system for combined back-design calculation of reinforcement and thickness of shield tunnel segments. Background Technology

[0002] Shield tunnels often use precast concrete segments as permanent support structures. During construction and operation, these segments bear ground pressure, water pressure, construction loads, and the structure's own weight, resulting in significantly uneven stress distribution along the circumferential direction. Existing design methods rely on finite element analysis or analytical calculations to determine bending moments and axial forces at different circumferential angles of the segments, using this information to design the cross-sectional reinforcement and thickness. In engineering practice, the segment design process involves first determining the segment cross-sectional thickness and reinforcement layout, then verifying whether the bearing capacity of each circumferential section under the most unfavorable conditions meets the specifications. If not, the reinforcement area is increased or the cross-sectional thickness is adjusted. This method is widely used, and the calculation process is mature and easy to master. Furthermore, to balance construction convenience and fabrication consistency, existing projects often adopt a uniform main reinforcement configuration across the entire circumference, resulting in a constant segment thickness along the circumferential direction.

[0003] However, the application of existing technologies still has certain limitations. First, the design sequence of reinforcement and section thickness is too simplistic, making it difficult to balance structural safety and economy. A forward design approach of "determining thickness first, then calculating reinforcement" is typically adopted, with section thickness determined based on experience or similar projects. If the bearing capacity at a local angle is insufficient, it is often corrected by increasing the overall reinforcement or thickness, leading to over-reinforcement or redundant concrete usage in most circumferential locations, resulting in poor overall economy. Second, there is a lack of a reverse design calculation mechanism based on the ultimate bearing state. Existing methods are mostly verification-based, i.e., checking the bearing capacity when the section parameters are known, rarely solving for the minimum section thickness and reinforcement area to satisfy the ultimate bearing state from the known internal force requirements. This design mode struggles to identify the actual requirements for section thickness and reinforcement at different circumferential angle locations, and the design results rely on experience, limiting the degree of optimization. Third, there is a contradiction between uniform reinforcement throughout the entire ring and the demand for optimal local cross-sections. To meet construction and prefabrication requirements, projects often adopt a uniform main reinforcement configuration throughout the entire ring. However, the stress requirements at different circumferential angles vary greatly. If the reinforcement is uniformly configured throughout the entire ring based on the most unfavorable cross-section, significant over-reinforcement will occur at most angles. Furthermore, current technology lacks a systematic method for adjusting the cross-sectional thickness in the reverse direction under uniform reinforcement to adapt to different circumferential stress requirements. Fourth, it is difficult to achieve continuous and smooth changes along the circumferential direction, affecting the continuity of structural stress and the feasibility of the project. That is, empirical thickening or segmented adjustment at locally unfavorable stress locations often results in discontinuous changes in thickness along the circumferential direction. There is a lack of systematic mathematical constraints and optimization methods, making it difficult to simultaneously meet structural safety and manufacturing requirements. Summary of the Invention

[0004] To address the technical challenge of simultaneously ensuring structural safety, economy, and engineering feasibility in existing reinforcement and section thickness designs under conditions of significant circumferential stress differences, this invention aims to provide a combined back-design calculation method for the reinforcement and thickness of shield tunnel segments. The specific technical solution adopted is as follows: Determine the internal forces at any circumferential position of the shield tunnel segment and set the stress area of ​​the reinforcing steel; Based on the segment cross-section of the shield tunnel, the objective function of concrete and steel reinforcement usage is constructed by combining the stress area of ​​the steel reinforcement, and the trial thickness is set. The effective height is determined based on the test thickness, and the height of the compression zone is set based on the shield tunnel segments. The strain compatibility equation, constitutive equation and section equilibrium equation are established in sequence in combination with the internal forces. The height of the compression zone and the area of ​​the steel reinforcement at the corresponding position are obtained by solving. The optimal reinforcement area at each location is determined by combining the height of the compression zone and the stress area of ​​the reinforcement with the objective function. The optimal rebar area is selected to unify the rebar throughout the ring, the optimal thickness at each position is re-determined, and the optimal thickness is smoothed to obtain a smooth thickness distribution. This determines the circumferential thickness of the shield tunnel segment and the corresponding rebar area.

[0005] Preferably, the segment cross-section is determined based on the shield tunnel segments, and an objective function for the amount of concrete and steel reinforcement is constructed by combining the stress area of ​​the steel reinforcement, and a trial thickness is set, including: The width and initial thickness of the tunnel segment are obtained respectively. The ratio of concrete cost to steel cost is determined based on the tunnel segment of the shield tunnel. The cost equivalence weight coefficient is then used to construct the objective function of concrete and steel usage based on the steel stress area. The thickness range and the trial step size are preset respectively. The initial thickness is individually tested according to the trial step size based on the thickness range. The current trial thickness of the segment section is determined by minimizing the objective function.

[0006] Preferably, the objective function for the amount of concrete and steel reinforcement is constructed, and the corresponding calculation formula is as follows:

[0007] in, Represents the cost function; Indicates the width of the segment cross-section; Indicates the initial thickness of the segment cross-section; This represents the cost equivalence weighting coefficient; This indicates the area of ​​the reinforcing steel bar under stress.

