Economical prediction and design method for bonding and anchoring performance of UHPC (Ultra High Performance Concrete) double ribs
By constructing a full-curve constitutive model and introducing constraint effect correction coefficients, the problem of describing the entire bond-slip process of double-reinforced UHPC in an economical system was solved, enabling accurate prediction and design of anchorage performance and improving the scientific and economical nature of the design.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-11-21
- Publication Date
- 2026-03-13
AI Technical Summary
Existing technologies cannot accurately describe the constitutive relationship of the entire bond-slip process in economical UHPCs, resulting in inaccurate prediction of anchorage performance, lack of design reliability, and potential material waste or safety hazards.
A full-curve constitutive model was constructed. By obtaining initial parameters, the bond stress-slip relationship curve was divided into three stages. A constraint effect correction coefficient was introduced, key technical indicators were extracted, anchoring design was carried out, and the model was optimized through iterative verification.
This approach enables a comprehensive and detailed assessment of anchoring performance, enhancing the scientific rigor and safety of the design, reducing costs, and avoiding the blind and conservative nature of traditional methods.
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Figure CN121659541A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of ultra-high performance concrete technology, specifically to an economical method for predicting and designing the performance of double-reinforced bonded anchorage in UHPC. Background Technology
[0002] Ultra-high performance concrete (UHPC) has been widely used in modern engineering structures due to its superior mechanical properties and durability. In reinforced concrete members, the bond and anchorage performance between the reinforcing steel and concrete is fundamental to ensuring their coordinated work and load transfer, directly affecting the safety and reliability of the overall structure. To meet high load-bearing capacity requirements and optimize structural layout, double-reinforced anchorage is very common in practical engineering. Meanwhile, to promote the widespread use of UHPC materials and reduce their high cost, the development of economical UHPC has become a research and application hotspot. Therefore, accurate prediction and design of the bond and anchorage performance of double-reinforced UHPC is a key step in achieving structural safety and reliability and maximizing material performance. Existing technologies typically obtain relevant design parameters through physical pull-out tests or simplified empirical formulas.
[0003] However, existing physical testing methods are costly, time-consuming, and produce highly variable results, making it difficult to cover all engineering parameters and variables, and thus unable to provide rapid and economical guidance for diverse design scenarios. Most existing theoretical models or empirical formulas are based on fitting test data from mono-reinforced anchorages of ordinary concrete or standard UHPC. These models typically only estimate the ultimate bond strength and cannot describe the entire response process of the interface between the reinforcement and the economical UHPC, from elastic micro-slip and elastoplastic slip to anchorage failure, particularly failing to accurately reflect the behavior during the decline phase after the bond stress reaches its peak. This lack of understanding of the constitutive relationship of the entire bond-slip curve leads to an inability to accurately assess the ductility, toughness, and final failure mode of anchorage joints, resulting in blind design methods. The results may be overly conservative, leading to material waste, or pose safety hazards, failing to achieve refined and reliable prediction and design of the performance of bi-reinforced anchorages in economical UHPCs. Summary of the Invention
[0004] The purpose of this invention is to address the problem that existing technologies cannot provide a complete and accurate description of the constitutive relationship between the bond and slip process of an economical UHPC and its double reinforcement, which leads to inaccurate prediction of anchorage performance and a lack of reliable design basis. Therefore, this invention proposes a method for predicting and designing the bonded anchorage performance of economical UHPC double reinforcement.
[0005] The technical solution of the present invention to solve the above-mentioned technical problems is as follows:
[0006] An economical method for predicting and designing the performance of double-reinforced bonded anchorage in UHPC includes the following steps:
[0007] S1. Obtain the initial parameters of the economical UHPC double-reinforced anchorage assembly to be predicted and designed. The initial parameters include at least the material mechanical properties of the economical UHPC, the physical properties of the reinforcing steel, and the geometric parameters of the double-reinforced anchorage.
