UHPC-NC interface mechanical property prediction method and system considering size effect

Abstract

The invention relates to a UHPC-NC interface mechanical property prediction method and system considering a size effect, and the method comprises the steps: preparing a target test piece, collecting original data through a direct shear test and a pull-out test, and obtaining a shear stress-displacement curve and a tensile stress-displacement curve according to the original data; extracting shear performance parameters and a linear relation according to the curve, carrying out fitting analysis on the shear performance parameters to obtain a shear size effect law, further defining a shear macroscopic constitutive model, and carrying out fracture mechanical quantitative evaluation on the shear performance parameters to obtain a shear macroscopic constitutive model. Deriving and constructing a prediction expression of shear resistance and a shear-displacement constitutive model according to a quantitative evaluation result; extracting tensile property parameters according to the curve, performing series analysis on the tensile property parameters to obtain an interface tensile relationship, performing probability distribution analysis on the tensile property parameters to obtain a tensile size effect law, and performing derivation according to the interface tensile relationship and the tensile size effect law to obtain a tensile property prediction expression and a tensile-fracture constitutive model.

Description

Technical Field

[0001] This invention relates to the field of concrete reinforcement performance evaluation technology, specifically to a method and system for predicting the mechanical properties of the UHPC-NC interface considering size effects. Background Technology

[0002] Ordinary concrete, as a traditional cement-based material with excellent performance, has been widely used in modern civil engineering structures. Reinforcing ordinary concrete (NC) structures with ultra-high performance concrete (UHPC) can form a new UHPC-NC composite. UHPC reinforcement can not only improve the load-bearing capacity of the original concrete structure, but also enhance its impermeability and durability, thereby effectively extending the service life of the structure. It is especially suitable for bridge deck reinforcement projects.

[0003] In bridge deck reinforcement projects, UHPC-NC is often used for large-area composite bonding. Existing technologies improve the reliability of UHPC-NC composite bridge decks by densely embedding short steel bars or studs into the NC bridge deck based on the design of small-sized UHPC-NC composite cross sections. However, this increases material consumption and construction difficulty. Currently, there is limited research on the interfacial bonding effect of large-sized UHPC-NC. The interfacial bonding constitutive models used in existing technologies do not consider the influence of interface geometry on peak strength, stiffness, and ultimate displacement, which will lead to a significant increase in the prediction error of the mechanical properties of UHPC-NC in large-area composite scenarios, seriously affecting the promotion and application of bridge deck reinforcement projects.

[0004] Therefore, given the shortcomings of traditional technologies, there is an urgent need to address the problem of large prediction errors in the mechanical properties of the UHPC-NC interface. Summary of the Invention

[0005] The primary objective of this application is to address at least one of the aforementioned problems by providing a method and system for predicting the mechanical properties of UHPC-NC interfaces that takes into account size effects.

[0006] To achieve the various objectives of this application, the following technical solution is adopted:

[0007] A method for predicting the mechanical properties of UHPC-NC interfaces considering size effects, provided to suit one of the purposes of this application, includes the following steps:

[0008] Multiple UHPC-NC target specimens were prepared, and raw data were collected through direct shear tests and pull-out tests. Based on the raw data, shear stress-displacement curves and tensile stress-displacement curves were obtained.

[0009] Shear performance parameters and linear relationships are extracted from the shear stress-displacement curve. The shear size effect law is obtained by fitting analysis of the shear performance parameters. Based on the linear relationship and the shear size effect law, a macroscopic constitutive model of shear is defined. The fracture mechanics quantitative evaluation of the shear performance parameters is carried out. Based on the quantitative evaluation results, the predictive expression of shear resistance and the shear-displacement constitutive model are derived and constructed.

[0010] Tensile performance parameters are extracted from the tensile stress-displacement curve. The interfacial tensile relationship is obtained by performing a series analysis on the tensile performance parameters. The tensile size effect law is obtained by performing a probability distribution analysis on the tensile performance parameters. Based on the interfacial tensile relationship and the tensile size effect law, the predictive expression for tensile performance and the tensile-fracture constitutive model are derived.

[0011] In an optional embodiment, multiple UHPC-NC target specimens are prepared, and raw data are collected through direct shear tests and pull-out tests. Based on the raw data, shear stress-displacement curves and tensile stress-displacement curves are obtained, as follows:

[0012] Set the interface height condition for the direct shear test and the core diameter condition for the pull-out test, and set the baseline parameters for the interface height and core diameter;

[0013] Interfacial composite specimens of different geometric dimensions were prepared based on interface height and core diameter conditions. The interfacial composite specimens included direct shear specimens and pull-out specimens.

[0014] Shear displacement and load of direct shear specimens with different geometric dimensions were collected under direct shear test. Shear stress was calculated based on load and bond area to obtain shear stress-displacement curve. Pull-out displacement and load of pull-out specimens with different geometric dimensions were collected under pull-out test. Tensile stress was calculated based on load and bond area to obtain tensile stress-displacement curve.

[0015] In an optional embodiment, a shear size effect law is obtained by fitting the shear performance parameters. Based on the linear relationship and the shear size effect law, a macroscopic constitutive model of shear is defined, including the following steps:

[0016] The shear performance parameters of the target specimen are normalized based on the baseline parameters;

[0017] The relationship between the shear performance parameters and the interface height was fitted using the generalized Logistic function on the normalized results to obtain the shear size effect law.

[0018] The quantitative relationship between shear stress, shear stiffness and displacement is determined based on the linear relationship. The shear stress, shear stiffness and ultimate displacement are characterized based on the shear size effect law. A macroscopic constitutive model of shear is defined.

[0019] The shear size effect law is expressed as:

[0020]

[0021] In the formula, τ c τ represents the peak shear stress of the target specimen. c,100 S represents the peak shear stress of the reference specimen. c S represents the ultimate displacement of the target specimen. c,100 K represents the ultimate displacement of the reference specimen. c K represents the shear stiffness of the target specimen. c,100 3.5 represents the shear stiffness of the reference specimen, 3.5 represents the curvature exponent of the logistic curve steepness, and h represents the interface height. 100 This indicates that the interface height of the reference specimen is 100mm, A τ A s and A k B represents the convergence limit parameter. τ B s and B k Indicates the parameters of the curve inflection point;

[0022] The expression for the shearing macroscopic constitutive model is:

[0023]

[0024] In the formula, τ(s1) represents the shear stress, and K c (h) represents the energy-size coupled shear stiffness function, s1 represents the cumulative interface displacement, and S c This indicates the ultimate displacement.

[0025] In an optional embodiment, the shear performance parameters are subjected to fracture mechanics quantitative evaluation, and a predictive expression for shear performance is derived based on the quantitative evaluation results, including the following steps:

[0026] The linear elastic fracture mechanics method is used to evaluate the shear performance parameters. The resistance of the interface to crack propagation is quantified by fracture toughness, and the energy consumption per unit area of ​​crack propagation is quantified by fracture energy. The energy consumption is represented by the total energy consumed per unit fracture area, and the fracture area is calculated by the specimen thickness and maximum displacement.

[0027] Based on the linear relationship between shear stress and displacement curves in direct shear tests, a linear elastic assumption is made between external load and displacement curves, converting local shear stiffness into overall load stiffness.

[0028] The relationship between external load and displacement is established based on the overall load stiffness and the cumulative displacement of the interface. The work done by the external load on the interface is calculated within the displacement range from the initial displacement to the maximum displacement.

[0029] Based on the energy conservation relationship between fracture energy and work done by external load, the expression for the energy-size coupled shear stiffness function is derived by using the expressions for fracture energy and work done by external load.

[0030] By quantifying the linear relationship between the energy of the interface crack propagation area and the external load and displacement, the relationship between shear stress, shear stiffness and displacement is determined, and a predictive expression for shear performance is derived.

[0031] The expression for the energy-size coupled shear stiffness function is as follows:

[0032]

[0033] In the formula, K c (h) represents the energy-size coupled shear stiffness, G f (h) represents the functional relationship between the interface height and the energy consumed per unit fracture area, S c (h) represents the functional relationship between the interface height and the ultimate displacement, h represents the interface height of the target specimen, B represents the thickness of the target specimen, mg represents the self-weight of the target specimen, and b represents the interface width of the target specimen.