[0008] Preferably, the effective height is determined based on the test thickness, and the height of the compression zone is set based on the shield tunnel segments. Strain compatibility equations, constitutive equations, and section equilibrium equations are established sequentially in conjunction with internal forces. Solving these equations yields the height of the compression zone and the area of ​​the reinforcing steel at the corresponding location, including: Determine the thickness of the protective layer for shield tunnel segments, and determine the effective height based on the thickness test; Based on the height of the compression zone of the shield tunnel segments, strain compatibility equations for the tensile and compressive reinforcements are established by combining the effective height and the thickness of the protective layer. Based on the steel grade corresponding to the shield tunnel segments, determine the steel yield strain, steel elastic modulus and steel tensile strength, and establish the constitutive equation; By combining the strain compatibility equation and the constitutive equation, the section equilibrium equation is established, and the height of the compression zone and the area of ​​the reinforcing steel at the corresponding location are obtained by solving.

[0009] Preferably, strain compatibility equations are established for tension reinforcement and compression reinforcement respectively, and the corresponding calculation formulas are as follows:

[0010]

[0011] in, Indicates the strain of the tensile steel reinforcement; This indicates the strain of the compressed steel reinforcement; Indicates the height of the pressure zone; This represents the ultimate compressive strain of concrete; Indicates the effective height; This indicates the thickness of the protective layer.

[0012] Preferably, a constitutive equation is established, and the corresponding calculation formula is as follows:

[0013] in, Indicates the stress in the reinforcing steel; Indicates the elastic modulus of the steel reinforcement; This represents the strain of the reinforcing steel, specifically the strain of the tensile reinforcing steel. or strain of compressed steel bars ; Indicates the yield strain of the steel reinforcement; This indicates the tensile strength of the steel reinforcement.

[0014] Preferably, the cross-sectional equilibrium equation is established, and the corresponding calculation formula is as follows:

[0015]

[0016] in, Indicates axial force; Indicates bending moment; Indicates the coefficients of the equivalent rectangular stress diagram; Indicates the axial compressive strength of concrete; Indicates the width of the segment cross-section; Indicates the height of the pressure zone; This indicates the stress in the tensile steel reinforcement. This indicates the stress in the compressed steel reinforcement. Indicates the area of ​​the reinforcing steel bar under stress; Indicates the effective height; This indicates the thickness of the protective layer.

[0017] Preferably, the optimal rebar area is selected to unify the entire circumferential rebar, the optimal thickness at each location is re-determined, and the optimal thickness is smoothed to obtain a smooth thickness distribution. This process determines the circumferential thickness of the shield tunnel segment and the corresponding rebar area, including: The optimal steel reinforcement area of ​​the most unfavorable section in the entire ring of shield tunnel segments is selected as a unified area, and the optimal thickness at each location is updated based on the unified area. By combining the optimal thickness at all locations, a smoothness objective function is established, and constraints are set to obtain a smooth thickness distribution; The smooth thickness distribution is defined as the circumferential thickness of the shield tunnel segment, and the uniform area is the corresponding reinforcement area.

[0018] Preferably, a smoothness objective function is established by combining the optimal thickness at all locations, and constraints are set to obtain a smooth thickness distribution. The corresponding calculation formula is as follows:

[0019]

[0020] in, This represents the least squares operation; , These represent the circumferential center positions of the shield tunnel segments. and The optimal thickness after smoothing; , Both represent position indices; This indicates the optimal thickness of the shield tunnel segment at the corresponding location.

[0021] To address the aforementioned problems, this invention also provides a joint reverse design calculation system for the reinforcement and thickness of shield tunnel segments. The system includes a processor, a communication interface, a memory, and a communication bus. The processor, communication interface, and memory communicate with each other via the communication bus. The processor calls logical instructions from the memory to execute the joint reverse design calculation method for the reinforcement and thickness of shield tunnel segments as described in any of the preceding claims.

[0022] The present invention has the following beneficial effects: 1. In the calculation method of this application, the internal force at any location is used as the design input. The structural requirements at each location are determined through back-design calculation, which avoids the deviation caused by the traditional uniform cross-section design that only determines parameters based on a single control section. This makes the cross-section parameters more consistent with the actual stress state of the tunnel segment, that is, it can truly reflect the stress distribution characteristics of the tunnel segment along the circumferential direction, and improve the pertinence of the structural design. The minimum cross-section requirement that meets the bearing capacity requirements and the optimal steel reinforcement area are identified at different circumferential locations. Under the condition of uniform reinforcement throughout the ring, the amount of concrete is adjusted accordingly. Compared with uniform thickness design, it can significantly reduce the redundancy of concrete in non-control areas, improve material utilization efficiency, and thus improve the design economy.

[0023] By using strain compatibility equations, constitutive equations, and section equilibrium equations, the height of the compression zone and the area of ​​the reinforcing steel at the corresponding locations are calculated in reverse. This transforms the requirement for uniform reinforcement throughout the entire ring, which must be met in shield tunnel segment engineering, into an explicit design constraint. Under this constraint, the cross-sectional thickness is solved and optimized in reverse, avoiding the problem of forced amplification of overall parameters due to uniform reinforcement in traditional methods. This ensures that the design results meet construction and prefabrication requirements while maintaining structural rationality. It achieves thickness synergistic optimization under uniform reinforcement conditions, taking into account engineering feasibility. In addition, based on the optimal thickness, a smooth thickness distribution is obtained. Under the premise of ensuring that the cross-sectional thickness at each angle position is not lower than the mechanical requirements, the thickness is continuously transitioned along the circumferential direction, avoiding the local abrupt problems that may occur in the design of uniform cross-section or segmented thickening. This is beneficial to improving the continuity of structural stress and reducing the potential risk of stress concentration.

