A unified calculation method for rebar anchorage length and lap length

Abstract

This invention relates to a unified calculation method for rebar anchorage length and lap length, encompassing a unified design method and software system for rebar anchorage length and lap length in ultra-high performance concrete (UHPC) and UHPC-CA structures containing coarse aggregate. First, based on theoretical bond models and experimental databases, the unreduced bond strength is calculated to establish a design baseline bond strength. Second, utilizing the stress-slip relationship between rebar and UHPC and the energy equivalence principle, unified expressions are derived under different end conditions, such as single-end / double-end tension and anchorage / lap, within a unified theoretical framework. Furthermore, multi-parameter dimensionless design graphs are pre-calculated, and computer software is developed to automatically provide minimum anchorage and lap lengths for different code safety requirements, achieving integrated, parametric design of UHPC and UHPC-CA, improving safety and economy, and providing a quantitative tool for code revision.

Description

Technical Field

[0001] This invention relates to the field of concrete structure design, and in particular to the calculation method and software implementation of the anchorage length and lap length of steel bars in ultra-high performance concrete (UHPC) and ultra-high performance concrete with coarse aggregate (UHPC-CA). It belongs to the interdisciplinary technical field of structural design theory, engineering design tools and their standard applications. Background Technology

[0002] Ultra-high performance concrete (UHPC) has attracted widespread attention in bridge construction, prefabricated components, and reinforcement and strengthening projects due to its ultra-high compressive strength, excellent ductility, and durability. In recent years, in order to reduce material costs and shrinkage and improve volume stability, UHPC-CA systems, which incorporate coarse aggregates into UHPC, have emerged. The bond and anchorage performance between UHPC and high-strength steel bars has become a key issue in structural design.

[0003] Existing design codes for reinforced concrete structures in various countries, such as China's "Code for Design of Concrete Structures" GB 50010, the American ACI 318, fib Model Code 2010, and some regional technical specifications (such as DBJ 43 / T 325), regarding the provisions on rebar anchorage length and lap length are mainly based on extensive experimental regressions of ordinary concrete or conventional high-strength concrete. They typically simplify the design reference bond strength to the concrete cube compressive strength f. ck Alternatively, empirical expressions of these functions are used to calculate the allowable bond stress using an overall safety factor or empirical reduction factor, which is then combined with structural limits to determine the anchorage and lap length. Most of these methods do not explicitly consider the coupled effects of steel fiber volume fraction, coarse aggregate parameters, protective layer thickness, and bond length, and do not systematically distinguish between UHPC and UHPC-CA.

[0004] Extensive research has been conducted in recent years on the bond properties between UHPC and UHPC-CA and reinforcing steel. Existing literature has analyzed the effects of factors such as steel fiber volume fraction, reinforcing steel diameter, and anchorage length on bond strength and stress-slip relationship through pull-out tests, anchored beam tests, or hinged beam tests, and has provided ultimate bond strength or constitutive models. Other studies have specifically investigated the critical anchorage length between UHPC-CA and high-strength reinforcing steel, proposing formulas for calculating anchorage length based on experimental regression. These studies provide an important foundation for understanding the bond mechanism and local load-bearing behavior of UHPC and UHPC-CA.

[0005] However, existing technologies still have the following shortcomings:

[0006] 1. Lack of integrated bond strength design parameters oriented towards design specifications: Existing bond strength models mostly use the ultimate bond strength τ uOr given in the form of local constitutive parameters, serving experimental analysis or nonlinear numerical simulation. Design reference bond strength required for specification design. Strength is usually obtained through simple reduction of strength or empirical coefficients, which is difficult to reflect the UHPC strength grade, steel fiber volume fraction, coarse aggregate parameters, and protective layer thickness. and bond length ratio The combined effect of [various factors]. Most studies on UHPC-CA directly introduce coarse aggregate parameters into the experimental fitting formula, without forming a system with clear safety semantics that can be directly integrated with the specification's partial factor system. index.

[0007] 2. Anchorage length and lap length are mostly based on scattered empirical formulas, lacking a unified theoretical framework: Existing standards typically provide empirical expressions for tensile anchorage length, compressive anchorage length, and lap length separately, based on different assumptions and experimental databases, resulting in inconsistent parameter values ​​and reduction rules. In UHPC and UHPC-CA studies, anchorage or lap length formulas are often proposed for specific structural forms or test arrangements, without consolidating different end conditions such as single-end tension, double-end tension, anchorage, and lap length within a unified stress-slip and energy equivalence framework. In the expression, different constructs are distinguished only by the combination of parameters.

[0008] 3. Failure to systematically and explicitly consider the coupling effect of multiple parameters on design anchorage and lap length: Existing code formulas generally only use a few parameters such as concrete strength grade, rebar diameter, stress characteristics, and cover thickness, and these are mostly presented in a multiplicative correction manner; in UHPC and UHPC-CA related studies, although the influencing factors such as steel fiber volume fraction, coarse aggregate volume, and particle size were investigated, sensitivity analysis was usually conducted under the condition that other parameters were basically fixed, lacking coverage of V f V CA d CA c / d, l a System design methods and available graphs for multiple parameter combinations such as / d.

[0009] 4. Lack of design tools and software systems directly applicable to engineering: Existing research on UHPC / UHPC-CA bond-slip models and anchorage lengths largely remains at the academic level, consisting of theoretical derivations and limited numerical examples. In practical designs, engineers are often forced to equate UHPC or UHPC-CA with ordinary high-strength concrete, or to adopt empirical safety reductions and larger structural anchorage lengths, leading to potential safety risks, significant conservatism, and even material waste. Currently, there is a lack of solutions that encapsulate complex theoretical models and experimental databases into multi-parameter design maps and software systems, enabling designers to quickly obtain reasonable minimum anchorage and lap lengths under given code safety requirements.

