Method for constructing bridge force model of ductile concrete considering fiber pull-out randomness

Abstract

This invention discloses a method for constructing a ductile concrete bridging force model considering the randomness of fiber pull-out, belonging to the field of model construction technology. The method involves modeling and calculating the number of fibers in a cross-section; randomly assigning embedment depth and angle to each fiber; obtaining random distribution parameters of characteristic values ​​for each fiber; generating a simplified pull-out curve model for each fiber; establishing a fiber truncation algorithm; superimposing the pull-out curves of single fibers to establish a fiber bridging force model with randomness in single fiber pull-out; and applying the bridging force model. This construction method introduces randomness into single fiber pull-out, calculates the number of fibers in the cross-section and the fiber breakage rate to fit the pull-out curve of a single fiber, and sequentially superimposes the pull-out curves of all fibers on the cross-section according to the minimum step size of data acquisition, establishing a random bridging force model based on a three-segment line of single fiber pull-out. The analysis results show strong consistency with experimental data, making it suitable for guiding the design and optimization of the macroscopic properties of composite materials.

Description

Technical Field

[0001] This invention relates to the field of model building technology, and more specifically to a method for constructing a ductile concrete bridge joint model that takes into account the randomness of fiber pull-out. Background Technology

[0002] Promoting the construction of resilient cities is of great significance for enhancing urban safety and sustainable development, and the research and development of high-performance concrete materials is a key technological link in the path of infrastructure resilience development. Ultra-high ductility concrete (UHDC), as a new type of building material, has excellent mechanical properties and crack control capabilities. Its engineering applications can improve the seismic resistance, fire resistance, and blast resistance of infrastructure, contributing to the systematic construction of resilient cities.

[0003] Fiber bridging relationships are crucial principles connecting the microscopic characteristics and macroscopic properties of composite materials. They describe the relationship between fiber bridging stress and crack opening displacement across cracks, determining the value of fiber bridging supplementary energy and being a key factor in achieving steady-state cracking and strain hardening behavior in ultra-high ductility concrete (UHDC). Due to the highly complex distribution of fiber and matrix defects within UHDC, the interfacial bond-slip behavior between fibers and the matrix often exhibits strong stochastic characteristics. However, previous fiber bridging force models did not consider this factor, instead relying on numerous assumptions and simplifications derived through theoretical analysis. Deterministic theoretical models struggle to describe the stochastic characteristics during fiber pull-out. Therefore, establishing a stochastic distribution-based UHDC bridging force model can provide a theoretical foundation for the design and prediction of UHDC's tensile properties.

[0004] The bridging stress-displacement model is a probabilistic micromechanical model used to describe the tensile properties of short-fiber composites in brittle matrices, particularly considering fiber pull-out, fiber breakage, and local friction effects. However, this model does not account for the randomness of fiber pull-out under the same loading conditions. Furthermore, it does not consider the influence of fiber embedment depth on bridging stress when inclined fibers are pulled out of the matrix, nor the possibility of partial fiber breakage due to crack propagation during loading. Introducing randomness into the single-fiber pull-out process and considering the relationship between fiber breakage rate, fiber embedment depth, and pull-out angle, and superimposing the single-fiber pull-out curves at the cross-section, could yield an ultra-high ductility concrete bridging stress model that satisfies various fiber embedment depths and angles. This would be of great significance for the research and development of composite materials. Summary of the Invention

[0005] The purpose of this invention is to provide a method for constructing a ductile concrete bridge joint force model that takes into account the randomness of fiber pull-out, so as to solve the problems in the prior art.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a method for constructing a ductile concrete bridge joint force model considering the randomness of fiber pull-out, the method comprising the following steps:

[0007] Modeling and calculating the number of fibers in the cross-section;

[0008] Randomly assign burial depth and angle to each fiber;

[0009] Obtain the random distribution parameters of the characteristic values ​​of each fiber;

[0010] Generate a pull-out curve for each fiber;

[0011] Establish a fiber truncation algorithm;

[0012] By superimposing the pull-out curves of single fibers, a bridging force model for the randomness of single fiber pull-out is established.

[0013] Apply the bridging force model.