[0008] S2. Based on the initial parameters, construct and solve a full-curve constitutive model to characterize the bond-slip behavior of the interface between the reinforcing steel and the economical UHPC in the double-reinforced anchorage assembly, thereby obtaining the bond stress-slip relationship curve of the assembly during the full loading process;
[0009] S3. Based on the bond stress-slip relationship curve, extract at least one key technical indicator for evaluating anchoring performance, and complete the anchoring design of the economical UHPC double-reinforced anchoring assembly based on the key technical indicator.
[0010] Based on the above technical solution, the present invention can be further improved as follows.
[0011] Furthermore, the material mechanical properties of the economical UHPC in S1 include: cubic compressive strength, tensile strength, elastic modulus, and volumetric fiber content; the physical properties of the reinforcing bars include: type, diameter, yield strength, ultimate tensile strength, and surface rib morphology; and the geometric parameters of the double-reinforced anchorage include: anchorage length of the reinforcing bars, thickness of the concrete cover, and center-to-center spacing of the double reinforcement.
[0012] Furthermore, the full-curve constitutive model constructed in S2 divides the bond stress-slip relationship curve into at least three stages: a microslip segment, a slip segment, and a descending segment, and defines them through piecewise functions to describe the mechanical response throughout the entire process from initial loading to anchorage failure.
[0013] Furthermore, the full-curve constitutive model is specifically defined by the following mathematical expression:
[0014]
[0015] Where τ(s) is the bond stress corresponding to slip s; τ u The ultimate bond strength; s u α represents the slip value corresponding to the ultimate bond strength; α is the shape parameter of the ascending segment of the curve; p is the shape parameter of the descending segment of the curve.
[0016] Furthermore, the ultimate bond strength τ in the model u and the limiting slip s u It is a function of the material mechanical properties of the economical UHPC, the physical properties of the reinforcing bars, and the geometric parameters of the double-reinforced anchorage.
[0017] Furthermore, the full-curve constitutive model constructed in S2 introduces a constraint effect correction coefficient that considers the mutual influence of double reinforcement anchorage. This correction coefficient is related to the center-to-center spacing of the double reinforcement and the thickness of the concrete cover, and is used to adjust the single-reinforcement anchorage model to the double-reinforcement anchorage state.
[0018] Furthermore, the key technical indicators extracted in S3 include: ultimate bond strength, peak slip, residual bond strength, and bond toughness; the bond toughness is obtained by integrating the bond stress-slip relationship curve.
[0019] Furthermore, the anchorage design in S3 is an anchorage length design; the anchorage length design specifically includes: determining the target anchorage force required for the reinforcing steel according to the bearing capacity requirements of the component, and using the ultimate bond strength to calculate the minimum anchorage length L required to satisfy the target anchorage force. a .
[0020] Furthermore, the minimum anchorage length L a The calculation further considers the non-uniform bond stress distribution defined by the bond stress-slip relationship curve, and integrates the bond stress over the anchorage length to make the resultant force equal to or greater than the target anchorage force.
[0021] Furthermore, the method also includes a verification step: the prediction and design results obtained through S2 and S3 are compared with the preset physical test database or finite element numerical simulation results. If the error between the two is greater than a preset threshold, the method returns to step S1 to iteratively correct the initial parameters or the constitutive model in step S2.
[0022] Compared with the prior art, the technical solution of this application has the following beneficial technical effects:
[0023] This invention obtains accurate initial parameters for economical UHPC and double-reinforced anchorage, and constructs a "bond-slip full-curve constitutive model" based on these parameters. This model can completely describe the entire process from micro-slip, slip rise to peak and subsequent failure. This completely solves the problem that existing technologies cannot reflect the performance degradation behavior of anchorage nodes after reaching the ultimate load. Based on this complete constitutive curve, multiple key performance indicators, including ultimate strength, residual strength, ductility, and bond toughness, can be quantitatively extracted. This enables a comprehensive and refined evaluation of anchorage performance, overcoming the limitations of traditional methods that can only perform single strength checks. Ultimately, this makes anchorage design no longer based on rough experience or conservative assumptions, but on a reliable mechanical model, greatly improving the scientific nature, economy, and structural safety of the design. Attached Figure Description
[0024] Figure 1 This is a diagram showing the bonding and slippage curve of the present invention. Detailed Implementation
[0025] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0026] This invention provides an economical method for predicting and designing the performance of double-reinforced bonded anchorage in UHPC. Its core lies in establishing a theoretical model that accurately reflects the intrinsic relationship between material properties, geometric structure, and interfacial mechanical behavior, thereby achieving scientific prediction and refined design of anchorage performance. The method includes the following steps:
[0027] S1. Obtain the initial parameters of the economical UHPC double-reinforced anchorage assembly to be predicted and designed. The initial parameters shall include at least the material mechanical properties of the economical UHPC, the physical properties of the reinforcing steel, and the geometric parameters of the double-reinforced anchorage.