[0010] 5. Lack of a unified framework for UHPC and UHPC-CA: Existing studies on UHPC and UHPC-CA mostly involve separate modeling and analysis. Even when the same study involves both materials, qualitative or empirical conclusions are often drawn by comparing experimental results, rather than explicitly introducing the coarse aggregate volume fraction V at the model level. CA and particle size d CA Parameters such as V CA When the value is 0, it automatically degenerates into a pure UHPC case, thus achieving a unified design tool. However, this makes it difficult for engineers to complete the zonal design and overall verification of anchorage and lap length within a consistent theoretical framework when both UHPC and UHPC-CA zones exist in the same component.

[0011] In summary, current technologies do not yet provide a unified theoretical basis that simultaneously covers both UHPC and UHPC-CA, explicitly considers the influence of multiple parameters such as coarse aggregate, steel fiber, protective layer thickness, and bond length, and directly addresses the integrated design method and supporting software system for rebar anchorage length and lap length that meet code safety requirements. Therefore, it is necessary to propose new technical solutions to improve the rationality, consistency, and operability of design calculations, providing quantitative basis and tool support for relevant code revisions and engineering implementation. Summary of the Invention

[0012] The purpose of this invention is to address the following problems in the design of steel reinforcement anchorage and lap splices in ultra-high performance concrete (UHPC) and UHPC-CA with coarse aggregate: the design bond strength index is disconnected from the specification partial factor system, failing to systematically reflect the coupling effect of multiple parameters such as steel fibers, coarse aggregate, protective layer thickness, and bond length; the calculation formulas for anchorage length and lap length are scattered, relying on empirical regression and lacking a unified theoretical framework; and there is a lack of multi-parameter design charts and calculation software tools for engineering applications, leading to unsafe or overly conservative adoption of UHPC / UHPC-CA in actual design. This invention proposes a standardized method and software system for calculating the anchorage length and lap length of UHPC / UHPC-CA steel reinforcement. This method establishes a unified design benchmark bond strength. A unified expression for anchorage and lap length. Furthermore, through pre-calculated design maps and supporting software systems, the integrated, parametric, and visual design of UHPC and UHPC-CA is achieved.

[0013] This invention mainly solves the following technical problems:

[0014] 1. How to construct a design benchmark bond strength index applicable to UHPC and UHPC-CA that can be directly connected to the standard reliability system: Based on the existing ultimate bond strength theoretical model and experimental database, establish an index that explicitly depends on the UHPC strength grade and steel fiber volume fraction. Coarse aggregate volume fraction and maximum particle size Relative protective layer thickness Relative bond length Equal parameters Calculation method.

[0015] 2. How to characterize the rebar anchorage length and lap length using the same expression within a unified theoretical framework: Based on the stress-slip relationship and energy equivalence principle at the rebar-UHPC / UHPC-CA interface, a unified model is constructed for single-end tension anchorage, double-end tension lap splice, and transitional load cases, deriving a unified form. And by using different parameter combinations, it distinguishes between anchoring and overlapping, as well as different behavior modes.

[0016] 3. How to transform complex multi-parameter theoretical results into engineering-usable graphs and software tools: By pre-calculating various combinations of reinforcement and UHPC / UHPC-CA parameters, a dimensionless design surface is constructed. – – , – – We will develop graphs and software systems to support rapid design and result comparison under multiple security requirements.

[0017] 4. How to achieve compatibility between UHPC and UHPC-CA within a unified framework and support component partitioning design: Explicitly import into the model. , Coarse aggregate parameters, making It automatically degenerates into pure UHPC; at the software level, it supports partition calculation and unified verification of UHPC area and UHPC-CA area in the same component.

[0018] To achieve the above objectives, the present invention adopts the following technical solution:

[0019] 1. Unified design benchmark bond strength Construction method

[0020] Based on the theoretical bond model and experimental database of the steel reinforcement-UHPC / UHPC-CA interface, the ultimate bond strength without reduction is calculated. and peak slip Based on the target reliability indicators and the current standard safety framework, several sub-items or reduction factors are introduced: material strength and brittleness correlation coefficients. Steel fiber bridging effect coefficient Coarse aggregate correlation coefficient Protective layer thickness effect coefficient Bond length effect coefficient Construction and environmental impact coefficient wait.

[0021] The above coefficient function form was determined through theoretical analysis and database fitting, and then... This allows for the attainment of a unified design benchmark bond strength.

[0022] 2. A unified expression for anchorage length and lap length

[0023] Construct the interfacial stress-slip relationship including the rising segment, peak segment, and softening segment. And provide the parameterized form.

[0024] Based on the principle of energy equivalence, the interfacial energy is obtained by integrating the interfacial bond stress-slip curve over the effective bond length. The development of steel reinforcement from zero stress to yield stress strain energy Equal to each other, the required dimensionless bond length can be obtained. .

[0025] Within a unified framework, by applying boundary conditions for single-end tension, double-end tension, lap joint, or anchored ends, we obtain results with consistent parameter forms but different coefficients or boundary conditions: ,when and When, the formula degenerates into the pure UHPC case; when The formula can be used for fiber-free UHPC-CA or high-strength concrete.

[0026] 3. Generation of multi-parameter design maps

[0027] Given several typical steel reinforcement strength grades and UHPC / UHPC-CA strength grades, with , , , , , As independent and dependent variables, pre-calculate: – – Design curved surfaces; – – Design curved surfaces; – – Design surfaces or families of curves; store the calculation results in a database and export them as tables and graphs for engineers to look up and for software to use.

[0028] 4. Software System Structure and Functions

[0029] The software system includes: an input module, a bond strength calculation module, a reduction factor and design bond strength calculation module, a length calculation module, a graph calling and interpolation module, a specification verification module, a result output and comparison module, and a component zoning design module, etc.

[0030] After the user inputs material parameters, structural parameters, and target specifications or reliability requirements, the software automatically completes the process. and The calculation is performed, and recommendations and comparisons are provided for anchorage and lap lengths under different specifications.