[0014] Preferably, the fiber truncation algorithm includes the following steps:

[0015] Obtain two-dimensional grouping units;

[0016] The fiber breakage rate at the boundary points of two-dimensional grouped units is calculated using the cutoff rate calculation formula.

[0017] The arithmetic mean of the fracture rates at the boundary points is taken as the average fracture rate of this two-dimensional grouped element. ;

[0018] Calculate the number N of broken fibers in this two-dimensional grouping unit. b The expression is: N b = • N, where N is the total number of fibers in this two-dimensional grouping unit;

[0019] Within each two-dimensional grouping unit, the top N fibers are selected by sorting them from largest to smallest single-fiber pull-out peak force. b Root fibers are considered as candidates for fracture.

[0020] Determine the minimum peak force F among candidate fibers min and the minimum peak force F min Set as the cutoff threshold;

[0021] Traversing the pull-out curves of candidate fibers, the minimum peak force F is first reached in the rising segment of the pull-out curve. min The force is cut off at the corresponding displacement point, and the subsequent pull-out force is reduced to zero.

[0022] Preferably, the logic for obtaining the two-dimensional grouping unit is as follows:

[0023] Based on the fiber burial depth range, it is divided into Ng There are three equal-width groups, each with a width of w. For each burial depth group, it is further divided into M angle subgroups according to the range of extraction angles, forming an M×N group. g Two-dimensional grouping unit.

[0024] Preferably, each fiber is randomly assigned a burial depth and angle, including the following steps:

[0025] Input the total number of fibers N and the fiber length L. f and the fiber burial depth d distribution range [0, L] f The distribution range of [π / 2] and angle θ is [0, π / 3];

[0026] In Matlab software, the rand function is used to generate the fiber burial depth d for each fiber. i and angle θ i ;

[0027] A set of fiber parameters is formed based on the generation results. .

[0028] Preferably, the rand function in Matlab software is used to generate the fiber burial depth d for each fiber according to the following rules. i and angle θ i The expression is: , where L f Where θ is the fiber length, and π / 3 is the maximum value of the angle θ distribution range.

[0029] Preferably, a pull-out curve is generated for each fiber by randomly assigning the debonding force, debonding displacement, peak force and peak displacement of each fiber when it is pulled out from the random distribution parameters of the fiber characteristic values, thereby obtaining a three-fold line pull-out curve for each fiber.

[0030] Preferably, the modeling and calculation of the number of fibers in the cross-section includes the following steps:

[0031] Obtain the specimen dimensions, fiber volume fraction, and fiber length;

[0032] The total number of fibers N in the specimen was determined using Matlab software.

[0033] A three-dimensional rectangular coordinate system OXYH is constructed with the geometric center of the specimen as the origin, where the X and Y axes are parallel to the cross-section of the specimen, and the H axis is perpendicular to the cross-section.

[0034] The Monte Carlo random function is used to generate the midpoint coordinates of each fiber within the specimen boundary range, and the fiber orientation angle parameters α and β are randomly generated.

[0035] The fiber endpoint extends beyond the side boundary perpendicular to the XOY plane, with the boundary intersection as the reflection point, maintaining the original direction of the fiber's angular reflection extension;

[0036] Set the target cross-section position H=h0. If the two ends of the fiber satisfy dh1≤h0≤dh2 or dh2≤h0≤dh1, then it is determined that the fiber passes through the cross-section. Count the fibers that pass through the cross-section, repeat the count S times, and take the average value as the number of fibers in the cross-section.

[0037] Preferably, the total number of fibers N in the specimen is determined using Matlab software, and the expression is: In the formula: N is the total number of fibers within a given specimen size at the corresponding fiber content; V f The total fiber volume is represented by X, H, and Y, which represent the length, width, and height of the specimen, respectively; L represents the total fiber volume. f denoted as 'F', where 'D' is the fiber length and 'D' is the fiber diameter.

[0038] Preferably, the coordinates of the two ends of the fiber are calculated based on the coordinates of the fiber midpoint, the orientation angle, and the fiber length: Where (dx1, dy1, dh1) and (dx2, dy2, dh2) are the three-dimensional coordinates of the two ends of the fiber, α and β are the fiber orientation angle parameters, and L f f is the fiber length. x f h f y This represents the coordinate components of the midpoint of the fiber.