[0028] S2. Based on the initial parameters, construct and solve the full-curve constitutive model to characterize the bond-slip behavior of the interface between the steel reinforcement and the economical UHPC in the doubly reinforced anchored assembly, thereby obtaining the bond stress-slip relationship curve of the assembly during the full loading process;
[0029] S3. Based on the bond stress-slip relationship curve, extract at least one key technical indicator for evaluating anchoring performance, and complete the anchoring design of the economical UHPC double-reinforced anchoring assembly based on the key technical indicator.
[0030] The material mechanical properties of the economical UHPC in S1 include: cubic compressive strength, tensile strength, elastic modulus, and volumetric fiber content; the physical properties of the reinforcing bars include: type, diameter, yield strength, ultimate tensile strength, and surface rib morphology; the geometric parameters of the double-reinforced anchorage include: anchorage length, concrete cover thickness, and center-to-center spacing of the double reinforcement. Obtaining the initial parameters in step S1 of this invention is fundamental to the entire prediction and design method. Specifically, the material mechanical properties of the economical UHPC are measured through standard tests, for example, by using a 100mm × 100mm × 100mm cubic specimen to determine its compressive strength f. cu Its tensile strength f was determined by axial tensile test. t and elastic modulus E cThe volumetric fiber content V was determined by metallographic analysis or volumetric method. f The physical properties of the reinforcing steel, such as type (HRB400 or HRB500), diameter (d), and yield strength (f). y Ultimate tensile strength f u All parameters, such as the material's certificate of conformity or those obtained through standard tensile testing, can be obtained from the material's manufacturer's certificate of conformity. The surface rib morphology (e.g., crescent ribs, straight ribs) is also used as an input parameter. The geometric parameters for double-reinforced anchorage are directly taken from the component's design drawings, including the planned anchorage length L of the reinforcing bars. a The minimum concrete cover thickness *c* from the edge of the component to the surface of the reinforcing bars, and the center-to-center distance *s* between two side-by-side reinforcing bars. d These parameters constitute the complete dataset of the model input.
[0031] The full-curve constitutive model constructed in S2 divides the bond stress-slip relationship curve into at least three stages: microslip segment, slip segment, and descent segment, and defines them through piecewise functions to describe the mechanical response throughout the entire process from initial loading to anchorage failure.
[0032] The constitutive model of the entire curve is specifically defined by the following mathematical expression:
[0033]
[0034] Where τ(s) is the bond stress corresponding to slip s; τ u The ultimate bond strength; s u α represents the slip amount corresponding to the ultimate bond strength; α is the shape parameter of the ascending segment of the curve; p is the shape parameter of the descending segment of the curve. The core of this invention lies in the full-curve constitutive model of bond-slip constructed in step S2. For example... Figure 1 As shown in the bond-slip curve, typical bond-slip behavior exhibits nonlinear characteristics throughout the entire process. This invention preferably uses a piecewise function to accurately characterize this. The model decomposes the complex nonlinear process into two main stages: the first stage is the increase of the slip s from zero to the peak slip smax. u In the rising phase, the bonding stress τ increases non-linearly with the slip, reflecting the combined effects of chemical bonding force, mechanical interlocking force, and friction. In this embodiment, the power function τ = τ is preferably used. u (s / s u ) α The description explains that the shape parameter α (typically between 0.2 and 0.5) can flexibly adjust the convexity of the curve to match experimental results under different parameters. The second stage involves a slip s exceeding s0. uIn the subsequent descent phase, the concrete matrix is crushed and sheared in front of the ribs, leading to a weakening of the mechanical interlocking effect and a decrease in bond stress, reflecting the deterioration process of the anchorage performance. In this embodiment, a linear function τ = τ0 is used. u (1-p(s / s u -1))p describes this, where the falling segment parameter p controls the rate of stress decrease, characterizing the brittleness or ductility of the failure.