[0024] Based on the overall calculation method, the reinforcement and section thickness design process is transformed into a clear calculation flow and constraints, forming a programmable and scalable systematic design method. It is applicable to different internal force distribution conditions and segment parameter configurations, and has good versatility and scalability. It is conducive to the standardization and automation of the design process and reduces the reliance on personal experience in the design results. Moreover, the entire calculation method does not involve changes to the segment structure, material type or construction technology. It only improves the performance and economy by improving the reverse design calculation, which is easy to apply directly in the existing shield tunnel engineering system and has high engineering promotion value.

[0025] 2. The joint back-design calculation system for the reinforcement and thickness of shield tunnel segments provided by this invention has the same beneficial effects as the joint back-design calculation method for the reinforcement and thickness of shield tunnel segments provided by this invention, and will not be elaborated here. Attached Figure Description

[0026] To more clearly illustrate the technical solutions and advantages in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0027] Figure 1 The flowchart illustrates the steps of a method for joint back-design calculation of reinforcement and thickness of shield tunnel segments, as provided in an embodiment of the present invention. Detailed Implementation

[0028] To further illustrate the technical means and effects adopted by the present invention to achieve its intended purpose, the following, in conjunction with the accompanying drawings and preferred embodiments, details the specific implementation, structure, features, and effects of a joint back-design calculation method and system for the reinforcement and thickness of shield tunnel segments proposed according to the present invention. In the following description, different "one embodiment" or "another embodiment" do not necessarily refer to the same embodiment. Furthermore, specific features, structures, or characteristics in one or more embodiments can be combined in any suitable form.

[0029] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0030] The following description, in conjunction with the accompanying drawings, details the specific scheme of the combined back-design calculation method and system for the reinforcement and thickness of shield tunnel segments provided by this invention.

[0031] To better illustrate, tunnel segments are important components used in shield tunneling construction, mainly for the support and load-bearing of the tunnel structure. They are usually made of concrete and are ring-shaped or arc-shaped. The segments are assembled to form the inner lining structure of the tunnel, which can effectively resist external soil pressure, water pressure and ground load, while maintaining the overall stability and sealing of the tunnel. In actual engineering, the design and manufacturing quality of the segments directly affects the safety and service life of the tunnel.

[0032] The combined calculation of the reinforcement and thickness of the tunnel segments ensures the structural safety and economic rationality of the segments under complex loads. The reinforcement design mainly considers the bending, shear, and crack resistance of the segments, and improves the load-bearing capacity and durability of the concrete by rationally configuring the steel bars. The thickness design directly affects the stiffness, strength, and deformation resistance of the segments. If only the reinforcement or thickness is calculated separately, it may lead to insufficient structural safety or material waste. The combined calculation of the two can comprehensively consider the external load, internal force distribution, and the synergistic effect of concrete and steel bars, optimize the amount of material used, reduce engineering costs, and improve the overall performance and reliability of the tunnel while meeting the requirements of structural safety.

[0033] Existing methods for the joint design of segment reinforcement and thickness are usually based on finite element analysis or analytical calculations to obtain the bending moment and axial force of the segment at different circumferential angles, and then design the cross-section reinforcement and thickness accordingly. Although these methods have been widely used in engineering practice, they still have significant limitations in the coordinated design of reinforcement and cross-section thickness, especially under conditions where there are significant differences in circumferential stress, making it difficult to simultaneously consider structural safety, economy, and engineering feasibility. Therefore, a joint back-design calculation method for the reinforcement and thickness of shield tunnel segments is proposed.

[0034] Please see Figure 1 The diagram illustrates a flowchart of the steps in a combined back-design calculation method for the reinforcement and thickness of shield tunnel segments provided in the first embodiment of the present invention. The method includes: Step S1: Determine the internal forces at any circumferential position of the shield tunnel segment and set the stress area of ​​the reinforcing steel. Step S2: Determine the segment cross-section based on the shield tunnel segments, construct the objective function for concrete and steel reinforcement usage by combining the stress area of ​​the steel reinforcement, and set the trial thickness; Step S3: Determine the effective height based on the test thickness, and set the height of the compression zone based on the shield tunnel segments. Combine the internal forces to establish the strain compatibility equation, constitutive equation and section equilibrium equation in sequence, and solve to obtain the height of the compression zone and the area of ​​the steel reinforcement at the corresponding position. Step S4: Determine the optimal rebar area at each location by combining the height of the compression zone and the stress area of ​​the rebar with the objective function; Step S5: Select the optimal rebar area to unify the full ring rebar, redetermine the optimal thickness at each position, and smooth the optimal thickness to obtain a smooth thickness distribution, thereby determining the circumferential thickness of the shield tunnel segment and the corresponding rebar area.