[0031] 5. Unification and Degradation of UHPC and UHPC-CA

[0032] By explicitly setting in model and software parameters and A unified calculation process is adopted for UHPC and UHPC-CA; through parameter degradation, compatibility with various cases of ordinary high-strength concrete, UHPC and UHPC-CA is achieved, improving the versatility and scalability of the method; the component partition design module supports the design of anchorage and lap length for different material sections in the same component, and performs overall verification.

[0033] Compared with the prior art, the present invention has the following beneficial effects:

[0034] 1. Unified design bond strength index: This invention organically combines theoretical ultimate bond strength with multi-source uncertainty reduction, proposing an explicit dependence. , , , , , And multiple parameters This overcomes the limitations of existing standards that only reduce concrete strength or empirical coefficients, giving the bond design index a clear physical and reliability meaning.

[0035] 2. Integrated theoretical framework for anchorage and lap length: Based on the stress-slip and energy equivalence principle, this invention unifies single-end tension anchorage, double-end tension lap joint, and other end conditions into a single expression. This avoids the problem of scattered sources and difficulty in unified optimization of the formulas for anchorage length and lap length in existing technologies.

[0036] 3. Multi-parameter design atlas and software tools lower the threshold for engineering applications: This invention achieves rapid multi-parameter interpolation and visualization by pre-calculating dimensionless design surfaces and developing a software system. This enables designers to easily adopt reasonable anchorage and overlap lengths of UHPC and UHPC-CA within the existing safety framework, which improves safety and avoids excessive conservatism.

[0037] 4. Unified processing of UHPC and UHPC-CA and support for component zoning design: This invention achieves compatibility between UHPC and UHPC-CA in a single model through parameter degradation and extension, and supports zoning design and unified verification of different material sections within the same component. This is conducive to the standardized promotion of UHPC / UHPC-CA in bridges, prefabricated components, and reinforcement projects.

[0038] 5. Facilitates standardization and revision: This invention can provide quantifiable calculation basis and software tools for the compilation of clauses on anchorage and lap length of UHPC and UHPC-CA steel bars in subsequent structural design codes. It is expected to serve as a code appendix or recommended calculation method, thereby improving the consistency and operability of code clauses. Attached Figure Description

[0039] The accompanying diagrams are for illustrative purposes only and do not limit the scope of protection of this invention. The following explanation is provided:

[0040] Figure 1 This is a flowchart of the unified calculation method and software system for rebar anchorage length and lap length according to the present invention.

[0041] Figure 2 This is a schematic diagram of the stress-slip curve and energy equivalence principle at the steel bar-UHPC / UHPC-CA interface in this invention.

[0042] Figure 3 This is a schematic diagram showing the relationship between the various sub-items or reduction coefficients in this invention and the changes in key influencing parameters.

[0043] Figure 4 This is a schematic diagram of a typical dimensionless design surface obtained based on the method of this invention.

[0044] Figure 5 This is a schematic diagram of the functional structure and human-computer interaction interface of the software system of the present invention. Explanation of reference numerals and component numbers in the attached drawings

[0045] Figure 1 This paper illustrates the overall flow and module division of the unified calculation method and software system for rebar anchorage length and lap length according to the present invention. The component numbers and meanings are as follows: 101 — Material parameter input unit, used to input material parameters of UHPC or UHPC-CA, including compressive strength grade. Elastic modulus, steel fiber volume fraction Steel fiber shape parameters, coarse aggregate volume fraction Maximum particle size of coarse aggregate 102 — Construction and geometry parameter input unit, used to input the diameter of the reinforcing bars. Anchorage or lap splice type (anchorage / lap splice), stress characteristics (single-end tension / double-end tension), protective layer thickness Initial value of bonding length Or component geometry, etc. 103 — Specification and Reliability Requirements Input Unit: Used to select the target specification (such as specifications from different countries or regions) and target reliability index, inputting corresponding material partial factors, load partial factors, structural limits, and other parameters, or selecting configurations from a preset specification library. 104 — Ultimate Bond Strength Calculation Unit: Based on the theoretical bond model and experimental database, it calculates the input material and geometric parameters to obtain the unreduced ultimate bond strength. and peak slip It can also output key parameters of the stress-slip relationship. 105 — The reduction factor and design bond strength calculation unit calculates the material strength correlation coefficient based on the input reliability requirements and various influencing factors. Fiber effect coefficient Coarse aggregate effect coefficient Protective layer effect coefficient Bond length effect coefficient Environmental impact coefficient And so on, and based on this, the design reference bond strength is obtained. 106 — Design a bond strength output unit to output the calculated bond strength. and Outputs data in numerical, tabular, or graphical form for user viewing or for use in subsequent length calculation elements. 107 — Anchorage and lap length calculation element, used to invoke the stress-slip model and energy equivalence relation, based on... , , , , , , , Minimum anchorage length and minimum overlap length required for parameter calculation It can output results under different boundary conditions, such as single-end tension and double-end tension. Unit 108—Design Map Call and Interpolation—is used to access a pre-stored database of dimensionless design surfaces and curves, performing multidimensional interpolation or extrapolation on a given input point to quickly obtain... This reduces the amount of real-time numerical integration and iterative computation. 109 — Standard verification and multi-standard adaptation unit, based on the user-selected standard and reliability requirements, verifies the obtained... The system compares and verifies the minimum anchorage, lap length, and structural limits specified in various standards, providing recommended lengths that meet the requirements of each standard, and can simultaneously display results under multiple standards. Unit 110—Result Output and Comparison—summarizes the anchorage and lap lengths under various working conditions and standards, generates result reports and graphs, and compares them with results calculated based on traditional ordinary concrete or simplified UHPC formulas, highlighting differences in safety margins and economic efficiency.