[0034] The predictive expression for the shear resistance is as follows:

[0035] τ peak (h)=K C S C

[0036] F peak (h)=τ peak ×bh

[0037] In the formula, τ peak (h) represents the predicted peak shear stress, K C S represents shear stiffness. C b represents the limit displacement, h represents the interface width, and F represents the interface height. peak (h) represents the predicted interfacial shear strength.

[0038] In an optional embodiment, the shear performance parameters are quantitatively evaluated using fracture mechanics, and a shear-displacement constitutive model is derived and constructed based on the quantitative evaluation results, including the following steps:

[0039] The peak shear stress is determined based on the shear size effect law, and the shear stiffness and ultimate displacement are determined based on the energy conservation relationship. The cumulative interface displacement is used as a variable to derive the shear-displacement constitutive model on the basis of the macroscopic shear constitutive model.

[0040] The expression for the shear-displacement constitutive model is:

[0041]

[0042] In the formula, τ(s1) represents the shear stress, and K c (h) represents the energy-size coupled shear stiffness function, G f (h) represents the functional relationship between the interface height and the energy consumed per unit fracture area, S c (h) represents the functional relationship between the interface height and the ultimate displacement, where h represents the interface height of the target specimen, B represents the thickness of the target specimen, mg represents the self-weight of the target specimen, b represents the interface width of the target specimen, and s1 represents the cumulative displacement of the interface.

[0043] In an optional embodiment, the tensile property parameters are analyzed in series to obtain the interfacial tensile relationship, including the following steps:

[0044] Using the three-partition assumption, the interface displacement of UHPC-NC is calculated by connecting the UHPC layer, the interface transition layer and the NC layer in series by limiting displacement;

[0045] Linear regression was performed on the tensile stiffness, ultimate tensile stress, and ultimate displacement in the pull-out test, and the tensile stiffness of the interface with different geometric dimensions was calculated using a three-part series formula.

[0046] The expression for the interface displacement is:

[0047]

[0048] In the formula, ΔI I S represents the interface displacement of UHPC-NC. t σ represents the ultimate displacement. t E represents the peak tensile stress of the target specimen. UHPC t represents the elastic modulus of the UHPC layer. UHPC E represents the thickness of the UHPC layer. NC t represents the elastic modulus of the NC layer. NC Indicates the thickness of the NC layer;

[0049] The expression for the interface tensile stiffness is:

[0050]

[0051] In the formula, K t ΔI represents the interfacial tensile stiffness of the bonded interface. I σ represents the interface displacement of UHPC-NC. t t represents the peak tensile stress of the target specimen. UHPC E represents the thickness of the UHPC layer. UHPC t represents the elastic modulus of the UHPC layer. NCE represents the thickness of the NC layer. NC This represents the elastic modulus of the NC layer.

[0052] In an optional embodiment, the tensile property parameters are subjected to probability distribution statistical analysis to obtain the tensile size effect law, including the following steps:

[0053] The volume of the target specimen is characterized by introducing a geometric similarity dimension for the diameter feature dimension, and the shape parameters of the target specimen are characterized by Weibull modulus.

[0054] Weibull modulus quantization of tensile size effect law under tensile load using Weibull statistical function;

[0055] Peak tensile stress was calculated using the Weibull power law and the Weibull modulus.

[0056] The expression for the stretching dimension effect law is:

[0057]

[0058] V=D n

[0059] In the formula, P f (σ) represents the failure probability due to tensile dimensional effects, e represents the natural constant, and V represents the volume of the target specimen. r The reference volume of the specimen is represented by σ, which represents the external stress applied to the target specimen. The external stress is inversely proportional to the shear stress of the characteristic diameter. u σ0 represents the maximum tensile stress corresponding to a failure probability of 0, σ0 represents the scale parameter of the tensile stress, n represents the geometric similarity dimension, and m represents the shape parameter of the target specimen characterized by the Weibull modulus.

[0060] The expression for the peak tensile stress is:

[0061]

[0062] In the formula, σ t (D) represents the peak tensile stress corresponding to the size effect under different diameter characteristics, σ t,50 This represents the reference tensile stress of the specimen when the diameter characteristic is 50 mm, where D represents the diameter characteristic dimension, and m represents the shape parameter of the target specimen characterized by the Weibull modulus.

[0063] In an optional embodiment, a predictive expression for tensile properties is derived based on the interfacial stretching relationship and the tensile dimension effect law, including the following steps:

[0064] The predictive expression for tensile properties is derived based on the peak tensile stress and the tensile area of ​​the interface;

[0065] The predictive expression for the tensile properties is as follows:

[0066] F peak (D)=σ t (D)×A

[0067] In the formula, F peak (D) represents the predicted tensile strength, σ t (D) represents the peak tensile stress corresponding to the size effect under different diameter characteristics, and A represents the tensile area of ​​the interface.

[0068] In an optional embodiment, a tensile-fracture constitutive model is derived based on the interfacial stretching relationship and the tensile size effect law, including the following steps:

[0069] The interface displacement and interface tensile stiffness are determined based on the interface tensile relationship, the peak tensile stress is determined based on the tensile size effect law, and the tensile displacement is used as a variable to derive the tensile-fracture constitutive model.

[0070] The expression for the tension-fracture constitutive model is:

[0071]

[0072] In the formula, σ t (s2) represents the functional relationship between peak tensile stress and tensile displacement, where s2 represents the tensile displacement, S t This indicates the ultimate displacement.

[0073] On the other hand, a UHPC-NC interface mechanical property prediction system considering size effects, provided to suit one of the purposes of this application, includes:

[0074] The raw data acquisition module is used to prepare multiple UHPC-NC target specimens. Raw data is collected through direct shear tests and pull-out tests. Based on the raw data, shear stress-displacement curves and tensile stress-displacement curves are obtained.

[0075] The shear size effect analysis module is used to extract shear performance parameters and linear relationships from the shear stress-displacement curve, perform fitting analysis on the shear performance parameters to obtain the shear size effect law, define a macroscopic constitutive model of shear based on the linear relationship and the shear size effect law, perform fracture mechanics quantitative evaluation of the shear performance parameters, and derive and construct a predictive expression for shear resistance and a shear-displacement constitutive model based on the quantitative evaluation results.

[0076] The tensile size effect analysis module is used to extract tensile performance parameters from the tensile stress-displacement curve, perform cascade analysis on the tensile performance parameters to obtain the interfacial tensile relationship, perform probability distribution analysis on the tensile performance parameters to obtain the tensile size effect law, and derive the predictive expression for tensile performance and the tensile-fracture constitutive model based on the interfacial tensile relationship and the tensile size effect law.

[0077] On another note, a UHPC-NC interface mechanical property prediction device considering size effects, provided to suit one of the purposes of this application, includes a central processing unit and a memory, wherein the central processing unit is used to invoke and run a computer program stored in the memory to perform the steps of the UHPC-NC interface mechanical property prediction method considering size effects described in this application.

[0078] In another aspect, a computer-readable storage medium is provided to suit one of the purposes of this application, the computer-readable storage medium storing computer-executable instructions for causing a computer to perform a UHPC-NC interface mechanical property prediction method considering size effects as disclosed in any of the first aspects of the present invention.

[0079] The technical solution of this application has many advantages, including but not limited to the following aspects:

[0080] This application prepares direct shear and tensile specimens through experimental objectives. Shear stress-displacement and tensile stress-displacement curves are collected experimentally, and shear and tensile performance parameters are extracted from these curves. The influence of shear size effect on the shear performance parameters is analyzed using a Logistic function, thereby constructing a shear-displacement constitutive model in which peak shear stress, shear stiffness, and ultimate displacement are adaptively modified with interface height. A predictive expression for shear performance is also proposed. The influence of tensile size effect on the tensile performance parameters is analyzed using a Weibull statistical function, thereby constructing a tensile-fracture constitutive model in which peak tensile stress is adaptively modified with core diameter. A predictive expression for tensile performance is also proposed. Based on these two constitutive models, both can adapt to different size effects, reducing the error influence of different size effects on peak strength, stiffness, and ultimate displacement, thus improving the accuracy of the mechanical property prediction results. Attached Figure Description

[0081] The above and / or additional aspects and advantages of this application will become apparent and readily understood from the following description of the embodiments taken in conjunction with the accompanying drawings, wherein:

[0082] Figure 1 A flowchart of an embodiment of the UHPC-NC interface mechanical property prediction method considering size effects according to this application;

[0083] Figure 2This is a schematic diagram of the UHPC-NC interface mechanical property prediction system that considers size effects, used in this application.