[0035] The analysis of numerous engineering examples reveals that, under the influence of ground pressure and construction loads, the bending moment and axial force of shield tunnel segments exhibit continuous variations along the circumferential angle, with significant differences in internal force requirements at different angles. However, existing design methods only select the extreme values ​​of circumferential internal forces as control sections, employing uniform thickness and reinforcement—essentially using single-point control instead of a full-circumferential response design approach. This fails to reflect the true stress state of the segments, resulting in varying degrees of material redundancy at most angles. Therefore, to address this issue, it is possible to attempt reverse calculations of reinforcement and thickness for each angle section based on the bending moment and axial force requirements at any circumferential angle. This involves calculating the minimum section parameters that satisfy the ultimate bearing state under given internal force conditions. Furthermore, if the reinforcement area and thickness of each angle section are allowed to be determined independently, theoretically, the optimal material usage design can be obtained.

[0036] Further research revealed that the "angle-by-angle independent optimization" design method is difficult to implement in practical engineering. On the one hand, shield tunnel segments typically require uniform longitudinal main reinforcement within the same ring to meet the requirements of prefabrication and installation. On the other hand, the optimal section thickness obtained by angle-by-angle independent back-calculation often exhibits discontinuous changes in the circumferential direction, with abrupt changes or unevenness, affecting the structural stress continuity and the feasibility of segment manufacturing. Therefore, it is clear that the difficulty in shield tunnel segment design lies in how to simultaneously coordinate local mechanical requirements and overall engineering constraints within the entire ring. Consequently, a unified ring reinforcement is proposed as a global design constraint. For different circumferential angle positions, the minimum section thickness required to meet bending moment and axial force requirements is recalculated, establishing a circumferential thickness requirement distribution under unified reinforcement conditions.

[0037] Finally, based on this, the circumferential discrete thickness requirements obtained by direct back-calculation may still have local discontinuities or drastic changes. Therefore, through smoothing processing, while ensuring that the thickness at each angular position is not lower than the mechanical requirement value, a thickness distribution result with smooth overall changes and meeting engineering processing requirements is obtained, i.e., smooth thickness distribution. This ultimately forms a complete back-calculation method for the reinforcement and thickness of shield tunnel segments, realizing a design process from obtaining internal force requirements, local limit back-calculation, unified constraints of the entire ring, and continuous thickness optimization. This breaks through the traditional design mode of single-point control and experience correction, and provides a new technical approach for the safe, economical, and feasible design of shield tunnel segments.

[0038] As an alternative implementation method, shield tunnel segments refer to the precast concrete lining structure used in tunnel engineering constructed using the shield tunneling method. These segments are prefabricated in a factory, have uniform specifications and high strength, and are then assembled ring by ring at the tunnel construction site using a shield tunneling machine to ultimately form the main support system of the tunnel.

[0039] It can be explained that in step S1, based on the shield tunnel segments, the internal force at any position in the circumferential direction is determined. In this embodiment, the force is determined by the angular position. This will be explained, and the angular position will be obtained through finite element analysis or analytical methods. The corresponding bending moment is obtained and denoted as . Axial force, denoted as The process involves taking the bending moment and axial force at any circumferential angle position of the shield tunnel segment as known input conditions. Then, considering that during the actual stress process, the shield tunnel segment may simultaneously bear positive and negative bending moments, and the inner or outer reinforcing bars may become tension reinforcements, preferably, in this embodiment, to ensure structural stress symmetry and design simplification, the principle of equal area configuration for inner and outer main reinforcements is adopted to define the stress-bearing area of ​​the reinforcement, i.e., the areas of both inner and outer main reinforcements are denoted as... .

[0040] Understandably, a positive bending moment results in tension on the inner arc surface of the tunnel segment and compression on the outer arc surface; both tension and compression require reinforcement. A negative bending moment, on the other hand, results in the opposite direction of force. In circular tunnels, positive and negative bending moments are generally close. In practical engineering, the required reinforcement area for both positive and negative bending moments is calculated separately, and the maximum value is taken as the area of ​​the inner and outer main reinforcement bars; that is, the same reinforcement area is used on both the inner and outer sides. Therefore, in this embodiment, equal reinforcement is used on both the inner and outer sides. This represents the area of ​​the reinforcing steel bar under stress.

[0041] Further, step S2 includes: Step S21: Obtain the width and initial thickness of the tunnel segment cross section respectively. Determine the cost-equivalent weight coefficient of concrete cost to steel reinforcement cost based on the tunnel segment of the shield tunnel. Combine the stress area of ​​the steel reinforcement to construct the objective function of concrete and steel reinforcement usage.

[0042] Optionally, at the angular position At this point, the segment section is treated as an independent stress section, and analysis is performed based on it to determine the optimal thickness and reinforcement of the section, that is, the circumferential thickness and corresponding steel reinforcement area determined in subsequent steps, to ensure the safety and economy of the segment structure.

[0043] Further, in step S21, the objective function for the amount of concrete and steel reinforcement is constructed, and the corresponding calculation formula is as follows:

[0044] in, Represents the cost function; Indicates the width of the segment cross-section; Indicates the initial thickness of the segment cross-section; This represents the cost equivalence weighting coefficient; This indicates the area of ​​the reinforcing steel bar under stress.

[0045] It can be explained that the objective function for concrete and steel reinforcement usage, i.e., the cost function, is used to balance the safety and optimal economy of the tunnel segment structure. While meeting engineering specifications and usage requirements, it aims to minimize material costs and improve resource utilization efficiency, thereby selecting a reinforcement scheme that is both safe, reliable, and economically reasonable. The cost equivalence weighting coefficient is used in this process. The ratio of concrete cost to steel reinforcement cost effectively reflects the relative cost relationship between the two, providing a quantitative basis for cost control and optimized design in engineering projects; the width of the segment cross-section. This refers to the distance between the outer edges of the tunnel segments along the tunnel axial direction on the cross-section, typically taken as 1m per unit width; the initial thickness of the tunnel segment cross-section. This refers to the distance from the outer edge perpendicular to the axis.

