New method for fitting UHPC load-crack opening displacement curve

Abstract

The invention belongs to the technical field of civil engineering, and discloses a novel method for fitting a UHPC load-crack opening displacement curve, which comprises the following steps: S1, test preparation, pretreatment of a concrete test piece, measurement and calculation of basic data of the test piece, and recording of parameter data of the test piece; according to the method, through the performance parameter c and the mechanical coefficient d of the UHPC, the corrected formula can more accurately reflect the mechanical characteristics of the UHPC in the crack expansion process; by correcting a fitting formula, a P-CMOD curve with higher goodness of fit is obtained, the explanation ability and the prediction ability of the model are enhanced, the fracture energy and the like of UHPC are convenient to calculate in the next step, a more applicable fracture energy calculation method is provided for UHPC, and wide application of UHPC in the engineering field is promoted; although new parameters are introduced into the correction fitting formula, a relatively simple form is still kept on the whole, so that the formula can be more conveniently applied in the actual calculation process, and the calculation complexity and the time cost are reduced.

Description

Technical Field

[0001] The invention belongs to the technical field of civil engineering, and in particular relates to a new method for fitting a UHPC load-crack opening displacement curve. Background Art

[0002] Concrete fracture energy is used to characterize the ability of materials to resist crack propagation. Fracture energy, also known as breaking energy, refers to the energy required for crack propagation per unit area. For the calculation of fracture energy, a fitting curve is introduced in the calculation of fracture energy to achieve a mathematical description of the relationship between crack opening displacement (CMOD) and load (P). By fitting the P-CMOD curve, quantitative information about the crack propagation behavior of concrete materials under stress can be obtained, and the crack propagation law of concrete materials under load can be revealed by fitting the P-CMOD curve. By observing the shape, slope and other characteristics of the curve, the elasticity, plasticity, damage evolution and other characteristics of the material can be understood.

[0003] The fitting curves and fitting formulas in the existing fracture energy calculation have significant deficiencies in describing the fracture behavior of concrete. As concrete is a multiphase composite material, the complexity of its internal structure and defects has an important influence on the fracture behavior. However, in the fitting process, these complex factors are often simplified into a single mechanical parameter, such as tensile strength, elastic modulus, etc., resulting in the fitting curve being unable to accurately reflect the true fracture characteristics of concrete. Moreover, this simplified processing not only ignores the characteristics of pores, microcracks, and uneven aggregate distribution inside the concrete, but also fails to fully capture the nonlinear characteristics in the fracture process, such as the effects of elastic-plastic transition and damage evolution, thereby limiting the accuracy and applicability of the fitting curve.

[0004] In addition, the existing fitting formulas are derived based on simplified material models and linear or simplified nonlinear models, which fail to fully consider the complexity of the concrete fracture process and more nonlinear factors. They have limitations in predicting the fracture behavior of concrete and cannot accurately reflect the fracture performance of materials under different load conditions. As a result, the fracture energy calculated by the existing technology deviates greatly from the actual situation, thereby limiting the accuracy of the evaluation of the crack resistance of concrete structures and resulting in poor calculation and application effects. Summary of the invention

[0005] The object of the present invention is to provide a new method for fitting the UHPC load-crack opening displacement curve to solve the problems raised in the above background technology.

[0006] In order to achieve the above object, the present invention provides the following technical solution: a new method for fitting the UHPC load-crack opening displacement curve, comprising the following steps:

[0007] S1. Experimental preparation

[0008] Specimen pretreatment, prefabrication of cracks, speckle production, and posting of strain gauges;

[0009] Record specimen parameter data;

[0010] Select the fixture and obtain the fixture parameters;

[0011] Select the load and obtain the load structure parameters;

[0012] S2. Perform three-point bending test

[0013] A three-point bending load was applied to the specimen on the test device, and the changes in load and crack opening displacement were recorded simultaneously;

[0014] A micro-displacement measuring device is installed near the crack mouth to measure the tiny opening displacement of the crack mouth with high precision, and DIC (digital image correlation technology) and displacement meter are used to measure at the same time, and CMOD is recorded together to ensure accuracy;