[0046] Figure 2 The stress-slip curves at the steel reinforcement-UHPC / UHPC-CA interface and the internal force-slip curves of the steel reinforcement are shown, along with the energy equivalence principle between them. The component numbers and their meanings are as follows: 201 — Interfacial bond stress-slip curve This reflects the bond stress at the interface between the reinforcing steel and UHPC / UHPC-CA as a function of relative slip. The changes include the rising segment, the peak segment, and the softening segment. 202 — Reinforcing bar internal force-slip relationship curve, which shows the relationship between the axial internal force or average stress of the reinforcing bar and end slip under a given anchorage or lap splice condition, used to characterize the development of the reinforcing bar's strain energy. 203 — Interfacial bond energy area , which is the area between curve 201 and the horizontal axis within the effective bonding length, through the... Obtained by double integration along slip and length, representing the total bond energy available at the interface. 204 — Reinforcement strain energy area , which is the area between curve 202 and the horizontal axis, reflecting the development of the steel reinforcement from zero stress to yield stress. The strain energy accumulated during the process. 205 — Peak slip point The corresponding interfacial bonding stress reaches its limit value. The slip value at time 206 is a key inflection point on the stress-slip curve 201. 206 — Schematic diagram of the softening segment, representing the portion of curve 201 that descends from the peak point 205, corresponding to softening mechanisms such as interfacial crack propagation, fiber pull-out, and cracking around coarse aggregate. 207 — Effective bond length segment, the interfacial length portion marked on linear or axial coordinates. Within this segment, bond stress and slip act together, forming the spatial interval for integration in energy equivalence analysis.

[0047] Figure 3 The diagram illustrates the functional relationship curves between various reduction coefficients and influencing parameters in this invention, serving to explain... The construction method is based on parameter dependence. The component numbers and meanings are as follows: 301 — Correlation coefficient curve between material strength and brittleness. This indicates the compressive strength grade of UHPC. The influence of material brittleness and spalling tendency on the reduction of design bond strength when the strength is increased. 302 — Steel fiber effect coefficient curve. Characterizing the volume fraction of steel fibers When increased, the improvement in interfacial bond strength and ductility corrects for the reduction factor, demonstrating its effect on... The positive contribution. 303 — Coarse aggregate effect coefficient curve This indicates different coarse aggregate volume fractions. With maximum particle size Under these conditions, the effects on local splitting failure mode and mean bond stress can be illustrated using multiple curves or surface sections. 304 — Protective layer thickness effect coefficient curve Characterizing the relative protective layer thickness The influence of varying lateral confinement capacity and splitting tendency of concrete on the reduction of design bond strength. 305 — Bond length effect coefficient curve. , indicating relative bonding length The influence on the development of average bond stress shows different trends in the short bond length region and the long bond length region. 306 — Parameter coordinate axis and legend area, used to distinguish the value range of different influencing parameters and their corresponding curve relationships, to facilitate the explanation of the construction logic and applicable scope of the multi-parameter reduction coefficient.

[0048] Figure 4 A typical dimensionless design surface pre-calculated based on the method of this invention is shown, illustrating how to perform table lookup and interpolation using a pre-generated atlas. The component numbers and meanings are as follows: 401 — Design Surface – – , indicating that at a given yield strength of steel reinforcement UHPC strength rating steel fiber volume fraction Under the same conditions, the dimensionless length required for anchoring or lap splicing With relative protective layer thickness With coarse aggregate volume fraction The relationship of change. 402 — Design contour lines or family of contour curves, which are the contour lines or projections of the design surface 401 on a specific cross section, used to more intuitively find the relationship between one parameter and another when one parameter is fixed. The impact. 403 — Representative design point, representing the design working point selected by the software or specified by the user under actual engineering input parameters. The corresponding point is obtained by locating it on surface 401. Value. 404 — Pure UHPC slice plane ( ), indicating when the volume fraction of coarse aggregate At that time, the cross-section of surface 401 on this plane corresponds to the anchorage and lap joint design results of pure UHPC. 405 — UHPC-CA cross-sectional area ( (), representing the curved area within different coarse aggregate volume fraction ranges, corresponding to the design results of UHPC-CA material, used for intuitive comparison with 404.

[0049] Figure 5 The functional structure diagram and typical human-computer interaction interface layout of the software system of this invention are shown. The component numbers and meanings are as follows: 501 — Main software interface, the overall interface container, including parameter input area, specification selection area, result display area, and graph visualization area, etc. 502 — Parameter input window, used to input material parameters, structural parameters, and working condition information; it can be further subdivided into material parameter subpages and structural parameter subpages, which can be called... Figure 1 Input functions for 101 and 102. 503 — Specification selection window, providing a list of multiple specification selections and reliability level options, allowing users to select or customize specification coefficients, corresponding to... Figure 1 The front-end interfaces of 103 and 109 in the diagram. 504 — Calculation results window, displaying the design baseline bond strength calculated according to the method of the present invention. Dimensionless anchorage and lap length And the converted actual anchorage length and lap length. 505 — Traditional specification result comparison window, displaying the anchorage and lap lengths calculated according to traditional ordinary concrete or existing single UHPC empirical formulas, compared with the results of this invention in 504, intuitively showing the differences in safety and economy. 506 — Design atlas visualization window, used to call up pre-stored dimensionless design surfaces and contour lines (e.g. Figure 4 Points 401 and 402 are displayed in 3D view or contour map form, allowing users to interactively select design point 403. 507—Component partitioning design window, used to divide the same component into pure UHPC zone and UHPC-CA zone, setting material parameters for each zone and calling calculations, displaying the required anchorage and lap lengths for each section and the overall component safety verification results. 508—Database and map storage module (backend), storing the experimental database, theoretical model parameters, and pre-calculated design drawings and curve data, providing data support for 108 and 506. 509—Calculation core module (backend), implementing core algorithms such as ultimate bond strength calculation, reduction factor calculation, design bond strength solution, and anchorage and lap length solution under energy equivalence, supporting… Figure 1Functions 104, 105, and 107 are included. Module 510—User Interaction and Data Management—is responsible for handling user operations, parameter validation, file import / export, and project management in the front-end interfaces 501-507, and for generating result reports and archiving data.