[0046] Step S22: Preset the thickness range and the trial step size respectively. Perform single trial probing on the initial thickness according to the trial step size based on the thickness range. Minimize the objective function to determine the current trial thickness of the segment cross section.

[0047] Specifically, a preset thickness range is denoted as... The trial step size is recorded as The unit is mm, and The step size can be specifically set according to the actual situation. While a step size that is too small, such as 1mm, is more accurate, it has little engineering significance. A step size that is too large, such as 50mm, may cause the optimal solution to be missed. Then, based on the trial step size... The thickness of the tunnel segment cross-section is individually tested, i.e., the current test thickness is selected. In order to determine the relevant input parameters for subsequent operations, i.e. .

[0048] Understandably, during the aforementioned steps, the area of ​​the reinforcing steel bar subjected to stress... All are unknowns, given the current trial thickness. Based on the known internal forces in step S1, the bending moment and axial force This process determines the area of ​​reinforcing steel and the height of the compression zone to achieve stress balance, facilitating subsequent back-calculation of reinforcement to obtain the reinforcement area and neutral axis position that meet design requirements, thus ensuring the safety and reliability of the segment structure under given loads.

[0049] Furthermore, step S3 includes: Step S31: Determine the thickness of the protective layer for the shield tunnel segments, and determine the effective height based on the test thickness.

[0050] Specifically, the protective layer refers to the distance between the outermost layer of reinforcing steel bars in a shield tunnel segment and the concrete surface. It serves to prevent direct erosion of the reinforcing steel bars by the external environment, ensuring the durability of the steel bars and the overall safety of the structure. The thickness of the protective layer is determined according to specifications and is denoted as... The current probe thickness corresponds to the position and angle analyzed. Determine the effective height, that is , Indicates the effective height.

[0051] Step S32: Based on the height of the compression zone of the shield tunnel segments, establish the strain compatibility equations for the tensile reinforcement and the compressive reinforcement respectively, taking into account the effective height and the thickness of the protective layer.

[0052] To clarify, the height of the compression zone, also known as the neutral axis height, is the distance from the point where the strain of the segment cross-section is zero to the edge of the compression zone. It satisfies strain compatibility, meaning that the height of the pressure zone meets certain geometric compatibility conditions during deformation to ensure the continuity and integrity of the tunnel segments and avoid discontinuities such as cracks or overlaps. This is achieved through the height of the pressure zone. Establish strain compatibility equations.

[0053] Further, in step S32, strain compatibility equations for tension reinforcement and compression reinforcement are established respectively, and the corresponding calculation formulas are as follows:

[0054]

[0055] in, Indicates the strain of the tensile steel reinforcement; This indicates the strain of the compressed steel reinforcement; Indicates the height of the pressure zone; This represents the ultimate compressive strain of concrete; Indicates the effective height; This indicates the thickness of the protective layer.

[0056] It can be explained that in the design of concrete structures, the strain of tensile reinforcement and compressive reinforcement corresponds to the different stress states of the tension zone and compression zone section under bending moment, respectively. The tension zone refers to the area of ​​the section subjected to tensile stress, while the compression zone refers to the area subjected to compressive stress.

[0057] Step S33: Determine the yield strain, elastic modulus, and tensile strength of the steel bars based on the corresponding steel bar grades measured for the shield tunnel segments, and establish the constitutive equation; Further, in step S33, the constitutive equation is established, and the corresponding calculation formula is:

[0058] in, Indicates the stress in the reinforcing steel; Indicates the elastic modulus of the steel reinforcement; This represents the strain of the reinforcing steel, specifically the strain of the tensile reinforcing steel. or strain of compressed steel bars ; Indicates the yield strain of the steel reinforcement; This indicates the tensile strength of the steel reinforcement.

[0059] Explanation: Yield strain of steel bars This refers to the strain value of a steel bar when it transitions from the elastic stage to the plastic stage under tensile load. When the steel bar is subjected to external force, it undergoes elastic deformation. If the force is unloaded, the steel bar can return to its original shape. Conversely, when the stress in the steel bar reaches the yield strength, the steel bar begins to undergo significant plastic deformation. Even if the force is unloaded, it cannot fully recover. The strain corresponding to this is the yield strain.

[0060] It can be explained that the stress of the reinforcing steel Using an ideal elastic-plastic constitutive model, i.e., constitutive equations, when the strain of the tensile reinforcement is... or strain of compressed steel bars Less than the yield strain of steel bars When the stress in the steel reinforcement is at a certain point, it is in a linear elastic state, and the stress in the steel reinforcement is determined by the combined elastic modulus and strain of the steel reinforcement; conversely, when the strain in the steel reinforcement is at a certain point, the stress in the steel reinforcement is determined by the combined elastic modulus and strain of the steel reinforcement. When the stress is greater than or equal to the yield strain of the steel bar, the tensile strength of the steel bar is directly taken as the stress of the steel bar. This value is the corresponding design value of the steel bar, that is, the strength index that has been confirmed by relevant design specifications and has sufficient safety reserve.