[0015] S3. Obtain P-CMOD curve

[0016] Obtain test data, and process and verify the data;

[0017] According to the corrected and processed test data, the relationship curve between load (P) and crack opening displacement (CMOD), namely P-CMOD curve, is drawn;

[0018] S4. Select and modify the fitting formula

[0019] Select the fitting formula of ordinary concrete, and according to the characteristics of UHPC, the correction coefficient is used to obtain the corrected fitting formula;

[0020] S5. Perform curve fitting

[0021] Mathematical software was used to fit the P-CMOD curve;

[0022] According to the fitting formula and test data, solve the parameters in the formula;

[0023] Check the accuracy and reliability of the fitting results, and use goodness of fit and residual analysis to make judgments;

[0024] When fitting the P-CMOD curve, the nonlinear dynamic analysis method is introduced to reveal the nonlinear dynamic behavior of concrete during crack propagation.

[0025] S6. Calculation of fracture energy

[0026] According to the parameters and formula obtained by fitting, substitute them into the formula for calculating the fracture energy of concrete;

[0027]

[0028] Among them, f(CMOD) is the fitted formula; g(CMOD) is also a function of θ about CMOD, where θ is the crack opening angle, which can be calculated by CMOD, CMOD0 is the crack opening displacement corresponding to the complete fracture of the beam, S is the span of the specimen, and m is the mass of the specimen.

[0029]

[0030] Where E is the elastic modulus, B is the thickness, and D is the height;

[0031] S7. Result analysis and verification

[0032] Analyze and compare the calculation results to evaluate the influence of different parameters on the fracture energy;

[0033] Compare and verify with other test methods.

[0034] Preferably, in S1, the basic data include: specimen length, width, thickness, compressive strength, elastic modulus and mass; the fixture parameters include: stiffness, fixture friction coefficient; the load structure data include: contact area, load structure friction coefficient, specimen data acquisition stage, excluding specimens with no obvious defects, defects include: cracks, bubbles, inclusions.

[0035] Preferably, in S2, the micro-displacement measuring device is one or any one of a laser interferometer, a vibrating wire joint meter, and a capacitive displacement sensor.

[0036] Preferably, in S3, data processing includes data cleaning and data verification, wherein data cleaning specifically includes: removing abnormal data points caused by sensor failure and external interference, and smoothing the data to reduce the impact of noise; data verification specifically includes: using digital image technology to verify the full-field displacement and strain information to make the displacement data accurate, and determining the synchronization and consistency of the load and CMOD data through cross-validation and comparative analysis.

[0037] Preferably, in S3, in the P-CMOD curve, the vertical axis represents the load P, and the horizontal axis represents the crack opening displacement CMOD (i.e., the width or opening degree of the crack). The shape of the P-CMOD curve can reflect the mechanical properties and crack propagation characteristics of the specimen structure.

[0038] Preferably, in S4, the P-CMOD curve fitting formula of ordinary concrete is:

[0039]

[0040] Where f(CMOD) is the crack opening displacement, x is the load force P, and a 1is a high-order nonlinear parameter, a 2 is a medium nonlinear parameter, a 3 is the load influence factor, a 4 is the fixture influence factor, b 1 is the material coefficient of the specimen, b 2 is the load deviation coefficient.

[0041] Preferably, in S4, the modified P-CMOD curve fitting formula is:

[0042]

[0043] Among them, c is the performance parameter of UHPC ultra-high performance concrete, and d is the mechanical coefficient of UHPC ultra-high performance concrete.

[0044] Preferably, the performance parameters of the UHPC ultra-high performance concrete are determined by the following formula:

[0045]

[0046] Among them, α fcu , α fck , α ft They are the compressive coefficient, axial compressive coefficient, and tensile coefficient of UHPC ultra-high performance concrete, respectively. cu 、f ck 、f t They are the compressive strength, axial compressive strength and tensile strength of UHPC ultra-high performance concrete.