[0050] The above figures and their component numbers correspond to the claims and other parts of the specification of this invention, and are used to more clearly understand the structure and workflow of this invention, but do not constitute a limitation on the scope of protection of this invention. Detailed Implementation

[0051] The specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings. It should be understood that these embodiments are only used to illustrate the present invention and are not intended to limit the scope of protection of the present invention; various equivalent modifications or substitutions can be made by those skilled in the art without departing from the concept of the present invention, and all such modifications or substitutions should fall within the scope of protection of the present invention.

[0052] I. Unified Design Benchmark Bond Strength Implementation methods

[0053] 1. Selection of Input Parameters and Basic Model

[0054] like Figure 1 As shown, in this embodiment, the following input parameters are first obtained through the material parameter input unit 101 and the construction and geometry parameter input unit 102:

[0055] (1) UHPC or UHPC-CA matrix parameters: compressive strength grade (e.g., representative values ​​of compressive strength for cubes or cylinders); modulus of elasticity Stress-strain curve characteristic parameters (peak strain, softening slope, etc., typical models can be built into the software).

[0056] (2) Reinforcing steel parameters: yield strength Elastic modulus ;Nominal diameter .

[0057] (3) Fiber and coarse aggregate parameters: steel fiber volume fraction Steel fiber geometric parameters (length, diameter, shape factor, etc., which can be simplified to a comprehensive influencing factor); coarse aggregate volume fraction. Maximum particle size of coarse aggregate .

[0058] (4) Construction geometric parameters: protective layer thickness Relative protective layer thickness Bonding length Relative bonding length Working condition type (single-end tension anchorage, double-end tension lap joint, mixed working condition, etc.).

[0059] Subsequently, in the ultimate bond strength calculation unit 104, a theoretical bond model for the steel-concrete interface applicable to UHPC / UHPC-CA is invoked. The model may take the form of, but is not limited to: an analytical model based on local bond-slip constitutive model; a comprehensive mechanism model combining compression zone splitting, fiber bridging, and coarse aggregate interlocking; or a mechanism-empirical hybrid model obtained by regression from a large-scale experimental database.

[0060] Based on the above model and experimental database, unit 104 outputs the unreduced ultimate bond strength. With corresponding peak slip Furthermore, it can provide stress-slip curve parameters for subsequent energy equivalence analysis.

[0061] 2. Parameterized construction of the reduction factor

[0062] To convert ultimate bond strength into specification-oriented design reference bond strength In this embodiment, a series of explicitly multi-parameter-dependent reduction or partial factors are introduced in the reduction factor and design bond strength calculation unit 105. Specifically, these include:

[0063] (1) Correlation coefficient between material strength and brittleness As the strength of UHPC increases, the material becomes more brittle and more susceptible to bursting, with the interface failure mode shifting from ductile pull-out to brittle splitting. To reflect this adverse effect, this embodiment assumes: ,in For reference strength (e.g., 120 MPa). These are coefficients determined through experiments and reliability analysis. The higher, Increase appropriately.

[0064] (2) Steel fiber effect coefficient Steel fiber bridging helps suppress crack propagation and splitting failure, and improves effective bonding capacity, thus reducing the degree of reduction. Possible methods include: ,in and Determined by regression and safety assessment. When it increases, Gradually decrease, but do not fall below the safety lower limit.

[0065] (3) Coarse aggregate effect coefficient Coarse aggregates, on the one hand, enhance the matrix stiffness and load-bearing capacity, but on the other hand, they can cause localized splitting and stress concentration. This embodiment uses a two-parameter approach: ,in For reference aggregate particle size (e.g., 10 mm). Determined by data fitting. When or hour, It automatically degenerates into a pure UHPC case.

[0066] (4) Protective layer thickness effect coefficient Insufficient protective layer thickness can easily induce concrete splitting and reduce available bond strength. This embodiment can use a piecewise function: ,in , For the waist point, Let be the slope. Thus, in a smaller... The interval is significantly reduced, and so on. Gradually recover.

[0067] (5) Bond length effect coefficient In the short bond length region, the average bond stress has not yet fully developed, while in the long bond length region, non-uniform stress distribution and localized weakening of peak stress occur. This embodiment can take the form of: By selecting appropriate make In the middle The interval is the smallest (weakest reduction), and it increases in extremely short or extremely long intervals.

[0068] (6) Additional reduction factors for construction and environment Based on factors such as the design and usage environment, construction quality level, and durability requirements, the recommended values ​​are adopted from the specifications or obtained through unified reliability calculations. .

[0069] The above function form is an exemplary construction, and can be adjusted according to database regression and standardization.

[0070] 3. Design reference bond strength calculation process

[0071] The reduction factor and design bond strength calculation unit 105 combine the above factors to obtain: The calculation results are displayed by the design bond strength output unit 106, allowing users to view the contribution of each reduction factor and the overall safety margin. For a given material and geometric condition, the software can output: Theoretical ultimate bond strength; overall reduction factor ; Values ​​and percentages of the reduction coefficients for each item. When hour, Automatically obtain pure UHPC ;when hour, Take the value based on the case of no fibers.

[0072] II. Implementation of the Unified Expression for Anchorage and Lap Length

[0073] 1. Construction of stress-slip relationship

[0074] like Figure 2 As shown, in this embodiment, the interfacial bonding stress-slip curve 201 is represented by a piecewise function, for example:

[0075] (1) Ascending segment : ,in For initial stiffness, This is the slip value before entering nonlinearity.

[0076] (2) Nonlinear rising segment to peak value : ,in For the initial slip, For shape parameters.

[0077] (3) Softening section : Alternatively, a piecewise linear degenerate function can be used, with parameters... and Related to...

[0078] The internal force-slip curve of the reinforcing bar 202 can be represented by a simplified model based on bar elements: the end slip of the reinforcing bar is related to the strain integral along its length, and the slip occurs when the stress of the reinforcing bar reaches the yield point. At that time, corresponding to a certain end slip value .

[0079] 2. Application of the principle of energy equivalence

[0080] This embodiment equates interfacial bond energy with steel reinforcement strain energy, such as... Figure 2 As shown:

[0081] (1) Interfacial bonding energy: The outer layer integral along the bonding length The inner integral moves along the slip. The perimeter.