[0035] Ultimate bond strength τ in the model u and the limiting slip s u It is a function of the material mechanical properties of the economical UHPC, the physical properties of the reinforcing steel, and the geometric parameters of the double-reinforced anchorage. The key parameter in the constitutive model mentioned above is the ultimate bond strength τ. u and peak slip s u τ is not a fixed constant, but a function closely related to the initial parameters obtained in S1. This invention establishes τ through multivariate nonlinear regression analysis of a large amount of physical experimental data or calibrated finite element simulation results. u and s u Quantitative relationships between the ultimate bond strength and various influencing factors. For example, the ultimate bond strength τ. u Expressed as a function of the compressive strength f of UHPC cu The diameter d of the reinforcing bar, the thickness c of the protective layer, and the spacing s of the reinforcing bars d A function whose general form can be τ u =k·(f cu ) a ·(c / d) b ·(s d / ) c This approach gives the constitutive model strong adaptability, enabling it to generate unique, customized bond-slip curves for any given combination of initial parameters.
[0036] The full-curve constitutive model constructed in S2 further introduces a constraint effect correction coefficient to consider the mutual influence of double-reinforced anchorage. This correction coefficient is related to the center-to-center spacing of the double reinforcements and the concrete cover thickness, used to adjust the single-reinforced anchorage model to a double-reinforced anchorage state. When dealing with double or multiple-reinforced anchorages, stress fields are superimposed between the reinforcements, compressing the intermediate concrete and causing earlier splitting failure than in single-reinforced anchorage. This "group anchorage effect" weakens the overall anchorage performance. To reflect this effect in the constitutive model, this invention introduces a constraint effect correction coefficient β. This coefficient is related to the center-to-center spacing s of the reinforcements. dThis is a function of the ratio of the rebar diameter *d* to the concrete cover thickness *c* and the rebar diameter *d*. When calculating double-reinforced anchorage, the bond stress τ(s) calculated using the single-reinforced model is multiplied by this correction factor β (whose value is less than or equal to 1) to obtain the actual bond stress considering the adverse effects of group anchorage. The smaller the spacing and the thinner the concrete cover, the smaller the value of β, and the greater the reduction in bond strength. This allows the model to reasonably reflect the true stress state of double-reinforced anchorage.
[0037] Key technical indicators extracted in S3 include: ultimate bond strength, peak slip, residual bond strength, and bond toughness. Bond toughness is obtained by integrating the bond stress-slip curve. In step S3, based on the complete bond stress-slip curve generated in step S2, a comprehensive and in-depth evaluation of anchorage performance can be performed. Besides directly reading the ultimate bond strength τ from the curve... u and the corresponding peak slip s u In addition, a value much larger than s can be defined. u The bond stress corresponding to the slip amount (e.g., 10 mm) is taken as the residual bond strength τ. r This is used to evaluate the load-bearing capacity of a component after significant deformation. More importantly, by integrating the bond stress-slip curve over a specified slip range (e.g., from 0 to the residual strength point), the bond toughness G can be obtained. f This refers to the energy that a unit area of the bonded surface can absorb. This indicator is crucial for evaluating the dynamic performance of a structure, such as its seismic and impact resistance, and cannot be provided by traditional single strength indicators.
[0038] The anchorage design in S3 is the anchorage length design; the anchorage length design specifically includes: determining the target anchorage force required for the reinforcing steel based on the load-bearing capacity requirements of the component, and calculating the minimum anchorage length L required to meet the target anchorage force using the ultimate bond strength. a .