[0047] Preferably, the mechanical coefficient of the UHPC ultra-high performance concrete is determined by the following formula:

[0048]

[0049] Among them, f cu is the compressive strength, S is the specimen span, k is the fracture toughness, and H is the specimen cross-sectional area.

[0050] Preferably, the mathematical software adopts one or any one of MATLAB and Python, and the nonlinear dynamic analysis method is a phase space reconstruction method.

[0051] The beneficial effects of the present invention are as follows:

[0052] 1. The present invention takes into account the unique properties of UHPC, including ultra-high strength, ductility, fiber bridging effect, etc., by introducing and using a modified fitting formula, thereby more accurately reflecting the mechanical behavior of UHPC in a three-point bending test, and by introducing UHPC performance parameters and mechanical coefficients, the modified formula can more accurately describe the relationship between the load and the crack opening displacement during the crack extension process, thereby improving the calculation accuracy of the UHPC fracture energy, and by introducing the UHPC ultra-high performance concrete performance parameter c and mechanical coefficient d, the modified formula can more accurately reflect the mechanical properties of UHPC during the crack extension process; by modifying the fitting formula, a P-CMOD curve with a higher goodness of fit is obtained, the explanatory and predictive capabilities of the model are enhanced, and the next step of calculating the fracture energy of UHPC is convenient, and a more suitable method for calculating the fracture energy of UHPC is provided, which is helpful to promote the wide application of UHPC in the engineering field; although the modified fitting formula introduces new parameters, it still maintains a relatively simple form as a whole, which makes it more convenient to apply the formula in the actual calculation process, reducing the calculation complexity and time cost.

[0053] 2. The present invention installs a micro-displacement measuring device near the crack mouth. The micro-displacement measuring device has high-precision measurement capability and can accurately capture the tiny opening displacement of the crack mouth, thereby improving measurement accuracy. The micro-displacement measuring device can be used to monitor the expansion of the crack in real time. The high-precision data provided by the micro-displacement measuring device can provide strong data support for scientific research. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 It is a schematic diagram of the calculation process of the present invention. DETAILED DESCRIPTION

[0055] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0056] like Figure 1 As shown, an embodiment of the present invention provides a new method for fitting a UHPC load-crack opening displacement curve, comprising the following steps:

[0057] S1. Experimental preparation

[0058] Specimen pretreatment, prefabrication of cracks, speckle production, and posting of strain gauges;

[0059] Record specimen parameter data;

[0060] Select the fixture and obtain the fixture parameters;

[0061] Select the load and obtain the load structure parameters;

[0062] S2. Perform three-point bending test

[0063] A three-point bending load was applied to the specimen on the test device, and the changes in load and crack opening displacement were recorded simultaneously;

[0064] A micro-displacement measuring device is installed near the crack mouth to measure the tiny opening displacement of the crack mouth with high precision, and DIC (digital image correlation technology) and displacement meter are used to measure at the same time, and CMOD is recorded together to ensure accuracy;

[0065] S3. Obtain P-CMOD curve

[0066] Obtain test data, and process and verify the data;

[0067] According to the corrected and processed test data, the relationship curve between load (P) and crack opening displacement (CMOD), namely P-CMOD curve, is drawn;

[0068] S4. Select and modify the fitting formula

[0069] Select the fitting formula of ordinary concrete, and according to the characteristics of UHPC, the correction coefficient is used to obtain the corrected fitting formula;

[0070] S5. Perform curve fitting

[0071] Mathematical software was used to fit the P-CMOD curve;

[0072] According to the fitting formula and test data, solve the parameters in the formula;

[0073] Check the accuracy and reliability of the fitting results, and use goodness of fit and residual analysis to make judgments;

[0074] When fitting the P-CMOD curve, the nonlinear dynamic analysis method is introduced to reveal the nonlinear dynamic behavior of concrete during crack propagation.

[0075] S6. Calculation of fracture energy

[0076] According to the parameters and formula obtained by fitting, substitute them into the formula for calculating the fracture energy of concrete;

[0077]

[0078] Among them, f(CMOD) is the fitted formula; g(CMOD) is also a function of θ about CMOD, where θ is the crack opening angle, which can be calculated by CMOD, CMOD0 is the crack opening displacement corresponding to the complete fracture of the beam, S is the span of the specimen, and m is the mass of the specimen.