[0084] Figure 3 This is a schematic diagram of the fitting curve of shear stiffness in a direct shear test, which is an example of this application.

[0085] Figure 4 This is a schematic diagram of the fitting curve of the ultimate displacement in the direct shear test, which is an example of this application.

[0086] Figure 5 This is a schematic diagram of the fitting curve of shear stress in a direct shear test, which is an example of this application.

[0087] Figure 6 This is a schematic diagram of the fitting curve of the fracture energy in the exemplary direct shear test of this application;

[0088] Figure 7 This is a schematic diagram of the fitting curve of the interface displacement in the direct shear test exemplified in this application;

[0089] Figure 8 The Welb probability diagram of tensile strength in a pull-out test is an example of that in this application.

[0090] Figure 9 A Welbright probability plot for another tensile strength in a pull-out test exemplified in this application;

[0091] Figure 10 This is a logarithmic scatter plot of tensile strength in a pull-out test exemplified in this application.

[0092] Figure 11 A logarithmic scatter plot of another tensile strength in a pull-out test exemplified in this application;

[0093] Figure 12 This is a front view of a direct shear specimen in an exemplary direct shear test according to this application;

[0094] Figure 13 This is a schematic diagram of an exemplary direct shear specimen in a direct shear test according to this application;

[0095] Figure 14 This is a schematic diagram of the structure of the pull-out specimen in the pull-out test, which is an example of this application.

[0096] Figure 15 This is a schematic diagram of an exemplary pull-out specimen in a pull-out test according to this application. Detailed Implementation

[0097] The technical solution of this application is applicable to the field of concrete reinforcement performance evaluation, and is particularly suitable for bridge deck reinforcement scenarios. In this context, the technical solution of this application can be applied in a typical UHPC-NC mechanical performance prediction scenario.

[0098] In existing technologies, short steel bars or studs are densely implanted into the NC bridge deck on the basis of a small-sized UHPC-NC composite interface to improve the safety and reliability of the UHPC-NC composite bridge deck. However, this increases material consumption and construction difficulty. Currently, there is little research on the interfacial bonding effect of large-sized UHPC-NC. The interfacial bonding constitutive model used in existing technologies does not consider the influence of interface geometry on peak strength, stiffness and ultimate displacement, which will lead to a significant increase in the prediction error of the mechanical properties of UHPC-NC in large-area composite scenarios, seriously affecting the progress of bridge deck reinforcement projects.

[0099] To address the problem that the influence of the aforementioned interface geometry on peak strength, stiffness, and ultimate displacement leads to a significant increase in the prediction error of mechanical properties, the technical solution provided by the embodiments of this application has the following general idea:

[0100] Direct shear and tensile specimens were prepared according to the experimental objectives. Shear stress-displacement and tensile stress-displacement curves were collected through experiments. Shear and tensile performance parameters were extracted from the curves. The influence of shear size effect on the shear performance parameters was analyzed using the Logistic function, thereby deriving the predictive expression for shear performance and constructing a shear-displacement constitutive model in which peak shear stress, shear stiffness, and ultimate displacement are adaptively modified with interface height. The influence of tensile size effect on the tensile performance parameters was analyzed using the Welbull statistical function, thereby deriving the predictive expression for tensile performance and constructing a tensile-fracture constitutive model in which peak tensile stress, tensile stiffness, and ultimate displacement are adaptively modified with core diameter.

[0101] To better understand the above technical solutions, the following will provide a detailed explanation of the technical solutions in conjunction with the accompanying drawings and specific implementation methods.

[0102] The specific embodiments described below can be combined with each other, and the same or similar concepts or processes will not be described again in some embodiments. The embodiments of this application will be described below with reference to the accompanying drawings.

[0103] See Figure 1 This application discloses a method for predicting the mechanical properties of the UHPC-NC interface considering size effects. In a typical embodiment for predicting shear performance, it includes the following steps:

[0104] Step 110: Prepare multiple UHPC-NC target specimens, collect raw data through direct shear test and pull-out test, and obtain shear stress-displacement curves and tensile stress-displacement curves based on the raw data;

[0105] Optionally, the target specimen is an interface composite specimen. Reference specimens and interface composite specimens of different sizes can be prepared according to experimental needs. The target specimen is divided into direct shear specimens and pull-out specimens based on the target test. Specifically, in the direct shear test, the reference specimen is a specimen with a bond interface height of 100 mm, and in the pull-out test, the reference specimen is a specimen with a bond interface height of 50 mm. It should be noted that the composite interface specimen is a dedicated test sample used to study the bond performance, shear strength, fracture behavior, and force transfer mechanism of the two types of concrete at the composite interface in UHPC-NC. Its goal is to quantify the interfacial collaborative working ability and can be used to construct a constitutive model of the UHPC-NC interface bond behavior, providing parameter basis for the design of practical engineering projects (such as composite beams, reinforcement layers, and assembly joints).

[0106] In practice, the shear displacement, pull-out displacement, and load of the target specimen under different geometric conditions are collected to obtain shear stress-displacement curves and tensile stress-displacement curves.

[0107] Optionally, the direct shear test and pull-out test can be a Z-type direct shear test under different height conditions and a core pull-out test under different diameter conditions. The test data of the target test can be recorded synchronously by displacement sensors and digital image correlation (DIC) technology, thereby obtaining shear displacement test data, pull-out fracture test data and load test data of the composite interface specimens under different geometric dimensions. Based on the relationship between load and bonding area, shear stress and tensile stress are calculated, and then the shear stress-displacement curve of the relationship between shear displacement and shear stress, as well as the tensile stress-displacement curve of the relationship between pull-out displacement and tensile stress are obtained. The obtained test data and curves can be used as the data basis for constructing the constitutive model of the interface bonding behavior of UHPC-NC.

[0108] Please see Figures 12-13 It should be noted that the Z-type direct shear test is a push-off method used to measure the shear bond performance of the UHPC-NC interface. In the Z-type direct shear test, UHPC and ordinary concrete are cast in layers with staggered joints to form a "Z"-shaped specimen. When axial pressure is applied unidirectionally in a press, the stress redistribution caused by geometric discontinuity transforms the axial pressure into controlled pure shear stress at the interface, thereby simulating the interface slip behavior in actual engineering. The Z-type direct shear test process mainly includes: specimen preparation, loading device installation, and load-displacement data acquisition. By recording the peak axial load and combining it with the shear area of ​​the interface, a shear stress-displacement relationship curve can be plotted and the peak shear bond strength can be determined, thus focusing on reflecting the pure shear failure characteristics of the interface.

[0109] Please see Figures 14-15To further clarify, the specific test steps of the core pull-out test are as follows: First, an annular groove is drilled at the test site to fix the potential failure section at the UHPC-NC interface; then, an epoxy adhesive is used to bond a steel cap to the UHPC surface, and the pull-out device is installed after the adhesive has cured; during the loading process, a tensile force is uniformly applied along the interface normal until the specimen fails. The peak tensile force and failure mode are recorded. If the failure occurs along the interface, the tensile bond strength of the interface can be calculated, and the interface toughness can be evaluated through the load-displacement curve. The core pull-out test mainly examines the interfacial bond performance of the specimen, rather than the axial tensile strength of the concrete body. Therefore, the drilling location and bonding operation are crucial to the test results.

[0110] Step 210: Extract shear performance parameters and linear relationships from the shear stress-displacement curve, perform fitting analysis on the shear performance parameters to obtain the shear size effect law, define a macroscopic constitutive model of shear based on the linear relationship and the shear size effect law, perform fracture mechanics quantitative evaluation on the shear performance parameters, and derive and construct the predictive expression of shear resistance and the shear-displacement constitutive model based on the quantitative evaluation results.

[0111] It should be noted that, in order to comprehensively analyze the relationship between the shear performance and the interface geometry of the UHPC-NC interface, the interface shear stress, shear stiffness, and displacement are used as key shear mechanical performance indicators for analysis and evaluation. In order to ensure the consistency of the test and the accuracy of the quantitative evaluation, a direct shear specimen with a bonding interface height of 100 mm can be used as a benchmark in the direct shear test. The test results are derived and analyzed through a unified expression to facilitate the quantitative evaluation of the influence of interface size on shear performance.

[0112] In practical implementation, shear performance parameters and linear relationships are extracted based on the shear stress-displacement curve. The shear performance parameters include peak shear stress, shear stiffness, and ultimate displacement. The shear performance parameters of the target specimen are normalized based on the parameters of the reference specimen. The generalized Logistic function is used to fit the relationship between the shear performance parameters and the interface height on the normalization results to obtain the shear size effect law.