[0061] Step S34: Establish the section equilibrium equation by combining the strain compatibility equation and the constitutive equation, and solve for the height of the compression zone and the area of ​​the reinforcing steel at the corresponding location.

[0062] The section equilibrium equation refers to the balance between axial force and bending moment in the cross-section of a shield tunnel segment. That is, the effect of axial force and the effect of bending moment should cancel each other out, so that the entire cross-section is in a stable static equilibrium state, ensuring that the tunnel structure does not suffer damage or excessive deformation under external loads. Here, axial force refers to the force acting along the central axis of the tunnel segment cross-section; bending moment refers to the moment effect of external force causing the cross-section to bend and rotate, describing the degree of non-uniform stress distribution inside the cross-section.

[0063] Further, in step S34, the cross-sectional equilibrium equations are established, and the corresponding calculation formulas are as follows:

[0064]

[0065] in, Indicates axial force; Indicates bending moment; Indicates the coefficients of the equivalent rectangular stress diagram; Indicates the axial compressive strength of concrete; Indicates the width of the segment cross-section; Indicates the height of the pressure zone; This indicates the stress in the tensile steel reinforcement. This indicates the stress in the compressed steel reinforcement. Indicates the area of ​​the reinforcing steel bar under stress; Indicates the effective height; This indicates the thickness of the protective layer.

[0066] It can be explained that the equivalent rectangular stress diagram coefficients This refers to parameters used to simplify the calculation of the axial compressive strength of reinforced concrete members, transforming the actual non-uniformly distributed compressive stress pattern of concrete into an equivalent rectangular stress distribution pattern; axial compressive strength of concrete. It refers to the strength index of concrete materials under axial compression state, which is used in the design process of reinforced concrete structures according to relevant design specifications, to ensure the safety and reliability of the structure under normal use and ultimate state.

[0067] It should be noted that in the calculation formulas corresponding to the strain compatibility equation, constitutive equation, and section equilibrium equation, the unknown is the height of the compression zone. and the stress area of ​​the reinforcing steel Therefore, in the current analysis of the circumferential position angle Given a fixed value, the height of the compression zone at the corresponding position and angle can be calculated by combining the remaining exact data with the equation. and the stress area of ​​the reinforcing steel Similarly, determine the height of the pressure zone at all circumferential positions and angles within the tunnel segment. and the stress area of ​​the reinforcing steel .

[0068] It should be noted that in step S4, one position angle corresponds to multiple current probe thicknesses. The current test thickness is used to obtain the corresponding reinforcing bar stress area according to the aforementioned step S3. This allows us to determine the reinforcing steel stress area corresponding to all current test thicknesses at a given location angle, and then determine the cost function for each corresponding thickness by combining all current test thicknesses. By selecting the minimum value, the section parameters corresponding to the minimum cost at that location angle are obtained, which yields the optimal section thickness and optimal reinforcement area. Similarly, determine the optimal cross section for all positions and angles.

[0069] Understandably, steps S1-S4 can independently determine the optimal cross section that meets the limit state requirements at each circumferential position angle. However, the results still have certain problems in actual engineering. That is, the main reinforcement of the tunnel segment usually needs to be uniformly configured within a ring, and it is impossible to make differentiated arrangements based on the independent optimization results at each location. In addition, the thickness of the tunnel segment must remain continuous and smooth in the circumferential direction, and no obvious abrupt changes or turns are allowed, which limits the actual feasibility of cross section optimization.

[0070] Further, step S5 includes: Step S51: Select the optimal reinforcement area of ​​the most unfavorable section in the entire ring of shield tunnel segments as a unified area, and update the optimal thickness at each location based on the unified area.

[0071] To address the issue that independent design of single-position angles cannot be directly applied in engineering, the point-by-point limit state back-calculation results for circumferential position angles are transformed into a global optimization problem along the circumferential angle.

[0072] It can be explained that, based on step S4, the optimal rebar area for each circumferential position angle can be determined, i.e. Then, the optimal steel reinforcement area of ​​the most unfavorable section of the entire ring is selected as the unified main reinforcement configuration, i.e., the unified area. The corresponding calculation formula is:

[0073] in, Indicates a uniform area.

[0074] Next, after obtaining a uniform area Then, the optimal cross-sectional thickness originally determined in step S4... Since this is not satisfied, the optimal thickness at each circumferential angle position is recalculated based on the uniform area, i.e., the circumferential angle position is solved based on the cross-sectional equilibrium equation. Corresponding optimal cross-sectional parameters Optimal thickness ,Right now:

[0075]

[0076] Step S52: Establish a smoothness objective function by combining the optimal thickness at all locations, and set constraints to obtain a smooth thickness distribution.

[0077] As an optional implementation method, based on the optimal thickness The least squares smoothing method with inequality constraints is adopted. That is, by introducing inequality constraints, the smoothing effect is optimized on the basis of least squares fitting, which can effectively control the fluctuation range of data and improve the fitting accuracy.

[0078] Furthermore, in step S52, the corresponding calculation formula is:

[0079]

[0080] in, This represents the least squares operation; , These represent the circumferential center positions of the shield tunnel segments. and The optimal thickness after smoothing; , Both represent position indices; This indicates the optimal thickness of the shield tunnel segment at the corresponding location.