[0079]

[0080] Where E is the elastic modulus, B is the thickness, and D is the height;

[0081] S7. Result analysis and verification

[0082] Analyze and compare the calculation results to evaluate the influence of different parameters on the fracture energy;

[0083] Compare and verify with other test methods.

[0084] By introducing and using the modified fitting formula, the unique properties of UHPC, including ultra-high strength, ductility, fiber bridging effect, etc., are taken into account, thereby more accurately reflecting the mechanical behavior of UHPC in the three-point bending test. By introducing UHPC performance parameters and mechanical coefficients, the modified formula can more accurately describe the relationship between load and crack opening displacement during crack propagation, thereby improving the calculation accuracy of UHPC fracture energy. By introducing UHPC ultra-high performance concrete performance parameter c and mechanical coefficient d, the modified formula can more accurately reflect the mechanical properties of UHPC during crack propagation. By modifying the fitting formula, a P-CMOD curve with higher goodness of fit is obtained, which enhances the explanatory and predictive capabilities of the model, facilitates the next step of calculating the fracture energy of UHPC, and provides a more applicable method for calculating fracture energy for UHPC, which helps to promote the widespread application of UHPC in the engineering field. Although the modified fitting formula introduces new parameters, it still maintains a relatively simple form as a whole, which makes it more convenient to apply the formula in the actual calculation process, reducing the calculation complexity and time cost.

[0085] By installing a micro-displacement measuring device near the crack mouth, the micro-displacement measuring device has high-precision measurement capabilities and can accurately capture the tiny opening displacement of the crack mouth, thereby improving the measurement accuracy. Moreover, through the micro-displacement measuring device, the expansion of the crack can be monitored in real time. Moreover, the high-precision data provided by the micro-displacement measuring device can provide strong data support for scientific research.

[0086] Among them, in S1, the basic data include: specimen length, width, thickness, compressive strength, elastic modulus and mass; the fixture parameters include: stiffness, fixture friction coefficient; the load structure data include: contact area, load structure friction coefficient, specimen data acquisition stage, exclude specimens without obvious defects, defects include: cracks, bubbles, inclusions.

[0087] Specimen length, width, thickness, compressive strength, elastic modulus and mass: These parameters are the basis for mechanical analysis of concrete, directly affecting the bearing capacity, deformation characteristics and fracture behavior of the specimen, and determining the correlation coefficient in the original fitting formula through the parameter values, affecting the value of the reference coefficient.

[0088] The test pieces should be prepared in accordance with relevant standards or specifications to ensure the uniformity of their size, shape and internal structure. During the preparation process, defects such as cracks and bubbles should be avoided.

[0089] Among them, in S2, the micro-displacement measuring device is one or any one of a laser interferometer, a vibrating wire joint meter, and a capacitive displacement sensor.

[0090] The micro-displacement measurement device has high-precision measurement capabilities and can capture tiny displacement changes.

[0091] When using a laser interferometer, based on the principle of optical interference, the laser beam is split and then recombined after being reflected on both sides of the measured object to form interference fringes. The slight changes in the interference fringes reflect the displacement of the measured object:

[0092] Experimental calculation process using laser interferometer:

[0093] Step 1: Select the laser interferometer model, control the measurement environment under constant temperature, constant humidity and vibration-free conditions, ensure that there is no strong light interference in the measurement area to avoid affecting the normal operation of the laser interferometer, and calibrate the laser interferometer before use;

[0094] Step 2: Install the laser interferometer on a stable bracket, adjust the distance between the laser head and the concrete to be measured, ensure that the laser beam can accurately irradiate the surface of the concrete to be measured, adjust the reflector and the beam splitter to the best position, so that the laser beam can accurately reflect and interfere, then preheat the laser head for 5 minutes, dim it, rotate the laser head shutter to the dimming state, adjust the reflector and the beam splitter, so that the two points coincide with the center of the white circle at the near end and the far end;

[0095] Step 3: Set the measurement range, sampling frequency and resolution of the laser interferometer;

[0096] Run the laser interferometer measurement software and perform relevant settings and initialization;

[0097] The software interface should display clear interference fringes and measurement data;

[0098] Step 4: Start the measurement program, and the laser interferometer will begin to record the micro-displacement changes of the crack being measured;

[0099] Step 5: After the measurement is completed, the measurement data is exported to the computer for processing and analysis;

[0100] Use scientific methods and tools to process data, including data smoothing, filtering and fitting.