[0113] Please see Figures 3-5 As can be seen from the fitted curves, the changes in the interface geometry significantly affect the changes in parameters such as shear stress, shear stiffness, and ultimate displacement, which are characteristics of shear performance. Furthermore, there is a coexistence of decrease and increase between different dimensions. Although the increase in geometry has a gain effect on the mechanical properties of UHPC-NC, this gain effect is self-limiting and cannot grow indefinitely. Therefore, for the shear performance indicators that show a significant upward trend overall, the Logistic growth model is used for characterization.

[0114] Optionally, in order to further balance the fitting accuracy and monotonicity of multiple curves, the curvature index of the kurtosis of the Logistic curve can be uniformly set to 3.5, so that the fitting accuracy and monotonicity of at least three curves can be balanced in the regression analysis.

[0115] Optionally, by establishing the shear size effect law of UHPC-NC interface shear bonding, the characteristic that the interface shear performance first increases and then stabilizes with the expansion of area is obtained, and then the shear size effect parameters are obtained, including convergence limit parameters and curve inflection point parameters.

[0116] Furthermore, the convergence limit parameter is A. τ A s and A k A τ A represents the limit convergence of the peak shear stress of the target specimen. k A represents the ultimate convergence of the shear stiffness of the target specimen. s This represents the ultimate convergence of the ultimate displacement of the target specimen in the direct shear test. The convergence limit parameter is used to represent the convergence limit of the peak shear stress relative to the reference value of the reference specimen (the parameter value when the reference height is 100 mm) as the specimen height approaches infinity. A τ It can be represented as:

[0117]

[0118] Furthermore, the inflection point parameter of the curve is B. τ B s and B k B τ B represents the inflection point of the peak shear stress in the shear performance curve. k B represents the inflection point of the shear stiffness of the target specimen in the fitted curve. s This represents the inflection point of the ultimate displacement of the target specimen in the fitted curve. According to the shear size effect law of interfacial shear bonding, the interfacial shear performance curve will first increase and then stabilize as the area increases. Usually, the interfacial height at which 50% convergence is achieved is the position where the inflection point of the control curve appears.

[0119] Specifically, the expression for the shear size effect law is:

[0120]

[0121]

[0122] In the formula, τ c τ represents the peak shear stress of the target specimen. c,100 S represents the peak shear stress of the reference specimen. c S represents the ultimate displacement of the target specimen.c,100 K represents the ultimate displacement of the reference specimen. c K represents the shear stiffness of the target specimen. c,100 3.5 represents the shear stiffness of the reference specimen, 3.5 represents the curvature exponent of the logistic curve steepness, and h represents the interface height. 100 This indicates that the height of the reference specimen interface is 100mm.

[0123] Furthermore, analysis using the shear size effect law reveals that as the interface geometry increases, the interface shear mechanical properties tend to stabilize, increase first and then decrease, or decrease first and then increase. This indicates that the shear mechanical properties of the UHPC-NC interface undergo bounded changes, which can be attributed to the simultaneous enhancement of chemical bonding force, aggregate mechanical interlocking force, friction, and inherent defects (e.g., inhomogeneity and discontinuity) at the interface as the bonding area of ​​the UHPC-NC interface increases. When the interface size grows to a certain threshold, the negative effects caused by local early failure due to inherent defects significantly increase, leading to a decrease in mechanical properties such as interface shear stress and slip. For shear stiffness, stress concentration and early internal failure caused by local damage within the interface always exist, significantly weakening the shear stiffness. However, when the specimen interface is not cracked, the continuous growth of the interface size produces an overall synergistic effect that weakens the local stress inhomogeneity of the reinforcing steel and promotes the recovery of shear stiffness Kc. By quantifying the influence of size on mechanical properties using parameters through the shear size effect law discovered in the experimental results, a data basis can be provided for proposing a macroscopic constitutive model of UHPC-NC interface shear.

[0124] In practical implementation, a macroscopic constitutive model of shear is defined based on the linear relationship of the shear stress-displacement curve and the shear size effect law; the expression of the macroscopic constitutive model of shear is:

[0125]

[0126] In the formula, τ(s1) represents the shear stress, and K c (h) represents the energy-size coupled shear stiffness function, s1 represents the cumulative interface displacement, and S c This indicates the ultimate displacement.

[0127] In practical implementation, the shear performance parameters of the direct shear test data of the shear stress-displacement curve are evaluated using the linear elastic fracture mechanics method. The resistance of the interface to crack propagation is quantified by fracture toughness, and the energy consumption per unit area of ​​crack propagation at the interface is quantified by fracture energy. For the direct shear test proposed in this application, since the Z-shaped direct shear test can largely avoid the generation of interface bending moment, the normal stress is ignored for ease of analysis. It can be assumed that the interface is subjected to pure shear stress. When the normal stress is ignored, type II initial crack propagation based on interface slip will occur. Therefore, by deriving the calculation expressions for pure type II fracture toughness and fracture energy of the Z-shaped direct shear specimen, the resistance of the interface to crack propagation and the energy consumption per unit area of ​​crack propagation are quantified, thereby evaluating the shear performance and improving the accuracy of the evaluation.

[0128] Alternatively, linear elastic fracture mechanics methods can be used to evaluate the total energy consumed per unit fracture area, thereby converting the macroscopic shear stress-displacement curve into an energy-dimensional parameter.

[0129] Furthermore, in order to convert the total work done in the experiment into energy consumed per unit area, the area of ​​the newly generated or fully displaced ligament can be calculated using the specimen thickness and the maximum displacement.

[0130] Specifically, the expression for fracture toughness is:

[0131]

[0132] In the formula, K IIc Let Q represent fracture toughness, B represent fracture load, W represent the thickness of the target specimen, W represent the cross-sectional height of the target specimen, and a represent the depth of the pre-fabricated crack notch. The geometric correction function representing fracture toughness.

[0133] Furthermore, fracture toughness is the first step in quantifying the resistance to crack propagation at the interface into a measurable material constant. Subsequently, fracture energy can be used to bridge this to a macroscopic constitutive model of interface shear, thereby obtaining a shear-displacement constitutive model. In linear elastic fracture mechanics, the relationship between fracture toughness and fracture energy can be characterized by fracture toughness and the elastic modulus of concrete, expressed as:

[0134]

[0135] In the formula, G F The value of the actual discrete point of the fracture energy in the direct shear test is represented by E', which represents the equivalent elastic modulus of concrete considering the plane strain effect. Since the Z-type direct shear test in this application is a pure shear mode after neglecting the normal strain, the fracture energy can be further characterized as follows:

[0136]

[0137] In the formula, G F (h) represents the actual discrete points of fracture energy under different dimensions, v represents Poisson's ratio, and E represents the elastic modulus of concrete.

[0138] Furthermore, the calculation results of fracture toughness and fracture energy of the specimens in the direct shear test are summarized as shown in Table 1:

[0139] Table 1 - Summary of fracture toughness and fracture energy of direct shear specimens in direct shear test

[0140]

[0141] From Table 1 and Figure 6 It can be seen that the specific discrete points of fracture toughness and fracture energy can be calculated based on the expressions for fracture toughness and fracture energy. Since no pre-fabricated crack is set at the specimen interface, the pre-fabricated crack incision depth 'a' in the geometric correction function of fracture toughness is 0. (See [reference]). Figure 6 , Figure 6 In the equation, L, M, and N are parameters of the fracture energy fitting equation. L represents the ultimate fracture energy, which is the saturation value of the fracture energy when the interface height approaches infinity. It can be understood as the maximum adhesive energy that can be released at an infinitely high shear surface. M represents the size sensitivity coefficient, which determines the rate of rise of the curve. The larger the value of the size sensitivity coefficient, the faster the fracture energy increases with height, and it can control the slope of the curve. N represents the virtual starting height, which is used to shift the h-axis in the coordinate system to the left so that the exponential term is zero when h and N are equal, ensuring that the curve is still positive when h = 100 mm (i.e., the reference specimen). Figure 6 The trend of fracture energy with interface height is shown. As the interface height (i.e., the corresponding bonded surface area) increases, fracture toughness and fracture energy increase. However, as the interface height increases further, the curves will show a more stable trend, especially the fracture toughness. This indicates that increasing the interface height cannot infinitely increase the fracture toughness and fracture energy of the specimen. Both parameters have a maximum upper limit. Therefore, the expression for fracture energy can be obtained by fitting discrete point analysis.