[0039] Preferably, the superimposed pull-out curve of a single fiber includes the following steps:

[0040] Determine the minimum step size for data acquisition;

[0041] The pull-out curves of all fibers on the cross section are superimposed point by point in sequence;

[0042] The fiber bridging force-opening displacement curve of a single cross section is obtained, which is the fiber bridging force model.

[0043] The technical effects and advantages provided by the present invention in the above technical solution are as follows:

[0044] This application introduces randomness into single fiber pull-out. By calculating the number of fibers in the cross section and the fiber breakage rate, the pull-out curve of a single fiber is fitted. The pull-out curves of all fibers on the cross section are then superimposed point by point according to the minimum step size of data acquisition. A bridging force stochastic model based on the three-segment line of single fiber pull-out is established. The analysis results show strong consistency with the experimental data and are suitable for exploring the microscopic characteristics and macroscopic properties of composite materials. Attached Figure Description

[0045] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this invention. For those skilled in the art, other drawings can be obtained based on these drawings.

[0046] Figure 1 This is a flowchart of the construction method of the present invention;

[0047] Figure 2 This is a schematic diagram of the single-fiber drawing process of the present invention;

[0048] Figure 3 This is a bridging force model diagram considering the randomness of fiber pull-out under different fiber content conditions according to the present invention.

[0049] In the diagram: 1. Universal testing machine; 2. Load sensor; 3. Iron sheet; 4. Single fiber; 5. Matrix. Detailed Implementation

[0050] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0051] Example: This example provides a method for constructing a ductile concrete bridge splice model that considers the randomness of fiber pull-out. Please refer to [link / reference]. Figures 1-3 As shown, the construction method includes the following steps:

[0052] Modeling and calculating the number of fibers in the cross-section;

[0053] Randomly assign burial depth and angle to each fiber;

[0054] Obtain the random distribution parameters of the characteristic values ​​of each fiber;

[0055] Generate a pull-out curve for each fiber;

[0056] Establish a fiber truncation algorithm;

[0057] By superimposing the pull-out curves of single fibers, a bridging force model for the randomness of single fiber pull-out is established.

[0058] Apply the bridging force model.

[0059] The accuracy and applicability of the construction method can be estimated and verified by the measured values ​​of single fiber pull-out tests. The following is a specific implementation of the present invention:

[0060] Modeling and calculating the number of fibers in the cross-section:

[0061] Fiber length L f =18 mm, diameter D=24 μm, fiber content 2.0%; specimen dimensions X=30 mm (length), Y=13 mm (width), H=330 mm (height). Modeling and calculation were performed using Matlab. The formula for calculating the total number of fibers is: In the formula: N is the total number of fibers within a given specimen size at the corresponding fiber content; V f The total fiber volume is represented by X, H, and Y, which represent the length, width, and height of the specimen, respectively; L represents the total fiber volume. f denoted as , where D is the fiber length and D is the fiber diameter. A three-dimensional rectangular coordinate system OXYH is constructed with the geometric center of the specimen as the origin. The X and Y axes are parallel to the cross-section of the specimen, and the H axis is perpendicular to the cross-section (i.e., along the height of the specimen). A Monte Carlo random function is used to generate the midpoint coordinates of each fiber within the specimen boundary, and the fiber orientation angle parameters α and β are randomly generated. The coordinates of the two end points of the fiber are calculated based on the midpoint coordinates, orientation angles, and fiber length. .

[0062] Calculate the total number of fibers based on the given parameters. .

[0063] Known fiber length mm, diameter m=0.024 mm, fiber content The specimen is long mm, width mm, height mm.

[0064] First, calculate the formula. The value of the middle denominator: .

[0065] Then calculate the value of the molecule: .

[0066] Finally, calculate the total number of fibers. (root).

[0067] Next, let's assume the coordinates of the fiber midpoint ( , , ),for example , , (At the geometric center of the specimen), the fiber orientation angle parameters are then randomly generated.

[0068] , .

[0069] Based on the formula for the coordinates of the two ends of a fiber: First, calculate the values ​​of each trigonometric function: , , , .

[0070] calculate : .