[0039] Minimum anchorage length L aThe calculation further considers the non-uniform bond stress distribution defined by the bond stress-slip relationship curve. By integrating the bond stress along the anchorage length, the resultant force is made equal to or greater than the target anchorage force. Ultimately, this invention serves engineering design, with its core application being the precise design of anchorage lengths. Traditional anchorage length calculations are often based on an average or measured bond strength. This invention provides a more refined design method: First, the target anchorage force F to be transmitted by the reinforcing bar is determined based on structural analysis. Then, a mechanical equilibrium differential equation is established along the anchorage length x of the reinforcing bar, which relates the change in reinforcing bar stress to the bond stress τ(s(x)) at the interface. By solving this differential equation, the slip distribution s(x) and bond stress distribution τ(x) along the reinforcing bar under a given target anchorage force F can be obtained. Finally, through numerical integration, the minimum length that makes the total anchorage force (i.e., the integral of the bond stress along the entire anchorage length) exactly equal to the target anchorage force F is found; this is the required optimal anchorage length L. a This method takes into account the nonlinearity and non-uniform distribution of bond stress, resulting in more reliable and economical design results.
[0040] The method also includes a verification step: the prediction and design results obtained through S2 and S3 are compared with a preset physical test database or finite element numerical simulation results. If the error between the two exceeds a preset threshold, the process returns to step S1 to iteratively correct the initial parameters or the constitutive model in step S2. To ensure the accuracy and reliability of the method, a closed-loop process of verification and iterative optimization is designed. After completing a set of prediction and design calculations, the key results (such as ultimate load and load-slip curve morphology) are compared with a pre-established authoritative database. This database may contain a series of completed physical pull-out test results or numerical simulation results calculated by high-precision finite element software (such as ABAQUS, ATENA). An allowable error threshold is set, for example, 15%. If the difference between the prediction result of the method and the corresponding working condition result in the database exceeds this threshold, an iterative correction procedure is initiated. This procedure will automatically or with manual intervention adjust the key parameters of the constitutive model in step S2 and recalculate until the error converges within the allowable range. This mechanism ensures that the method of the present invention has the ability to self-improve and continuously optimize.
[0041] First, all initial parameters of the economical UHPC doubly reinforced anchorage component to be analyzed are systematically collected, including the material properties of the economical UHPC itself, the physical and mechanical properties of the reinforcing steel, and the geometric details of the anchorage area. Then, these discrete initial parameters are used as input variables and substituted into a mathematical framework with built-in complex mechanical relationships to construct and solve a dedicated full-curve constitutive model that can accurately describe the "bond stress-slip" relationship between the reinforcing steel and concrete interface during the entire loading process of this specific component. This model can not only depict the rising segment from the initial loading to the peak bond strength, but also, crucially, predict the performance degradation after exceeding the peak value. The system incorporates a correction mechanism that considers the mutual influence of double-reinforced anchorage. Based on this, through in-depth analysis of this complete constitutive relation curve, not only can the ultimate bond strength be extracted, but also a series of comprehensive performance indicators that cannot be obtained by traditional methods, such as residual strength, ductility, and bond toughness, can be quantitatively calculated. Finally, using these comprehensive performance indicators, especially based on the constitutive curve that reflects the true stress distribution, integral calculations are performed by solving the mechanical equilibrium differential equations to achieve refined and reliable design of key design parameters such as anchorage length. Optionally, iterative verification can be performed by comparing with experimental databases to ensure the scientificity and accuracy of the entire prediction and design process.
[0042] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.
[0043] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.