[0142] Specifically, the expression for fracture energy is:

[0143]

[0144] A lig =Bδ0

[0145] Among them, G f(h) represents the energy dimension parameter of the total energy consumed per unit fracture area as fracture energy, ω0 represents the work done quantified by the area enclosed by the shear stress-displacement curve and the horizontal axis, mg represents the self-weight of the target specimen, δ0 represents the maximum displacement, and A lig B represents the area of ​​the fractured ligament, and B represents the thickness of the target specimen.

[0146] Please see Figure 7 As shown in the figure, the interface displacement and interface height have a linear relationship in the fitted curve. In the figure, A represents the limit displacement of the upper platform. When the interface height is high enough, it is the maximum shear displacement required to reach the peak shear stress. With 0.233 as the reference displacement, the limit displacement of the benchmark test with an interface height of 100 mm is the average peak displacement (used to determine the starting point of the left end of the curve). The interface height of 330 mm is the half-response height. When h = 320 mm, the displacement is located at the midpoint of the upper and lower limits (i.e., the x-coordinate that determines the inflection point). p represents the steepness index, which is used to control the inclination of the S-shape of the curve, so that the displacement is consistent with the logistic regression of shear stiffness and peak shear stress.

[0147] In practice, based on the linear relationship presented by the shear stress-displacement curve in the direct shear test, a linear elastic assumption is made between the external load and the displacement curve, and the local shear stiffness is converted into the overall load stiffness. The relationship between the external load and the displacement is established based on the overall load stiffness and the cumulative displacement of the interface.

[0148] Specifically, the expression for the external load is:

[0149] F(s)=k′ c ·s1

[0150]

[0151] In the formula, F(s) represents the external load on the target specimen, and k' c The overall load-displacement stiffness of the target specimen is represented by s1, and the cumulative displacement at the interface is represented by k'. c (h) represents the energy-size coupled shear stiffness function, b represents the interface width, h represents the interface height of the target specimen, and K c (h) represents the energy-size coupled shear stiffness function. It should be noted that the linear elasticity assumption assumes that the relationship between the external load and the displacement is linear in the elastic stage.

[0152] In practical implementation, the work done by the external load on the interface is calculated within the displacement range from the initial displacement to the maximum displacement. This transforms the macroscopic experimental curve (the curve between the external load and the displacement) into an energy dimension, which is then compared with the theoretical fracture energy or the area of ​​the crack propagation resistance model for energy conservation.

[0153] Specifically, the expression for the work done by the external load on the interface is:

[0154]

[0155] In the formula, ω0 represents the work done by the external load on the interface, δ0 represents the maximum displacement, and s1 represents the cumulative displacement of the interface.

[0156] In practical implementation, based on the energy conservation principle, the expression for the energy-size coupled shear stiffness function is derived by using the expressions for fracture energy and work done by external loads:

[0157]

[0158] In the formula, K c (h) represents the energy-size coupled shear stiffness, G f (h) represents the functional relationship between the interface height and the energy consumed per unit fracture area, S c (h) represents the functional relationship between the interface height and the ultimate displacement, where h represents the interface height of the target specimen, B represents the thickness of the target specimen, mg represents the self-weight of the target specimen, and b represents the interface width of the target specimen.

[0159] In practical implementation, the predictive expression for shear performance is derived by using the relationship between shear stress, shear stiffness and displacement.

[0160] Specifically, the predictive expression for the shear resistance is as follows:

[0161] τ peak (h)=K C S C

[0162] F peak (h)=τ peak ×bh

[0163] In the formula, τ peak (h) represents the predicted peak shear stress, K C S represents shear stiffness. C b represents the limit displacement, h represents the interface width, and F represents the interface height. peak (h) represents the predicted interfacial shear strength.

[0164] As can be seen, the relationship between the selection of interface geometry and energy dissipation can be obtained through the above embodiments. The shear stiffness can be verified by the shear stiffness data in the direct shear test, thereby providing data support for the subsequent calculation of shear stress.

[0165] In practical implementation, a shear-displacement constitutive model is constructed based on the macroscopic constitutive model of shear, the energy-size coupled shear stiffness function, and the shear size effect law. Since the shear stress-displacement curve first rises and then stabilizes, specifically, the curve rises during the elastic stage, at which point the shear stress and displacement are linearly related. When the curve rises to the extreme point of the ultimate displacement, brittle fracture will occur. That is, the whole system can be regarded as a linear elastic-instantaneous fracture system. Therefore, when constructing a shear-displacement constitutive model that considers the shear size effect, a piecewise linear form is used.

[0166] Specifically, the expression for the shear-displacement constitutive model is:

[0167]

[0168] In the formula, τ(s1) represents the shear stress, and K c (h) represents the energy-size coupled shear stiffness function, G f (h) represents the functional relationship between the interface height and the energy consumed per unit fracture area, S c (h) represents the functional relationship between the interface height and the ultimate displacement, where h represents the interface height of the target specimen, B represents the thickness of the target specimen, mg represents the self-weight of the target specimen, b represents the interface width of the target specimen, and s1 represents the cumulative displacement of the interface. As can be seen from the above formula, the shear-displacement constitutive model can achieve dimensional adaptation to the interface height, interface width, specimen thickness, and specimen self-weight, thereby reducing the influence of shear size effect on the constitutive model's prediction of shear performance and improving the accuracy of shear performance prediction. It should be noted that in actual engineering, the interface roughness can be directly obtained from measurement calculations or empirical data. Therefore, during the experimental process of constructing the constitutive model, the interface roughness can also be set to conform to the actual engineering application scenario.

[0169] Step 310: Extract tensile performance parameters from the tensile stress-displacement curve, perform cascade analysis on the tensile performance parameters to obtain the interfacial tensile relationship, perform probability distribution analysis on the tensile performance parameters to obtain the tensile size effect law, and derive the prediction expression for tensile performance and the tensile-fracture constitutive model based on the interfacial tensile relationship and the tensile size effect law.

[0170] Optionally, the peak tensile stress, tensile stiffness, and ultimate displacement can be extracted from the tensile stress-displacement curve of the pull-out test.

[0171] In practical implementation, the three-part assumption is adopted, and the interface displacement of UHPC layer, interface transition layer and NC layer are connected in series by ultimate displacement to calculate the interface displacement of UHPC-NC. Since the modulus of UHPC layer and NC layer is higher than that of weak interface transition layer, the interface failure exhibits the characteristics of brittle chain fracture. Therefore, the whole of UHPC layer, interface transition layer and NC layer is regarded as a linear elastic-instantaneous fracture system, so the three parts can be connected in series by ultimate displacement.

[0172] Specifically, the expression for interface displacement is:

[0173]

[0174] In the formula, ΔI I S represents the interface displacement of UHPC-NC. t σ represents the ultimate displacement. t E represents the peak tensile stress of the target specimen. UHPC t represents the elastic modulus of the UHPC layer. UHPC E represents the thickness of the UHPC layer. NC t represents the elastic modulus of the NC layer. NC This indicates the thickness of the NC layer.

[0175] Optionally, at the limiting displacement S t In the experiment, the displacement at which the stress drops to 5% of the peak value was taken, and the ultimate displacement S was obtained by regression analysis on a conventional UHPC-NC combination. t ≈0.023mm, therefore the size can be ignored for a standard UHPC-NC assembly.

[0176] Furthermore, a spatial distribution of the tensile stress-displacement curve was established using pull-out test data. The results of the spatial distribution indicate that the behavior is regionally concentrated regardless of the change in interface size. Therefore, the influence of tensile size effect can be ignored in the pull-out test. Linear regression can be performed on the tensile stiffness, ultimate tensile stress, and ultimate displacement in the pull-out test to determine the interface tensile stiffness at different sizes.

[0177] In practical implementation, the interface tensile stiffness is calculated using a three-part series formula. The expression for the interface tensile stiffness is:

[0178]

[0179] In the formula, K t Indicates the tensile stiffness of the interface, ΔI I σ represents the interface displacement of UHPC-NC. t t represents the peak tensile stress of the target specimen. UHPC E represents the thickness of the UHPC layer. UHPC t represents the elastic modulus of the UHPC layer.NC E represents the thickness of the NC layer. NC This represents the elastic modulus of the NC layer.