[0082] (2) Strain energy of steel reinforcement: ,in The stress of the reinforcing steel along its length, This represents the cross-sectional area of ​​the reinforcing steel.

[0083] In the simplified model, the average stress and equivalent slip assumptions can be used to reduce the above integral form, yielding the dimensionless length. The equation is used to obtain the required dimensionless bond length through numerical solution. .

[0084] 3. Example of single-end tension anchoring

[0085] For single-end tension anchorage, where tension is applied at one end and the other end of the rebar is free or anchored in the joint, the bond length extends inward from the tension end. The main characteristic here is that the rebar stress gradually increases from 0 at the tension end to nearly [missing value]. The slippage is greatest at the tension end and decreases on the inner side; the softening zone of the interface is mainly concentrated in the area near the tension end.

[0086] In this embodiment, a simplified model can be used: the bond stress along the length is approximated by a linear distribution or exponential decay; the steel reinforcement stress is approximated by a linear or exponential increase.

[0087] Through energy balance and boundary conditions (tension end stress = Given that the stress at the free end is 0, the solution is as follows: .

[0088] In the software, this solution process is automatically completed by the anchorage and lap length calculation unit 107, and can be performed using iterative or interpolation methods: initial assumptions ; Calculations given by the bonding model ; Calculate the strain energy of steel reinforcement ;Compare and Adjust according to the difference ; until satisfied (Preset tolerance).

[0089] 4. Example of double-end tension lap joint

[0090] For double-ended tension lap splices, the two bars are subjected to forces in opposite directions in the lap zone, and the stress development and slip distribution in the lap zone are coupled. Its characteristics are: stress develops from the external stress point towards the lap zone at each end; stress superposition and symmetrical slip distribution may occur in the middle of the lap zone; and interfacial bond energy is distributed between the two bars.

[0091] In this embodiment, based on the balance and coordination conditions of the lapped reinforcing bars, the following simplified relationship is constructed: Let the lap length be... The dimensionless length is Establish a stress-slip equation similar to that for single-end tension for each steel bar, but apply symmetrical boundary conditions (slip or stress symmetry) at the midpoint of the lap joint; make the sum of the total strain energy of the two steel bars equal to the sum of the bond energy at the interfaces on both sides.

[0092] Therefore, we can conclude that: By using appropriate parameterization, it is possible to Rewritten in the same unified form as the anchorage length expression, only the coefficients and boundary conditions are different, namely: In the anchorage and lap length calculation unit 107, the software system automatically selects the corresponding solution path through the working condition flag.

[0093] 5. Other operating conditions and degradation scenarios

[0094] For transitional working conditions where one end is under tension and the other end is rigidly anchored, the boundary conditions can be changed within the framework described above. For example, the slippage at the rigid anchor end can be zero, and the stress in the reinforcing steel can be close to yield or remain at a certain high value. The stress and slippage at the tension end can be used as control variables.

[0095] For the pure UHPC case, this implementation will , Correspondingly , Automatic degradation; the lap and anchorage length expressions no longer include correction terms related to coarse aggregate.

[0096] For UHPC-CA or high-strength concrete that does not contain steel fibers, it can make , Use according to the fiber-free value, while allowing for... The basic model adopts a common high-strength concrete bonding model to achieve unified treatment with traditional high-strength concrete design.

[0097] III. Implementation Methods for Generating and Using Multi-Parameter Design Maps

[0098] 1. Design the pre-calculation process for the design graph.

[0099] like Figure 4 As shown, the process of generating the design map mainly includes the following steps:

[0100] (1) Parametric mesh generation: Given several typical combinations (such as...) =150, 180, 200 MPa; Under the premise of pressures such as 500, 600 MPa, construct a multidimensional parametric mesh, including: For example, from 1.0 to 5.0, the step size is 0.5; For example, from 0 to 0.4, with a step size of 0.05; For example, from 0 to 3%, with a step size of 0.5%; Several typical values ​​(10, 16, 20 mm); other parameters or dimensionless ratios that need to be investigated.

[0101] (2) Call the unified calculation method point by point: For each grid point, call the aforementioned unified calculation method: Calculate in cell 104 Calculate the reduction factors in unit 105. ;Calculate the required values ​​in unit 107 and transform into .

[0102] (3) Constructing a family of dimensionless design surfaces and curves: Based on the calculation results, generate, for example: and For independent variable, The three-dimensional surface 401 is the dependent variable; given a certain... or The contour lines 402 and the identification and recording of specific design points 403 are as follows:

[0103] (4) Data storage and access interface: The above-mentioned surfaces and curves are stored in the database and graph storage module 508 in the form of data tables or interpolation nodes. The corresponding access interface is provided by the design graph call and interpolation unit 108.

[0104] 2. Table lookup and interpolation in engineering applications

[0105] Engineers can choose between two modes when using the software system:

[0106] (1) Precise calculation mode: The entire process is calculated according to the aforementioned energy equivalence and iterative solution method. It is suitable for special working conditions or research applications that require high precision.

[0107] (2) Fast map mode: User input Parameters; the design atlas is called and the interpolation unit 108 automatically finds the nearest node in the corresponding dimensionless design surface 401; obtained through bilinear or multidimensional interpolation. Approximate value; if the interpolation point exceeds the preset range, it can be extrapolated to the nearest boundary or automatically switched to the accurate mode.

[0108] Figure 4 In the design, representative design point 403 is the projection point of the user input parameters on the surface; when the point is located in the pure UHPC slice plane 404, it means that the current design is a UHPC without coarse aggregate; when it is located in the UHPC-CA region 405, it is a UHPC-CA with coarse aggregate.

[0109] IV. Specific Implementation Methods of the Software System

[0110] like Figure 1 , Figure 5As shown, the software system of this invention can be implemented using languages ​​such as C++ and Python, and can also be deployed as a desktop application or a web application. The functions and interactions of the core modules are further explained below.