[0081] It can be explained that, That is, the smoothness objective function. The constraints are combined with the smoothness objective function and the constraints to transform the overall problem into a smoothness problem. By iteratively solving this least squares problem with inequality constraints, a smooth thickness distribution of the tube segment can be obtained that has a smooth overall change and meets the processing requirements, while satisfying mechanical safety requirements.

[0082] Step S53: Define the smooth thickness distribution as the circumferential thickness of the shield tunnel segment, and the uniform area as the corresponding reinforcement area.

[0083] It should be added that, at the optimal thickness In the solution process, it is a locally independent back-calculation stage. In this stage, the continuity of the segment thickness can be completely ignored. Instead, for each discrete position angle point, a theoretically minimum thickness value that just meets the safety requirements is calculated back based on the internal force requirements. The obtained value is discrete and may have jagged discontinuities in the circumferential direction. Then, based on the constraint conditions... Then, we enter the global optimization stage to avoid the problem that the optimal thickness cannot be directly used in production, which would lead to discontinuous processing.

[0084] Understandably, in the calculation method of this application, the internal force at any location is used as the design input, and the structural requirements at each location are determined through back design calculation. This avoids the deviation caused by the traditional uniform cross-section design which only relies on a single control section for parameter determination. This makes the cross-section parameters more consistent with the actual stress state of the tunnel segment, that is, it can truly reflect the stress distribution characteristics of the tunnel segment along the circumferential direction, and improve the pertinence of the structural design. The minimum cross-section requirement that meets the bearing capacity requirements and the optimal steel reinforcement area are identified at different circumferential locations. Under the condition of uniform reinforcement throughout the ring, the amount of concrete is adjusted accordingly. Compared with uniform thickness design, this can significantly reduce the redundancy of concrete in non-control areas, improve material utilization efficiency, and thus improve the design economy.

[0085] By using strain compatibility equations, constitutive equations, and section equilibrium equations, the height of the compression zone and the area of ​​the reinforcing steel at the corresponding locations are calculated in reverse. This transforms the requirement for uniform reinforcement throughout the entire ring, which must be met in shield tunnel segment engineering, into an explicit design constraint. Under this constraint, the cross-sectional thickness is solved and optimized in reverse, avoiding the problem of forced amplification of overall parameters due to uniform reinforcement in traditional methods. This ensures that the design results meet construction and prefabrication requirements while maintaining structural rationality. It achieves thickness synergistic optimization under uniform reinforcement conditions, taking into account engineering feasibility. In addition, based on the optimal thickness, a smooth thickness distribution is obtained. Under the premise of ensuring that the cross-sectional thickness at each angle position is not lower than the mechanical requirements, the thickness is continuously transitioned along the circumferential direction, avoiding the local abrupt problems that may occur in the design of uniform cross-section or segmented thickening. This is beneficial to improving the continuity of structural stress and reducing the potential risk of stress concentration.

[0086] Based on the overall calculation method, the reinforcement and section thickness design process is transformed into a clear calculation flow and constraints, forming a programmable and scalable systematic design method. It is applicable to different internal force distribution conditions and segment parameter configurations, and has good versatility and scalability. It is conducive to the standardization and automation of the design process and reduces the reliance on personal experience in the design results. Moreover, the entire calculation method does not involve changes to the segment structure, material type or construction technology. It only improves the performance and economy by improving the reverse design calculation, which is easy to apply directly in the existing shield tunnel engineering system and has high engineering promotion value.

[0087] The second embodiment of the present invention provides a joint reverse design calculation system for the reinforcement and thickness of shield tunnel segments. The system includes a processor, a communication interface, a memory, and a communication bus. The processor, the communication interface, and the memory communicate with each other through the communication bus. The processor calls logical instructions in the memory to execute the joint reverse design calculation method for the reinforcement and thickness of shield tunnel segments as described in any of the foregoing embodiments.

[0088] It can be noted that when a joint back-design calculation system for the reinforcement and thickness of shield tunnel segments is in operation, it needs to utilize a joint back-design calculation method for the reinforcement and thickness of shield tunnel segments. Therefore, whether the system and program data are integrated or different hardware is configured to produce functions with similar effects to those achieved by this invention, they all fall within the protection scope of this invention. Moreover, this system has the same beneficial effects as the aforementioned joint back-design calculation method for the reinforcement and thickness of shield tunnel segments, which will not be elaborated here.

[0089] It should be noted that the order of the above embodiments of the present invention is merely for descriptive purposes and does not represent the superiority or inferiority of the embodiments. The processes depicted in the accompanying drawings do not necessarily require a specific or sequential order to achieve the desired result. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0090] The various embodiments in this specification are described in a progressive manner. The same or similar parts between the various embodiments can be referred to each other. Each embodiment focuses on describing the differences from other embodiments.