[0180] For further details, please refer to Figure 8 and Figure 9 In the pull-out test, the Weibull probability diagram of the tensile stress of the tensile specimen shows that the samples in the pull-out test all fall between the upper and lower percentiles. Therefore, the tensile stress intensity conforms to the Weibull probability distribution. The size of the pull-out specimen in the pull-out test can be regarded as a statistical size consistent with Weibull theory. For the tensile stress of the UHPC-NC interface under different geometric dimensions, the only scale parameter is the diameter characteristic size of the pull-out specimen.

[0181] For further details, please refer to Figure 10 and Figure 11 The logarithmic scatter plot of the average tensile stress intensity for different diameter feature sizes shows that the Weibull modulus m in the pull-out test is usually 12. However, empirical values ​​cannot accurately capture the relationship between the tensile stress intensity and the interface geometry of the UHPC-NC interface. Therefore, the Weibull modulus m needs to be adjusted to provide a more accurate representation of the relationship. In this application, it is proposed to adjust the Weibull modulus m according to the Weibull distribution probability density. A trend line is plotted for the inverse relationship between tensile stress intensity and interface geometry (i.e., diameter feature size D). Figure 10 and Figure 11 As shown in the logarithmic scatter plot, the Weibull second trend line ( Figure 10 Weibull Line 2 and Weibull Third Trend Line (in the text) Figure 11 Weibull Line 3 in the text is compared to the first trend line of Weibull ( Figure 10 and Figure 11 The modified trend line (Weibull Line 1) allows for a better observation of the uniformity of tensile stress intensity. Consequently, the modified Weibull modulus m can better characterize the relationship between interface geometry and tensile stress intensity, thus providing a more accurate predictive capability for the tensile properties of UHPC-NC.

[0182] In practical implementation, the Weibull modulus of the Weibull statistical function is used to quantify the tensile size effect law under tensile load; the Weibull modulus m corresponds to the shape parameter of the target specimen. For the diameter characteristic dimension D, the geometric similarity dimension N is introduced to represent the volume of the target specimen. In addition to the volume variable of the target specimen, a reference volume also needs to be set as a reference value. The reference volume can be regarded as the minimum volume, that is, a continuum, and also a representative of the material. Usually, the reference volume is taken as the specimen volume of 50 mm.

[0183] Specifically, the expression for the stretching size effect law is:

[0184]

[0185] V=D n

[0186] In the formula, P f (σ) represents the failure probability due to tensile dimensional effects, e represents the natural constant, and V represents the volume of the target specimen. r The reference volume of the specimen is represented by σ, and the external stress applied to the target specimen is represented by σ. u σ0 represents the maximum tensile stress corresponding to a failure probability of 0, n represents the geometric similarity dimension, and m represents the shape parameter of the target specimen characterized by the Weibull modulus. It can be understood that there is an inverse relationship between the external stress and the diameter characteristic dimension direct shear.

[0187] Furthermore, the spatial distribution of load-displacement in the pull-out test indicates that the size effect is relatively weak, and the peak strength can usually be taken as the average value. In this application, the influence of the size effect also needs to be considered. Therefore, when characterizing and calculating the peak tensile stress, the calculation is performed using the Weibull modulus according to the Weibull power law.

[0188] Specifically, the expression for peak tensile stress is:

[0189]

[0190] In the formula, σ t (D) represents the peak tensile stress corresponding to the size effect under different diameter characteristics, σ t,50 This represents the reference tensile stress of the specimen when the diameter characteristic is 50 mm, where D represents the diameter characteristic dimension, and m represents the shape parameter of the target specimen characterized by the Weibull modulus.

[0191] In practical implementation, the prediction expression for tensile properties is derived based on the peak tensile stress and the tensile area of ​​the interface;

[0192] Specifically, the predictive expression for the tensile properties is as follows:

[0193] F peak (D)=σ t (D)×A

[0194] In the formula, F peak (D) represents the predicted tensile strength, σ t (D) represents the peak tensile stress corresponding to the size effect under different diameter characteristics, and A represents the tensile area of ​​the interface. It should be noted that in the experiment, the tensile area A of the interface is taken as πD.2 / 4.

[0195] In practical implementation, the interface displacement and interface tensile stiffness are determined based on the interface tensile relationship, and the peak tensile stress is determined based on the tensile size effect law. The tensile displacement is used as a variable for derivation to construct the tensile-fracture constitutive model. Similar to the shear-displacement constitutive model, the average curve of the pull-out specimen observed in the pull-out test has a significant linear correlation. Therefore, a piecewise linear form is used to express the tensile-fracture constitutive model. It can be understood that when the cumulative displacement does not exceed the ultimate displacement, the curve is in the rising stage. After the cumulative displacement reaches the critical point of the ultimate displacement, the residual force component is extremely low, approaching complete fracture, which can be simplified to the peak tensile stress returning to zero.

[0196] Specifically, the expression for the tension-fracture constitutive model is:

[0197]

[0198] Furthermore, substituting the above formula related to diameter, we obtain a further expression for the tension-fracture constitutive model:

[0199]

[0200] In the formula, σ t (s2) represents the functional relationship between peak tensile stress and tensile displacement, K t S represents the interfacial tensile stiffness characterizing the bonded interface, s2 represents the tensile displacement, and S t This indicates the ultimate displacement.

[0201] Furthermore, by characterizing the peak tensile stress using the Weibull modulus m, and considering the influence of tensile size effects, the accuracy of the tensile-fracture constitutive model in predicting shear performance can be improved. The interface displacement occurring in the UHPC-NC interface transition layer can be characterized by the peak tensile stress, ultimate displacement, UHPC layer parameters, and NC layer parameters. The interface tensile stiffness can be characterized by the interface displacement and peak tensile stress, and the influence of different interface geometries on the interface tensile stiffness can be analyzed.

[0202] Finally, the unique technical advantage of this application lies in the establishment of a constitutive model characterizing the bonding behavior of the UHPC-NC interface based on size effects. The model derivation incorporates a shear size effect Logistic function, a tensile size effect Weibull statistical function, and a fracture energy conservation equation. This allows peak shear stress, shear stiffness, ultimate displacement, peak tensile stress, tensile stiffness, and ultimate displacement to be adaptively corrected with variations in interface height h and core diameter D. The mechanical properties of the UHPC-NC interface can be predicted using expressions for tensile and shear strength. Through experimental data comparison, the maximum deviation of the prediction results does not exceed 15%, significantly outperforming traditional models that do not consider size effects. This application has high application potential in the field of concrete reinforcement performance evaluation.

[0203] Please see Figure 2 According to one aspect of this application, a UHPC-NC interface mechanical property prediction system considering size effects is provided, the system comprising:

[0204] The raw data acquisition module is used to prepare multiple UHPC-NC target specimens. Raw data is collected through direct shear and pull-out tests, and shear stress-displacement curves and tensile stress-displacement curves are obtained from the raw data. The shear size effect analysis module is used to extract shear performance parameters and linear relationships from the shear stress-displacement curves, perform fitting analysis on the shear performance parameters to obtain the shear size effect law, define a macroscopic constitutive model of shear based on the linear relationship and the shear size effect law, perform fracture mechanics quantitative evaluation of the shear performance parameters, and derive the predictive expression of shear performance and the shear-displacement constitutive model based on the quantitative evaluation results. The tensile size effect analysis module is used to extract tensile performance parameters from the tensile stress-displacement curves, perform series analysis on the tensile performance parameters to obtain the interfacial tensile relationship, perform probability distribution analysis on the tensile performance parameters to obtain the tensile size effect law, and derive the predictive expression of tensile performance and the tensile-fracture constitutive model based on the interfacial tensile relationship and the tensile size effect law.

[0205] Based on any embodiment of the system in this application, the system further includes: a curve construction module, configured to set interface height conditions for direct shear tests and core diameter conditions for pull-out tests, and to set reference parameters for interface height and core diameter; to prepare interface composite specimens of different geometric dimensions according to the interface height conditions and core diameter conditions, wherein the interface composite specimens include direct shear specimens and pull-out specimens; to collect shear displacement and load of direct shear specimens of different geometric dimensions under direct shear tests, and to calculate shear stress based on load and bond area to obtain shear stress-displacement curves; and to collect pull-out displacement and load of pull-out specimens of different geometric dimensions under pull-out tests, and to calculate tensile stress based on load and bond area to obtain tensile stress-displacement curves.