[0071] calculate : .

[0072] calculate : mm.

[0073] Therefore, the coordinates of the two ends of this fiber are respectively and (For the positive case), of course, since the direction angle is randomly generated, different... and The values ​​will yield different coordinates of the two ends of the fiber.

[0074] The number of fibers in the cross section under different fiber content is shown in Table 1:

[0075] Table 1:

[0076]

[0077] Randomly assign the burial depth and angle to each fiber:

[0078] Input the total number of fibers N, as shown in Table 1; fiber length L f =18 mm, and the fiber burial depth d distribution range [0, L f / 2] and angle The distribution range is [0, π / 3];

[0079] In Matlab software (Matlab is an abbreviation for Matrix-Laboratory), use the rand function to generate the fiber embedment depth d for each fiber according to the following rules. i and angle θ i : A set of fiber parameters is formed based on the generation results. .

[0080] The following example, using Table 1 and given rules, illustrates how to generate fiber parameters. Assuming a fiber content of 1.0%, the number of fibers in the cross-section is... Fiber length mm. To generate the burial depth of each fiber in Matlab software. and angle Regarding burial depth According to the rules The rand function here generates a random number between 0 and 1. The range of values ​​is mm, for example, if a random number rand=0.3 is generated for a certain fiber, then the burial depth of this fiber is... mm.

[0081] For angle The rule is The random numbers generated by rand are between 0 and 1, so The range of values ​​is If a random number rand = 0.6 is generated by a certain fiber, then radians (approximately) By generating the burial depth and angle for each of the 4022 fibers in this manner, a set of fiber parameters is ultimately formed. .

[0082] Determine the Weibull parameters for the characteristic values ​​of each fiber:

[0083] By randomly selecting numbers from the corresponding distribution, the proportional parameter λ of the debonding displacement of each fiber was obtained. DD The shape parameter is k DD The proportional parameter for deadhesion force is λ. DF Shape parameter k DF The proportional parameter λ of the peak displacement PD and shape parameter k PD The peak force proportionality coefficient λ PF and shape factor k PF .

[0084] Generate a simplified pull-out curve model for each fiber:

[0085] The debonding force, debonding displacement, peak force, and peak displacement of each fiber are randomly assigned from the Weibull distribution parameters calculated in the steps, thereby obtaining the three-fold line pull-out curve of each fiber.

[0086] The following example illustrates how to generate the three-segment pull-out curve characteristic values ​​for a single fiber:

[0087] Suppose that the proportional parameters of the debonding displacement are obtained by fitting the Weibull distribution. Shape parameters Detachment force ratio parameter Shape parameters , , Peak force proportional parameter Shape parameters According to the Weibull distribution random number generation rule, the probability density function of the random variable X is: Random numbers can be generated using the inverse transform method or built-in software functions:

[0088] For example, when generating random numbers for debonding displacement, let Then the debonding displacement ,like ,but ;

[0089] De-adhesion ,like hour, ;

[0090] Peak displacement ,like hour, .

[0091] Peak power ,like hour, .

[0092] Thus, the debonding stage of the fiber is from the origin (0, 0) to ( That is, (0.2986mm, 8.85N), the elastic segment extends to ( (0.744mm, 42.3N) is then used to form a three-fold curve in the plastic softening stage. Repeating this process will give all fibers a unique pull-out curve characteristic.

[0093] The fiber fracture algorithm is established, and the specific steps are as follows:

[0094] Based on the fiber burial depth range, it is divided into N g There are two equal-width groups, each with a width of w. For each burial depth group, the extraction angle range is calculated as follows (...). , , and It is further divided into 4 angle subgroups, ultimately forming 4N. g Two-dimensional grouping units;

[0095] For each two-dimensional grouped unit, the fiber breakage rate at the four boundary points of the unit is calculated using the cutoff rate calculation formula;

[0096]

[0097] The arithmetic mean of the fracture rates at the four boundary points is taken as the average fracture rate of the group unit. ;

[0098] Calculate the number N of broken fibers in this group. b = • N, where N is the total number of fibers in this group unit.

[0099] Within each group unit, the peak single-fiber pull-out forces are sorted from largest to smallest, and the top N are selected. b Root fibers are considered as candidates for fracture.