[0111] 1. Input and Interaction Module

[0112] (1) Parameter input window 502: Set material parameters subpage: Input And related information, select "UHPC" or "UHPC-CA" type; when selecting UHPC-CA, enable... Input box; Set construction parameters subpage: Enter rebar diameter Protective layer Types of overlap or anchorage, estimated initial bond length, etc.

[0113] (2) Specification Selection Window 503: Multiple specification templates are preset (such as “Specification A”, “Specification B”, etc.). Each template contains material partial factors, load partial factors, and construction limits. Users can customize specification configurations or fine-tune some coefficients on the templates for project-level calibration.

[0114] (3) Component partition design window 507: Supports defining multiple components or multiple areas (segments) in the same project, such as "mid-span UHPC area" and "support UHPC-CA area"; set material and construction parameters for different areas respectively, and specify the reinforcement layout and connection relationship; the system automatically calculates the anchorage and lap length for each area, and checks the reinforcement anchorage continuity at the area boundary.

[0115] 2. Core Computing Module

[0116] (1) Calculation of ultimate bond strength Figure 1 Unit 104, Figure 5 (Part of Module 509): It can call a unified bond model based on input material parameters, or call different models (including ordinary high-strength concrete models) based on user selection; if the user provides custom test data, some model coefficients can be updated through the regression interface; Output and The discrete points or parameters are expressed as such.

[0117] (2) Calculation of reduction factor and design bond strength ( Figure 1 Unit 105): Call the aforementioned Functions; can be automatically set according to user-selected specifications. Specifications and related parameters; output And the numerical decomposition of each reduction factor.

[0118] (3) Solving for anchorage and lap length ( Figure 1 Unit 107): Select the appropriate energy equivalent expression according to the working condition type (single-end tension anchorage, double-end tension lap joint, etc.); two solution modes are provided: a. Fast iteration mode: solve using Newton's iteration or secant method. b. Numerical integration mode: strictly for Integrating with the stress distribution of the reinforcing steel results in higher accuracy. It outputs the minimum length required for anchorage and / or lap splicing. and dimensionless form .

[0119] (4) Map calling and interpolation ( Figure 1 Unit 108, Figure 5 Module 508 (Coordination): Based on the input parameters, locate the closest design surface 401 data block; use multidimensional linear or higher-order interpolation to obtain an approximate value. When the parameter falls outside the preset range, a prompt will be issued and the system can switch to the precise calculation mode.

[0120] (5) Standard verification and multi-standard adaptation ( Figure 1 Unit 109): Comparison Minimum anchorage, lap length requirements, and construction limits as specified in various standards (or user-defined); if If the value is less than the construction limit of some specifications, a recommended value is given according to the construction limit; the results of multiple specifications are summarized and output for users to select or take the envelope value.

[0121] 3. Results Presentation and Report Output

[0122] (1) Calculation results window 504: The content displayed includes, but is not limited to: , Total reduction factor Under various working conditions , Its dimensionless form; a list of recommended anchorage and lap lengths under different specifications.

[0123] (2) Traditional Standard Result Comparison Window 505: Select the formula of the traditional standard (e.g., only relying on) and (Experience-based expression) Calculate anchorage and lap length; compare the results with the results of the method of the present invention in the form of tables and bar charts; indicate the relative difference and safety margin, such as "the new method saves about 15% of the anchorage length compared with the traditional standard, and the safety factor still meets the standard requirements".

[0124] (3) Design atlas visualization window 506: Presents the dimensionless design surface 401 in a three-dimensional view, which users can rotate, scale, and slice; adjust via sliders. , , The system can update parameters such as the position of the representative design point 403 in real time; it can also export data tables or images on a specified section for use in design documents or technical reports.

[0125] (4) Report and Data Management Figure 5 Module 510: Generate calculation reports in PDF / Word / Excel formats by project or component, including input parameters, calculation process summary, key intermediate results and final recommended values; supports project version management and parameter recording, facilitating data backtracking during subsequent review and specification revision.

[0126] V. Typical Implementation Examples (Numerical Examples)

[0127] To more intuitively illustrate the application process of the method of the present invention, a simplified numerical embodiment is given below. The numerical values ​​used are merely examples and are not intended to limit the present invention.

[0128] 1. Engineering conditions

[0129] (1) Material: UHPC-CA, compressive strength MPa; steel fiber volume fraction Coarse aggregate volume fraction , mm. Reinforcing steel: Yield strength MPa; diameter mm.

[0130] (2) Structure: thickness of protective layer mm, so It is designed for single-end tension anchoring.

[0131] 2. Bond strength calculation and reduction

[0132] (1) Ultimate bond strength: The software calls the bond model and obtains: .

[0133] (2) Reduction factor: Assuming that the database and standard are coordinated, the following is obtained: ; (Beneficial effect, coefficient less than 1); ; ; For this operating condition, take 1.00; Overall reduction: .

[0134] (3) Design reference bond strength: .

[0135] 3. Anchorage Length Calculation

[0136] Using energy equivalence and a unified expression, the software iteratively solves for the dimensionless anchorage length: Converted to actual length: .

[0137] The specification verification module 109 compares the result with the minimum structural anchorage length of the selected specification. For example, the minimum tensile anchorage length of a certain specification is... mm; then the software gives the following suggested value: "The minimum anchorage length calculated according to the theory of this invention is 560 mm, but in order to meet the standard construction requirements, it is recommended to use 800 mm."

[0138] If a specification allows for appropriate optimization of construction limits using a reliability approach, then the safety factor can be further evaluated and optimization suggestions can be proposed.

[0139] VI. Variations and Extensions

[0140] Without departing from the core idea of ​​this invention, the following modifications also fall within the scope of protection of this invention:

[0141] 1. Diversification of stress-slip models: Different shape functions (such as bi-segment, tri-segment, bi-exponential, etc.) can be used as alternatives. Figure 2 In a typical form, as long as the energy equivalence and parameterization dependency remain.