[0206] Based on any embodiment of the system in this application, the system of this application further includes: a fitting analysis module configured to normalize the shear performance parameters of the target specimen based on the reference parameters; and using a generalized Logistic function to fit the relationship between the shear performance parameters and the interface height on the normalization result to obtain the shear size effect law.

[0207] Based on any embodiment of the system in this application, the system further includes: a fracture mechanics evaluation module, configured to perform fracture mechanics evaluation on shear performance parameters using a linear elastic fracture mechanics method; quantifying the resistance to crack propagation at the interface through fracture toughness; and quantifying the energy consumption per unit area of ​​crack propagation at the interface through fracture energy, wherein the energy consumption is represented by the total energy consumed per unit fracture area, and the fracture area is calculated using the specimen thickness and maximum displacement; and based on the linear relationship of the shear stress-displacement curve in the direct shear test, making a linear elastic assumption on the external load and displacement curve, and converting the local shear stiffness... The overall load stiffness is replaced; based on the overall load stiffness and the cumulative displacement of the interface, the relationship between the external load and the displacement is established. For the displacement interval from the initial displacement to the maximum displacement, the work done by the external load on the interface is calculated; according to the energy conservation relationship between fracture energy and the work done by the external load, the expression of the energy-size coupled shear stiffness function is derived through the expression of fracture energy and the expression of the work done by the external load; by quantifying the energy of the interface crack propagation area and the linear relationship between the external load and the displacement, the relationship between shear stress, shear stiffness and displacement is determined, and the predictive expression of shear performance is derived.

[0208] Based on any embodiment of the system in this application, the system of this application further includes: a shear-displacement constitutive model construction module, configured to determine the peak shear stress according to the shear size effect law, determine the shear stiffness and ultimate displacement according to the energy conservation relationship, and derive the shear-displacement constitutive model by taking the cumulative interface displacement as a variable based on the shear macroscopic constitutive model.

[0209] Based on any embodiment of the system in this application, the system of this application further includes: a series analysis module, configured to use a three-partition assumption to connect the UHPC layer, the interface transition layer and the NC layer through the ultimate displacement to calculate the interface displacement of UHPC-NC; perform linear regression on the tensile stiffness, ultimate tensile stress and ultimate displacement in the pull-out test, and use the three-partition series formula to calculate the interface tensile stiffness of different geometric dimensions.

[0210] Based on any embodiment of the system in this application, the system of this application further includes: a probability distribution statistical analysis module, configured to introduce a geometric similarity dimension to characterize the volume of the target specimen for the diameter feature size, and to characterize the shape parameters of the target specimen using Weibull modulus; to quantify the tensile size effect law under tensile load using Weibull modulus of Weibull statistical function; and to calculate the peak tensile stress by characterizing it using Weibull modulus according to Weibull power law.

[0211] Based on any embodiment of the system in this application, the system of this application further includes: a tensile performance prediction module, configured to derive a prediction expression for tensile performance based on peak tensile stress and tensile area of ​​interface.

[0212] Based on any embodiment of the system in this application, the system of this application further includes: a tension-fracture constitutive model construction module, configured to determine the interface displacement and interface tensile stiffness according to the interface tension relationship, determine the peak tensile stress according to the tensile size effect law, and derive the tensile displacement as a variable to construct a tension-fracture constitutive model.

[0213] Based on any embodiment of the system in this application, the system of this application further includes: a shear performance verification module, configured to evaluate the accuracy of the constitutive model during the derivation process using the RMSE formula, the mutual information-RMR criterion, or the BP neural network formula.

[0214] Another embodiment of this application provides a UHPC-NC interface mechanical performance prediction device that considers size effects. This device includes a processor, a computer-readable storage medium, a memory, and a network interface connected via a system bus. The computer-readable, non-volatile storage medium stores an operating system, a database, and computer-readable instructions. The database may store information sequences. When the computer-readable instructions are executed by the processor, the processor can implement a UHPC-NC interface mechanical performance prediction method that considers size effects.

[0215] The processor of the UHPC-NC interface mechanical property prediction device considering size effects provides computational and control capabilities, supporting the operation of the entire device. The memory of the device can store computer-readable instructions, which, when executed by the processor, cause the processor to perform the UHPC-NC interface mechanical property prediction method considering size effects of this application. The network interface of the device is used for communication with a terminal.

[0216] In this embodiment, the processor is used to execute... Figure 2 The system defines the specific functions of each module, and the memory stores the program code and various data required to execute these modules or submodules. The network interface is used to enable data transmission between user terminals or servers.

[0217] The non-volatile readable storage medium in this embodiment stores the program code and data required to execute all modules in the UHPC-NC interface mechanical property prediction system that takes into account the size effect of this application. The server can call the program code and data of the server to execute the functions of all modules.

[0218] This application also provides a non-volatile readable storage medium storing computer-readable instructions, which, when executed by one or more processors, cause the one or more processors to perform the steps of the UHPC-NC interface mechanical property prediction method considering size effects according to any embodiment of this application.

[0219] This application also provides a computer program product, including a computer program / instructions that, when executed by one or more processors, implement the steps of the method described in any embodiment of this application.

Claims

1. A method for predicting the mechanical properties of UHPC-NC interfaces considering size effects, characterized in that, Includes the following steps: Multiple UHPC-NC target specimens were prepared, and raw data were collected through direct shear tests and pull-out tests. Based on the raw data, shear stress-displacement curves and tensile stress-displacement curves were obtained. Shear performance parameters and linear relationships are extracted from the shear stress-displacement curve. The shear size effect law is obtained by fitting analysis of the shear performance parameters. Based on the linear relationship and the shear size effect law, a macroscopic constitutive model of shear is defined. The fracture mechanics quantitative evaluation of the shear performance parameters is carried out. Based on the quantitative evaluation results, the predictive expression of shear resistance and the shear-displacement constitutive model are derived and constructed. Tensile performance parameters are extracted from the tensile stress-displacement curve. The interfacial tensile relationship is obtained by performing a series analysis on the tensile performance parameters. The tensile size effect law is obtained by performing a probability distribution analysis on the tensile performance parameters. Based on the interfacial tensile relationship and the tensile size effect law, the predictive expression for tensile performance and the tensile-fracture constitutive model are derived.

2. The method for predicting the mechanical properties of the UHPC-NC interface considering size effects according to claim 1, characterized in that, Multiple UHPC-NC target specimens were prepared, and raw data were collected through direct shear tests and pull-out tests. Based on the raw data, shear stress-displacement curves and tensile stress-displacement curves were obtained, as follows: Set the interface height condition for the direct shear test and the core diameter condition for the pull-out test, and set the baseline parameters for the interface height and core diameter; Interfacial composite specimens of different geometric dimensions were prepared based on interface height and core diameter conditions. The interfacial composite specimens included direct shear specimens and pull-out specimens. Shear displacement and load of direct shear specimens with different geometric dimensions were collected under direct shear test. Shear stress was calculated based on load and bond area to obtain shear stress-displacement curve. Pull-out displacement and load of pull-out specimens with different geometric dimensions were collected under pull-out test. Tensile stress was calculated based on load and bond area to obtain tensile stress-displacement curve.

3. The method for predicting the mechanical properties of the UHPC-NC interface considering size effects according to claim 1, characterized in that, The shear size effect law is obtained through fitting analysis of the shear performance parameters. Based on the linear relationship and the shear size effect law, a macroscopic constitutive model of shear is defined, including the following steps: The shear performance parameters of the target specimen are normalized based on the baseline parameters; The relationship between the shear performance parameters and the interface height was fitted using the generalized Logistic function on the normalized results to obtain the shear size effect law. The quantitative relationship between shear stress, shear stiffness and displacement is determined based on the linear relationship. The shear stress, shear stiffness and ultimate displacement are characterized based on the shear size effect law. A macroscopic constitutive model of shear is defined. The shear size effect law is expressed as: In the formula, τ c τ represents the peak shear stress of the target specimen. c,100 S represents the peak shear stress of the reference specimen. c S represents the ultimate displacement of the target specimen. c,100 K represents the ultimate displacement of the reference specimen. c K represents the shear stiffness of the target specimen. c,100 3.5 represents the shear stiffness of the reference specimen, 3.5 represents the curvature exponent of the logistic curve steepness, and h represents the interface height. 100 This indicates that the interface height of the reference specimen is 100mm, A τ A s and A k B represents the convergence limit parameter. τ B s and B k Indicates the parameters of the curve inflection point; The expression for the shearing macroscopic constitutive model is: In the formula, τ(s1) represents the shear stress, and K c (h) represents the energy-size coupled shear stiffness function, s1 represents the cumulative interface displacement, and S c This indicates the ultimate displacement.