Claims

1. A method for combined back-design calculation of reinforcement and thickness of shield tunnel segments, characterized in that, The method includes: Determine the internal forces at any circumferential position of the shield tunnel segment and set the stress area of ​​the reinforcing steel; Based on the segment cross-section determined by the shield tunnel segments, an objective function for the amount of concrete and steel reinforcement is constructed by combining the stress area of ​​the steel reinforcement, and a trial thickness is set, including: The width and initial thickness of the tunnel segment are obtained respectively. The ratio of concrete cost to steel cost is determined based on the tunnel segment of the shield tunnel. The cost equivalence weight coefficient is then used to construct the objective function of concrete and steel usage based on the steel stress area. The thickness range and the test step size are preset respectively. The initial thickness is tested individually according to the test step size based on the thickness range. The current test thickness of the segment section is determined by minimizing the objective function. The effective height is determined based on the tested thickness, and the height of the compression zone is set based on the shield tunnel segments. Strain compatibility equations, constitutive equations, and section equilibrium equations are established sequentially based on internal forces. Solving these equations yields the corresponding height of the compression zone and the area of ​​the reinforcing steel under stress, including: Determine the thickness of the protective layer for shield tunnel segments, and determine the effective height based on the thickness test; Based on the height of the compression zone of the shield tunnel segments, strain compatibility equations for the tensile and compressive reinforcements are established by combining the effective height and the thickness of the protective layer. Based on the steel grade corresponding to the shield tunnel segments, determine the steel yield strain, steel elastic modulus and steel tensile strength, and establish the constitutive equation; By combining the strain compatibility equation and the constitutive equation, the section equilibrium equation is established, and the height of the compression zone and the area of ​​the steel reinforcement at the corresponding location are obtained by solving the equation. The optimal steel reinforcement area at each location is determined by combining the height of the compression zone and the area of ​​the steel reinforcement under stress with the objective function. Specifically, the height of the compression zone and the area of ​​the steel reinforcement under stress at each location are determined by back-calculation using the strain compatibility equation, constitutive equation, and section equilibrium equation. Based on the area of ​​the steel reinforcement under stress and all the current test thicknesses at the corresponding location, the minimum value is selected by substituting it into the objective function to obtain the optimal steel reinforcement area. The optimal rebar area is selected to unify the entire circumferential rebar, the optimal thickness at each location is re-determined, and the optimal thickness is smoothed to obtain a smooth thickness distribution. This determines the circumferential thickness of the shield tunnel segment and the corresponding rebar area, including: The optimal steel reinforcement area of ​​the most unfavorable section in the entire ring of shield tunnel segments is selected as a unified area, and the optimal thickness at each location is updated based on the unified area. By combining the optimal thickness at all locations, a smoothness objective function is established, and constraints are set to obtain a smooth thickness distribution; The smooth thickness distribution is defined as the circumferential thickness of the shield tunnel segment, and the uniform area is the corresponding reinforcement area.

2. The method for combined back-design calculation of reinforcement and thickness of shield tunnel segments according to claim 1, characterized in that, The objective function for calculating the amount of concrete and steel reinforcement is constructed, and the corresponding calculation formula is as follows: in, Represents the cost function; Indicates the width of the segment cross-section; Indicates the initial thickness of the segment cross-section; This represents the cost equivalence weighting coefficient; This indicates the area of ​​the reinforcing steel bar under stress.

3. The method for combined back-design calculation of reinforcement and thickness of shield tunnel segments according to claim 1, characterized in that, Strain compatibility equations for tension reinforcement and compression reinforcement are established separately, and the corresponding calculation formulas are as follows: in, Indicates the strain of the tensile steel reinforcement; This indicates the strain of the compressed steel reinforcement; Indicates the height of the pressure zone; This represents the ultimate compressive strain of concrete; Indicates the effective height; This indicates the thickness of the protective layer.

4. The method for combined back-design calculation of reinforcement and thickness of shield tunnel segments according to claim 3, characterized in that, The constitutive equation is established, and the corresponding calculation formula is as follows: in, Indicates the stress in the reinforcing steel; Indicates the elastic modulus of the steel reinforcement; This represents the strain of the reinforcing steel, specifically the strain of the tensile reinforcing steel. or strain of compressed steel bars ; Indicates the yield strain of the steel reinforcement; This indicates the tensile strength of the steel reinforcement.

5. The method for combined back-design calculation of reinforcement and thickness of shield tunnel segments according to claim 4, characterized in that, The equilibrium equations for the cross section are established, and the corresponding calculation formulas are as follows: in, Indicates axial force; Indicates bending moment; Indicates the coefficients of the equivalent rectangular stress diagram; Indicates the axial compressive strength of concrete; Indicates the width of the segment cross-section; Indicates the height of the pressure zone; This indicates the stress in the tensile steel reinforcement. This indicates the stress in the compressed steel reinforcement. Indicates the area of ​​the reinforcing steel bar under stress; Indicates the effective height; This indicates the thickness of the protective layer.

6. The method for combined back-design calculation of reinforcement and thickness of shield tunnel segments according to claim 1, characterized in that, By combining the optimal thickness at all locations, a smoothness objective function is established, and constraints are set to obtain a smooth thickness distribution. The corresponding calculation formula is as follows: in, This represents the least squares operation; , These represent the circumferential center positions of the shield tunnel segments. and The optimal thickness after smoothing; , Both represent position indices; This indicates the optimal thickness of the shield tunnel segment at the corresponding location.

7. A combined back-design calculation system for the reinforcement and thickness of shield tunnel segments, characterized in that, The system includes a processor, a communication interface, a memory, and a communication bus. The processor, the communication interface, and the memory communicate with each other through the communication bus. The processor calls logical instructions in the memory to execute the joint back-design calculation method for the reinforcement and thickness of shield tunnel segments as described in any one of claims 1 to 6.

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