[0142] 2. Adjustment of the reduction coefficient function: The function form and parameters can be refitted and updated based on new test data or new specification requirements without changing the overall framework of the unified design bond strength and unified anchorage / lap length expression.

[0143] 3. Software platform changes: These can be implemented using a cloud platform, mobile application, or a plugin that integrates with BIM / structural analysis software, as long as it is implemented... Figure 1 , Figure 5 The functional modules shown are all considered as embodiments of the present invention.

[0144] 4. Expansion of new steel reinforcement and new UHPC system: For stainless steel reinforcement, FRP reinforcement or new UHPC mix proportions, it is only necessary to introduce the corresponding parameters and test data into the ultimate bond model and reduction factor for calibration, so that the application can be expanded within the same framework.

[0145] Through the above specific implementation methods, the present invention theoretically realizes the integrated design of UHPC and UHPC-CA rebar anchorage and lap length. In engineering practice, it significantly reduces the application threshold through design drawings and software systems, and provides calculable, verifiable and visualized technical support for the revision of specifications.

Claims

1. A unified calculation method for the anchorage length and lap length of reinforcing bars, characterized in that, The steps include: (1) obtaining material and geometric parameters, including the compressive strength grade f of the UHPC matrix. c , yield strength of steel bars f y , Rebar diameter d, Steel fiber volume fraction V f Coarse aggregate volume fraction V CA and maximum particle size d CA Bonding length l a 1. Protective layer thickness c and structural type (anchoring or lap splicing, single-end or double-end tension); (2) Based on the theoretical bond model and experimental database of the steel bar-UHPC / UHPC-CA interface, calculate the unreduced ultimate bond strength τ according to the material parameters. u,calc and corresponding peak slip s u (3) Based on the target reliability index, construct the material partial factor γ. m Construction partial factor γ c Environmental partial factor γ e and other influence coefficients, which are explicitly expressed as UHPC strength grade, V f V CA d CA Relative protective layer thickness c / d and relative bond length l a The function of / d is used to determine the design baseline bond strength using the following formula: (4) Based on the stress-slip relationship and the energy equivalence principle, the bond energy provided along the steel-concrete interface and the steel reinforcement from zero stress to yield stress f are compared. y Given that the required strain energy is equal, the required dimensionless bond length is derived under the premise of considering the end force boundary conditions. (5) Different structural conditions (anchoring, lap joint, single-end tension, double-end tension) are uniformly written in the following form: The expression is used to obtain the minimum anchorage length or minimum overlap length through the corresponding parameter combination; (6) when V CA When the value is 0, the method automatically degenerates into a calculation method for the anchorage and lap length of pure UHPC steel bars.

2. The method according to claim 1, characterized in that, The components or reduction factors in step (3) include: those used to characterize the strength and brittleness level of the UHPC matrix. ; used to characterize the contribution of steel fiber bridging and pull-out Used to characterize the effect of coarse aggregate volume fraction and maximum particle size on bond strength and localized splitting. ; Used to characterize the effect of relative protective layer thickness c / d on splitting failure mode Used to characterize the relative bond length l a The influence of / d on the development of average bond stress The form and parameters of the above functions were determined through a combination of theoretical analysis and database regression.

3. The method according to claim 1, characterized in that, The stress-slip relationship used in step (4) includes ascending, peak and softening segments, which are described by different analytical functions or piecewise linear functions, respectively. The energy equivalence condition is obtained by integrating the bond stress-slip curve along the effective bond length to get the interfacial energy, and setting it equal to the area under the internal force-slip relationship curve of the steel bar to solve λ req .

4. The method according to claim 1, characterized in that, A unified energy equivalent calculation framework is adopted for the following different end conditions: single-end tension anchorage; double-end tension lap joint; transition condition of one end tension and one end anchorage; and L req Differentiation of parameters or coefficients in unified expressions.

5. The method according to claim 1, characterized in that, Also includes: Given several typical steel reinforcement strength grades and UHPC strength grades, select c / d and V CA V f d CA and λ req Using variables such as independent or dependent, pre-calculate dimensionless design surfaces or families of design curves, including... – – , – – , – – The designed surfaces and curves are stored in the form of tables, graphs, or databases for engineering lookup or for use by software systems.

6. A software system for designing rebar anchorage and lap length to implement the method according to any one of claims 1-5, characterized in that, include: The input module is used to receive UHPC or UHPC-CA mix proportion parameters, reinforcement parameters, structural parameters, and target specifications or reliability requirements; the bond strength calculation module is used to calculate according to steps (2)-(3) of claim 1. and The length calculation module is used to calculate the required anchorage length and overlap length according to steps (4)-(5) of claim 1. The graph calling and interpolation module is used to perform interpolation or extrapolation in the pre-stored dimensionless design graph based on the input parameters, thereby improving calculation efficiency and stability. The specification verification module is used to verify the obtained L_req according to the safety factor and construction limit of the selected specification, and to provide the recommended anchorage and lap length under different specifications. The result output and comparison module is used to output the calculation results of UHPC and UHPC-CA respectively, and to compare and prompt with the calculation results of traditional ordinary concrete or existing UHPC empirical formulas.

7. The software system according to claim 6, characterized in that, The specification verification module has multiple preset libraries of safety factors, material component factors and construction limits, corresponding to concrete structure design specifications of different countries or regions, and allows users to select or customize combinations to achieve multi-specification adaptation under a unified theoretical framework.

8. The software system according to claim 6, characterized in that, It also includes a component zoning design module, which is used to divide the same component into pure UHPC zone and UHPC-CA zone, and respectively call the bond strength calculation module and length solving module to perform zoning design and overall verification of the rebar anchorage and lap length in different zones.

9. The software system according to claim 6, characterized in that, When input V CA =0 or d CA When V = 0, the software automatically adopts the bonding and anchoring model of pure UHPC; when V is input... f When the value is 0, it degenerates into a UHPC-CA or high-strength concrete bond model without steel fibers, thereby enabling the extended application of ordinary high-strength concrete, UHPC and UHPC-CA under a unified framework.

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