[0101] Among them, in S3, data processing includes data cleaning and data verification. Data cleaning is specifically: removing abnormal data points caused by sensor failure and external interference, and smoothing the data to reduce the impact of noise; data verification is specifically: using digital image technology to verify the full-field displacement and strain information to make the displacement data accurate, and through cross-validation and comparative analysis, determine the synchronization and consistency of load and CMOD data.

[0102] By identifying and removing abnormal data caused by sensor failure or external interference, we can avoid these data from misleading the overall data analysis results and improve the accuracy and credibility of the data; smoothing the data can effectively reduce the impact of noise, making the data smoother and more continuous, which is conducive to revealing the potential patterns and trends in the data.

[0103] By verifying the full-field displacement and strain information through digital imaging technology, the accuracy of the displacement data can be ensured, which is particularly important in the fields of structural health monitoring and engineering safety assessment. Through cross-validation and comparative analysis, the synchronization and consistency of load and displacement data can be determined, and the reliability and integrity of the data can be further verified, providing reliable data support for subsequent mechanical analysis, structural design, etc.

[0104] In the actual data processing process, missing data points can be filled by interpolation, mean filling, regression prediction and other methods to ensure the integrity of the data; and duplicate records in the data set can be removed to avoid the impact of data redundancy on the analysis results; and the data can be converted to the same dimension or range to facilitate subsequent data analysis and model training.

[0105] Among them, in S3, in the P-CMOD curve, the vertical axis represents the load P, and the horizontal axis represents the crack opening displacement CMOD (i.e., the width or opening degree of the crack). The shape of the P-CMOD curve can reflect the mechanical properties and crack extension characteristics of the specimen structure.

[0106] Among them, in S4, the P-CMOD curve fitting formula of ordinary concrete is:

[0107]

[0108] Where f(CMOD) is the crack opening displacement, x is the load force P, and a 1 is a high-order nonlinear parameter, a 2 is a medium nonlinear parameter, a 3 is the load influence factor, a 4 is the fixture influence factor, b 1 is the material coefficient of the specimen, b 2 is the load deviation coefficient.

[0109] x: represents the load force P, which is the main variable input into the formula and is used to calculate the corresponding crack opening displacement;

[0110] a 1 (High-order nonlinear parameter): It affects the high-order nonlinear part of the curve and determines the shape and change trend of the curve under a large load. 1 When is larger, the curve shows stronger nonlinearity at higher loads.

[0111] a 2 (Medium nonlinear parameter): affects the medium nonlinear part of the curve, has an important influence on the shape of the curve in the medium load range, and helps to adjust the slope and smoothness of the curve under medium load;

[0112] a 3 (Load influence factor): directly affects the linear relationship between load and crack opening displacement. 3 When changes, the overall slope of the curve (i.e., the degree of influence of the load on the crack opening displacement) will change;

[0113] a 4 (Fixture influence factor): reflects the effect of the fixture on the crack opening displacement. Factors such as fixture design, material and tightening degree may affect the crack opening displacement through a 4 Reflected in the P-CMOD curve;

[0114] b 1 (Specimen material coefficient): related to the material of the specimen, affecting the shape and position of the curve. Different specimen materials (such as concrete of different strength grades) make b 1 The value of is different, thus affecting the overall trend of the curve;

[0115] b 2 (Load Deviation Coefficient): reflects the deviation in the load measurement or application process. When the load measurement is inaccurate or there is a systematic error, b 2 The value of changes, thus affecting the accuracy and reliability of the curve.