[0100] Determine the minimum peak force F among candidate fibers min And set it as the cutoff threshold;

[0101] Traversing the pull-out curves of candidate fibers, the first F value is reached in the rising segment of the curve. min The force is cut off at the corresponding displacement point, and the subsequent pull-out force is forced to zero.

[0102] The following numerical examples illustrate the execution process of the fiber fracture algorithm:

[0103] Step 1: Divide into group units

[0104] Assuming the fiber burial depth range is mm, divided into Groups of equal width (group width) mm), pull-out angle is divided into , , , Four subgroups, forming a total of Two-dimensional grouping unit.

[0105] Step 2: Calculate the fracture rate

[0106] Taking one of the units as an example, assuming its burial depth range is... mm, pull-out angle is According to the formula Let the fiber length be... Substituting, we get:

[0107] If the calculated fracture rates at the four boundary points of this unit (e.g., at different burial depths or angles) are 0.04, 0.16, 0.17, and 0.32 respectively, then the average fracture rate is: .

[0108] Step 3: Determine the number of broken fibers

[0109] If the total number of fibers in this unit is N=100, then the number of broken fibers is: .

[0110] Step 4: Select candidate fracture fibers

[0111] All fibers within the unit are sorted from highest to lowest peak pull-out force, and the top 95 are selected as candidate fibers for breakage. Let the peak force of the fibers be [83N, 66N, ..., 17N], then the minimum peak force is... , as the cutoff threshold.

[0112] Step 5: Cut off the pull-out curve

[0113] Traversing the pull-out curve of the candidate fiber, the first peak is reached in the rising segment. The fiber is truncated at the corresponding displacement, forcing the subsequent pull-out force to zero. For example, the pull-out force-displacement curve of a certain fiber is as follows: (Linear increase), when When, displacement If mm, then the pull-out force of the fiber is... When mm, it is set to 0N. Through the above steps, the algorithm simulates the fiber fracture behavior and finally obtains the pull-out force-displacement curve of each fiber.

[0114] The specific steps for superimposing single-fiber pull-out curves are as follows:

[0115] To ensure the same number of fibers at each embedment depth and pull-out angle in the matrix, the ratio of fiber numbers at embedment depths of 0mm, 3mm, 6mm, and 9mm is 1:2:2:1, and the ratio of fiber numbers at pull-out angles of 0°, 15°, 30°, 45°, and 60° at the same embedment depth is 1:2:2:2:1. By constructing a symmetrical weighted distribution, the mean fiber embedment depth is 4.5mm, and the mean pull-out angle is 30°, while ensuring that the weights of fiber embedment depth and pull-out angle are consistent across any interval, meeting the requirement of uniform distribution.

[0116] Normalizing the displacement coordinates of single fiber pull-out curves. In single fiber pull-out tests, raw data is collected based on time intervals rather than displacement intervals. This results in each fiber's pull-out curve being built on different displacement coordinates, and the amount of data varies for each set of conditions, making direct superposition impossible. Therefore, it is necessary to normalize the displacement coordinates of all fiber pull-out curves. Here, a displacement interval of 0.01 mm is used, distributing the data to these coordinates according to the principle of proximity.

[0117] The results in the table are analyzed using fiber content of 0.5%, 1.0%, 1.5%, and 2.0% as examples. When the fiber content is 0.5%, the experimental bridging stress is 3.64 MPa, while the model-predicted bridging stress is 2.52 MPa. The experimental opening displacement is 0.56 mm, which is also the model-predicted opening displacement. This indicates that at lower fiber content, the model-predicted bridging stress is lower than the experimental value, but the opening displacement prediction is more accurate. When the fiber content increases to 1.0%, the experimental bridging stress rises to 5.30 MPa, while the model-predicted value is 4.98 MPa, narrowing the gap. The experimental opening displacement is 0.62 mm, while the model-predicted value is 0.53 mm, showing that the model has a slight deviation in predicting the opening displacement at higher fiber content. Increasing the fiber content further to 1.5% significantly increased the experimental bridging stress to 8.05 MPa, while the model predicted 7.45 MPa, close to the experimental value. The experimental opening displacement slightly decreased to 0.53 mm, compared to the model prediction of 0.52 mm, showing good consistency. Finally, when the fiber content was 2.0%, the experimental bridging stress was 7.26 MPa, compared to the model prediction of 6.81 MPa, and the experimental opening displacement was 0.55 mm, compared to the model prediction of 0.50 mm. This indicates that at the highest fiber content, the model-predicted bridging stress and opening displacement were slightly lower than the experimental values. Overall, the model's prediction trends for bridging stress and opening displacement at different fiber contents are generally consistent with the experimental results, but there are some deviations in absolute values, especially at higher fiber contents.