Claims
1. A method for predicting and designing the performance of economical UHPC double-reinforced bonded anchorage, characterized in that, Includes the following steps: S1. Obtain the initial parameters of the economical UHPC double-reinforced anchorage assembly to be predicted and designed. The initial parameters include at least the material mechanical properties of the economical UHPC, the physical properties of the reinforcing steel, and the geometric parameters of the double-reinforced anchorage. S2. Based on the initial parameters, construct and solve a full-curve constitutive model to characterize the bond-slip behavior of the interface between the reinforcing steel and the economical UHPC in the double-reinforced anchorage assembly, thereby obtaining the bond stress-slip relationship curve of the assembly during the full loading process; S3. Based on the bond stress-slip relationship curve, extract at least one key technical indicator for evaluating anchoring performance, and complete the anchoring design of the economical UHPC double-reinforced anchoring assembly based on the key technical indicator.
2. The method for predicting and designing the performance of economical UHPC double-reinforced bonded anchorage according to claim 1, characterized in that, The material mechanical properties of the economical UHPC in S1 include: cubic compressive strength, tensile strength, elastic modulus, and volumetric fiber content; the physical properties of the reinforcing bars include: type, diameter, yield strength, ultimate tensile strength, and surface rib morphology; the geometric parameters of the double-reinforced anchorage include: anchorage length of the reinforcing bars, thickness of the concrete cover, and center-to-center spacing of the double reinforcement.
3. The method for predicting and designing the performance of economical UHPC double-reinforced bonded anchorage according to claim 2, characterized in that, The full-curve constitutive model constructed in S2 divides the bond stress-slip relationship curve into at least three stages: microslip segment, slip segment, and descent segment, and defines them through piecewise functions to describe the mechanical response throughout the entire process from initial loading to anchorage failure.
4. The method for predicting and designing the performance of economical UHPC double-reinforced bonded anchorage according to claim 3, characterized in that, The full-curve constitutive model is specifically defined by the following mathematical expression: Where τ(s) is the bond stress corresponding to slip s; τ u The ultimate bond strength; s u α represents the slip value corresponding to the ultimate bond strength; α is the shape parameter of the ascending segment of the curve; p is the shape parameter of the descending segment of the curve.
5. The method for predicting and designing the performance of economical UHPC double-reinforced bonded anchorage according to claim 4, characterized in that, The ultimate bond strength τ in the model u and the limiting slip s u It is a function of the material mechanical properties of the economical UHPC, the physical properties of the reinforcing bars, and the geometric parameters of the double-reinforced anchorage.
6. The method for predicting and designing the performance of economical UHPC double-reinforced bonded anchorage according to claim 1, characterized in that, The full-curve constitutive model constructed in S2 further introduces a constraint effect correction coefficient that considers the mutual influence of double reinforcement anchorage. The correction coefficient is related to the center-to-center spacing of the double reinforcement and the thickness of the concrete cover, and is used to adjust the single-reinforcement anchorage model to the double-reinforcement anchorage state.
7. The method for predicting and designing the performance of economical UHPC double-reinforced bonded anchorage according to claim 1, characterized in that, The key technical indicators extracted in S3 include: ultimate bond strength, peak slip, residual bond strength, and bond toughness; the bond toughness is obtained by integral calculation of the bond stress-slip relationship curve.
8. The method for predicting and designing the performance of economical UHPC double-reinforced bonded anchorage according to claim 7, characterized in that, The anchorage design in S3 is an anchorage length design; the anchorage length design specifically includes: determining the target anchorage force required for the reinforcing steel according to the bearing capacity requirements of the component, and using the ultimate bond strength to calculate the minimum anchorage length L required to meet the target anchorage force. a .
9. The method for predicting and designing the performance of economical UHPC double-reinforced bonded anchorage according to claim 8, characterized in that, The minimum anchorage length L a The calculation further considers the non-uniform bond stress distribution defined by the bond stress-slip relationship curve, and integrates the bond stress over the anchorage length to make the resultant force equal to or greater than the target anchorage force.
10. The method for predicting and designing the performance of economical UHPC double-reinforced bonded anchorage according to claim 1, characterized in that, The method also includes a verification step: the prediction and design results obtained through S2 and S3 are compared with the preset physical test database or finite element numerical simulation results. If the error between the two is greater than the preset threshold, the method returns to step S1 to iteratively correct the initial parameters or the constitutive model in step S2.