[0116] The above formula describes and fits the nonlinear relationship between load (P) and crack opening displacement (CMOD) of ordinary concrete during loading. This formula can be used to predict the crack expansion of concrete under different loads, providing a mathematical tool for structural safety assessment and fracture performance research.

[0117] Among them, in S4, the modified P-CMOD curve fitting formula is:

[0118]

[0119] Among them, c is the performance parameter of UHPC ultra-high performance concrete, and d is the mechanical coefficient of UHPC ultra-high performance concrete.

[0120] Among them, the performance parameters of UHPC ultra-high performance concrete are determined by the following formula:

[0121]

[0122] Among them, α fcu , α fck , α ft They are the compressive coefficient, axial compressive coefficient, and tensile coefficient of UHPC ultra-high performance concrete, respectively. cu 、f ck 、f t They are the compressive strength, axial compressive strength and tensile strength of UHPC ultra-high performance concrete.

[0123] Among them, the mechanical coefficient of UHPC ultra-high performance concrete is determined by the following formula:

[0124]

[0125] Among them, f cu is the compressive strength, S is the specimen span, k is the fracture toughness, and H is the specimen cross-sectional area.

[0126] c: As a performance parameter of UHPC, c comprehensively reflects the influence of factors such as concrete hardness, thickness and aggregate strength on the P-CMOD relationship;

[0127] d: As the mechanical coefficient of UHPC ultra-high performance concrete, d reflects the influence of concrete compressive strength, tensile strength, toughness coefficient and effective section of specimen on the P-CMOD relationship.

[0128] The correction term is jointly affected by c and d, thereby affecting the shape and position of the entire P-CMOD curve.

[0129] By introducing the performance parameter c and mechanical coefficient d of UHPC ultra-high performance concrete, the revised formula can more accurately describe the P-CMOD relationship, especially under high load or complex stress states. The revised formula not only takes into account the basic relationship between load and crack opening displacement, but also takes into account the influence of multiple factors such as concrete hardness, thickness, aggregate strength, compressive strength, tensile strength, toughness coefficient and load contact area, making the formula more comprehensive and practical. Since UHPC ultra-high performance concrete has excellent mechanical properties and broad application prospects, the revised formula can better adapt to the research and application needs of this high-performance material. The revised formula provides new mathematical tools and ideas for the research in the field of concrete fracture mechanics, which is helpful to promote the improvement and innovation of related theories.

[0130] The mathematical software adopts one or any one of MATLAB and Python, and the nonlinear dynamic analysis method adopts the phase space reconstruction method.

[0131] The phase space reconstruction method can recover the system's multidimensional phase space from limited one-dimensional time series data, thereby revealing the dynamic characteristics and structure of the system; through phase space reconstruction, the one-dimensional time series can be expanded to a high-dimensional space, so that the behavior of the computational method can be described more accurately, which helps to improve the accuracy and reliability of computational analysis.

[0132] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A new method for fitting UHPC load-crack opening displacement curve, characterized by: The following steps are involved: S1. Experimental preparation Specimen pretreatment, prefabrication of cracks, speckle production, and posting of strain gauges; Record specimen parameter data; Select the fixture and obtain the fixture parameters; Select the load and obtain the load structure parameters; S2. Perform three-point bending test A three-point bending load was applied to the specimen on the test device, and the changes in load and crack opening displacement were recorded simultaneously; A micro-displacement measuring device is installed near the crack mouth to measure the tiny opening displacement of the crack mouth with high precision, and DIC (digital image correlation technology) and displacement meter are used to measure at the same time, and CMOD is recorded together to ensure accuracy; S3. Obtain P-CMOD curve Obtain test data, and process and verify the data; According to the corrected and processed test data, the relationship curve between load (P) and crack opening displacement (CMOD), namely P-CMOD curve, is drawn; S4. Select and modify the fitting formula Select the fitting formula of ordinary concrete, and according to the characteristics of UHPC, the correction coefficient is used to obtain the corrected fitting formula; S5. Perform curve fitting Mathematical software was used to fit the P-CMOD curve; According to the fitting formula and test data, solve the parameters in the formula; Check the accuracy and reliability of the fitting results, and use goodness of fit and residual analysis to make judgments; When fitting the P-CMOD curve, the nonlinear dynamic analysis method is introduced to reveal the nonlinear dynamic behavior of concrete during crack propagation. S6. Calculation of fracture energy According to the parameters and formula obtained by fitting, substitute them into the formula for calculating the fracture energy of concrete; Among them, f(CMOD) is the fitted formula; g(CMOD) is also a function of θ about CMOD, where θ is the crack opening angle, which can be calculated by CMOD, CMOD0 is the crack opening displacement corresponding to the complete fracture of the beam, S is the span of the specimen, and m is the mass of the specimen. Where E is the elastic modulus, B is the thickness, and D is the height; S7. Result analysis and verification Analyze and compare the calculation results to evaluate the influence of different parameters on the fracture energy; Compare and verify with other test methods.