4. The method for predicting the mechanical properties of the UHPC-NC interface considering size effects according to claim 3, characterized in that, The fracture mechanics parameters of the shear performance are quantitatively evaluated, and the predictive expression for the shear performance is derived based on the quantitative evaluation results, including the following steps: The linear elastic fracture mechanics method is used to evaluate the shear performance parameters. The resistance of the interface to crack propagation is quantified by fracture toughness, and the energy consumption per unit area of ​​crack propagation is quantified by fracture energy. The energy consumption is represented by the total energy consumed per unit fracture area, and the fracture area is calculated by the specimen thickness and maximum displacement. Based on the linear relationship between shear stress and displacement curves in direct shear tests, a linear elastic assumption is made between external load and displacement curves, converting local shear stiffness into overall load stiffness. The relationship between external load and displacement is established based on the overall load stiffness and the cumulative displacement of the interface. The work done by the external load on the interface is calculated within the displacement range from the initial displacement to the maximum displacement. Based on the energy conservation relationship between fracture energy and work done by external load, the expression for the energy-size coupled shear stiffness function is derived by using the expressions for fracture energy and work done by external load. By quantifying the linear relationship between the energy of the interface crack propagation area and the external load and displacement, the relationship between shear stress, shear stiffness and displacement is determined, and a predictive expression for shear performance is derived. The expression for the energy-size coupled shear stiffness function is as follows: In the formula, K c (h) represents the energy-size coupled shear stiffness, G f (h) represents the functional relationship between the interface height and the energy consumed per unit fracture area, S c (h) represents the functional relationship between the interface height and the ultimate displacement, h represents the interface height of the target specimen, B represents the thickness of the target specimen, mg represents the self-weight of the target specimen, and b represents the interface width of the target specimen. The predictive expression for the shear resistance is as follows: t peak (h)=K C S C F peak (h)=τ peak ×bh In the formula, τ peak (h) represents the predicted peak shear stress, K C S represents shear stiffness. C b represents the limit displacement, h represents the interface width, and F represents the interface height. peak (h) represents the predicted interfacial shear strength.

5. The method for predicting the mechanical properties of the UHPC-NC interface considering size effects according to claim 4, characterized in that, The fracture mechanics parameters of the shear performance are quantitatively evaluated, and a shear-displacement constitutive model is derived and constructed based on the quantitative evaluation results, including the following steps: The peak shear stress is determined based on the shear size effect law, and the shear stiffness and ultimate displacement are determined based on the energy conservation relationship. The cumulative interface displacement is used as a variable to derive the shear-displacement constitutive model on the basis of the macroscopic shear constitutive model. The expression for the shear-displacement constitutive model is: In the formula, τ(s1) represents the shear stress, and K c (h) represents the energy-size coupled shear stiffness function, G f (h) represents the functional relationship between the interface height and the energy consumed per unit fracture area, S c (h) represents the functional relationship between the interface height and the ultimate displacement, where h represents the interface height of the target specimen, B represents the thickness of the target specimen, mg represents the self-weight of the target specimen, b represents the interface width of the target specimen, and s1 represents the cumulative displacement of the interface.

6. The method for predicting the mechanical properties of the UHPC-NC interface considering size effects according to claim 1, characterized in that, The tensile property parameters are analyzed in series to obtain the interfacial tensile relationship, including the following steps: Using the three-partition assumption, the interface displacement of UHPC-NC is calculated by connecting the UHPC layer, the interface transition layer and the NC layer in series by limiting displacement; Linear regression was performed on the tensile stiffness, ultimate tensile stress, and ultimate displacement in the pull-out test, and the tensile stiffness of the interface with different geometric dimensions was calculated using a three-part series formula. The expression for the interface displacement is: In the formula, ΔI I S represents the interface displacement of UHPC-NC. t σ represents the ultimate displacement. t E represents the peak tensile stress of the target specimen. UHPC t represents the elastic modulus of the UHPC layer. UHPC E represents the thickness of the UHPC layer. NC t represents the elastic modulus of the NC layer. NC Indicates the thickness of the NC layer; The expression for the interface tensile stiffness is: In the formula, K t ΔI represents the interfacial tensile stiffness of the bonded interface. I σ represents the interface displacement of UHPC-NC. t t represents the peak tensile stress of the target specimen. UHPC E represents the thickness of the UHPC layer. UHPC t represents the elastic modulus of the UHPC layer. NC E represents the thickness of the NC layer. NC This represents the elastic modulus of the NC layer.

7. The method for predicting the mechanical properties of the UHPC-NC interface considering size effects according to claim 6, characterized in that, The tensile size effect law is obtained by performing probability distribution statistical analysis on the tensile property parameters, including the following steps: The volume of the target specimen is characterized by introducing a geometric similarity dimension for the diameter feature dimension, and the shape parameters of the target specimen are characterized by Weibull modulus. Weibull modulus quantization of tensile size effect law under tensile load using Weibull statistical function; Peak tensile stress was calculated using the Weibull power law and the Weibull modulus. The expression for the stretching dimension effect law is: V=D n In the formula, P f (σ) represents the failure probability due to tensile dimensional effects, e represents the natural constant, and V represents the volume of the target specimen. r The reference volume of the specimen is represented by σ, which represents the external stress applied to the target specimen. The external stress is inversely proportional to the shear stress of the characteristic diameter. u σ0 represents the maximum tensile stress corresponding to a failure probability of 0, n represents the geometric similarity dimension, and m represents the shape parameter of the target specimen characterized by the Weibull modulus. The expression for the peak tensile stress is: In the formula, σ t (D) represents the peak tensile stress corresponding to the size effect under different diameter characteristics, σ t,50 This represents the reference tensile stress of the specimen when the diameter characteristic is 50 mm, where D represents the diameter characteristic dimension, and m represents the shape parameter of the target specimen characterized by the Weibull modulus.

8. The method for predicting the mechanical properties of the UHPC-NC interface considering size effects according to claim 7, characterized in that, Based on the interfacial tensile relationship and the tensile size effect law, the predictive expression for tensile properties is derived, including the following steps: The predictive expression for tensile properties is derived based on the peak tensile stress and the tensile area of ​​the interface; The predictive expression for the tensile properties is as follows: F peak (D)=s t (D)×A In the formula, F peak (D) represents the predicted tensile strength, σ t (D) represents the peak tensile stress corresponding to the size effect under different diameter characteristics, and A represents the tensile area of ​​the interface.

9. The method for predicting the mechanical properties of the UHPC-NC interface considering size effects according to claim 7, characterized in that, Based on the interfacial stretching relationship and the stretching size effect law, the stretching-fracture constitutive model is derived, including the following steps: The interface displacement and interface tensile stiffness are determined based on the interface tensile relationship, the peak tensile stress is determined based on the tensile size effect law, and the tensile displacement is used as a variable to derive the tensile-fracture constitutive model. The expression for the tension-fracture constitutive model is: In the formula, σ t (s2) represents the functional relationship between peak tensile stress and tensile displacement, where s2 represents the tensile displacement, S t This indicates the ultimate displacement.

10. A UHPC-NC interface mechanical property prediction system considering size effects, characterized in that, The system is used to execute the UHPC-NC interface mechanical property prediction method considering size effects as described in any one of claims 1-9, the system comprising: The raw data acquisition module is used to prepare multiple UHPC-NC target specimens. Raw data is collected through direct shear tests and pull-out tests. Based on the raw data, shear stress-displacement curves and tensile stress-displacement curves are obtained. The shear size effect analysis module is used to extract shear performance parameters and linear relationships from the shear stress-displacement curve, perform fitting analysis on the shear performance parameters to obtain the shear size effect law, define a macroscopic constitutive model of shear based on the linear relationship and the shear size effect law, perform fracture mechanics quantitative evaluation of the shear performance parameters, and derive and construct the predictive expression of shear resistance and the shear-displacement constitutive model based on the quantitative evaluation results. The tensile size effect analysis module is used to extract tensile performance parameters from the tensile stress-displacement curve, perform cascade analysis on the tensile performance parameters to obtain the interfacial tensile relationship, perform probability distribution analysis on the tensile performance parameters to obtain the tensile size effect law, and derive the predictive expression for tensile performance and the tensile-fracture constitutive model based on the interfacial tensile relationship and the tensile size effect law.

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