2. The novel method for fitting UHPC load-crack opening displacement curve according to claim 1, characterized in that: In S1, the basic data include: specimen length, width, thickness, compressive strength, elastic modulus and mass; the fixture parameters include: stiffness, fixture friction coefficient; the load structure data include: contact area, load structure friction coefficient, specimen data acquisition stage, exclude specimens without obvious defects, defects include: cracks, bubbles, inclusions.

3. The novel method for fitting UHPC load-crack opening displacement curve according to claim 1, characterized in that: In S2, the micro-displacement measuring device is one or any one of a laser interferometer, a vibrating wire joint meter, and a capacitive displacement sensor.

4. The novel method for fitting UHPC load-crack opening displacement curve according to claim 1, characterized in that: In S3, data processing includes data cleaning and data verification. Specifically, data cleaning includes: removing abnormal data points caused by sensor failure and external interference, and smoothing the data to reduce the impact of noise; The data verification is specifically as follows: the full-field displacement and strain information is verified using digital image technology to make the displacement data accurate, and the synchronization and consistency of the load and CMOD data are determined through cross-validation and comparative analysis.

5. The novel method for fitting UHPC load-crack opening displacement curve according to claim 4, characterized in that: In S3, in the P-CMOD curve, the vertical axis represents the load P, and the horizontal axis represents the crack opening displacement CMOD (i.e., the width or opening degree of the crack). The shape of the P-CMOD curve can reflect the mechanical properties and crack extension characteristics of the specimen structure.

6. The novel method for fitting UHPC load-crack opening displacement curve according to claim 1, characterized in that: In S4, the P-CMOD curve fitting formula of ordinary concrete is: Among them, f(CMOD) is the crack opening displacement, x is the load force P, a1 is the high-order nonlinear parameter, a2 is the medium nonlinear parameter, a3 is the load influence factor, a4 is the fixture influence factor, b1 is the specimen material coefficient, and b2 is the load deviation coefficient.

7. The novel method for fitting UHPC load-crack opening displacement curve according to claim 6, characterized in that: In S4, the modified P-CMOD curve fitting formula is: Among them, c is the performance parameter of UHPC ultra-high performance concrete, and d is the mechanical coefficient of UHPC ultra-high performance concrete.

8. The novel method for fitting UHPC load-crack opening displacement curve according to claim 7, characterized in that: The performance parameters of the UHPC ultra-high performance concrete are determined by the following formula: Among them, α fcu , α fck , α ft They are the compressive coefficient, axial compressive coefficient, and tensile coefficient of UHPC ultra-high performance concrete, respectively. cu 、f ck 、f t They are the compressive strength, axial compressive strength and tensile strength of UHPC ultra-high performance concrete.

9. The novel method for fitting UHPC load-crack opening displacement curve according to claim 8, characterized in that: The mechanical coefficient of the UHPC ultra-high performance concrete is determined by the following formula: Among them, f cu is the compressive strength, S is the specimen span, k is the fracture toughness, and H is the specimen cross-sectional area.

10. The novel method for fitting UHPC load-crack opening displacement curve according to claim 1, characterized in that: The mathematical software adopts one or any one of MATLAB and Python, and the nonlinear dynamic analysis method is a phase space reconstruction method.

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