[0118] The single-fiber pull-out test curves for each working condition were superimposed, and the average value was taken. This yielded a model for the joint strength of an ultra-high ductility concrete bridge considering the randomness of fiber pull-out under different fiber contents, as shown in the attached figure. Figure 3 As shown in Table 2, a comparison between the model and experimental results is presented.

[0119] Table 2 Comparison of Bridge Connection Model and Experimental Results

[0120]

[0121] Table 2 shows a comparison between the experimental results and model predictions of the bridge bridging stress of ultra-high ductility concrete under different fiber content. As can be seen from the table, with the increase of fiber content, the experimental bridging stress exhibits a trend of first increasing and then decreasing. Specifically, it is 3.64 MPa at 0.5% fiber content, reaches 5.30 MPa at 1.0%, peaks at 8.05 MPa at 1.5%, and further decreases to 7.26 MPa at 2.0%. In contrast, the model-predicted bridging stress is lower than the experimental value at all fiber content levels, but the overall trend is similar, indicating that the model can capture the trend of bridging stress with fiber content to a certain extent. Especially at 1.0% fiber content, the model-predicted bridging stress is 4.98 MPa, with a relatively small difference from the experimental value. Furthermore, the experimental and model-predicted opening displacements are quite close at all fiber content levels, indicating that the model has high accuracy in predicting opening displacement. Overall, although the model has some deviation in the absolute value of the bridging force, it can reflect the law of bridging force variation with fiber content well, showing its applicability in the bridging force model of ultra-high ductility concrete.

[0122] The following are examples of application scenarios for this application:

[0123] The proposed method can accurately characterize the fiber bridging behavior of ultra-high ductility concrete (UHDC) during tensile or flexural cracking at a micro-to-macro scale, thus possessing broad and in-depth application value in engineering design and materials research and development. The following section, based on the document content, uses a real-world engineering project—the seismic strengthening design of key nodes in a frame structure—as an application scenario example to detail the implementation process and significance of this method, showcasing its complete chain from material parameter acquisition and stochastic modeling to macroscopic performance prediction.

[0124] A city plans to seismically strengthen a reinforced concrete frame structure to improve its energy dissipation and deformation capacity under rare earthquakes. The designers decided to use ultra-high ductility concrete incorporating PE fibers for local replacement and wrapping in key node areas, creating a tough zone with both high strength and high toughness to delay crack propagation and effectively transfer and disperse seismic energy. Due to the complex stress state in the node areas, cracks may propagate in multiple directions, and the fiber embedment depth, spatial orientation, and bond state with the matrix exhibit significant randomness. Traditional bridging force models based on uniformity assumptions cannot accurately reflect the impact of this microscopic non-uniformity on macroscopic bearing capacity. Therefore, the project team decided to introduce an ultra-high ductility concrete bridging force model construction method that considers the randomness of fiber pull-out. Based on a combination of material test data and stochastic mechanical modeling, the bridging performance of different fiber content schemes was precisely predicted to guide the optimization of material mix design and construction scheme.

[0125] The UHDC specimens used were 250 mm long, 450 mm wide, and 500 mm high. PE fibers with a diameter of 24 μm and a length of 18 mm were selected, and the designed fiber volume fractions were 0.5%, 1.0%, 1.5%, and 2.0%. Based on the calculation formulas provided in the documentation, the total number of fibers at each fraction was calculated using a Matlab program. Taking a 2.0% fraction as an example, substituting the specimen dimensions and fiber geometric parameters, the total number of fibers was approximately... Root. Subsequently, a three-dimensional coordinate system OXYH was established with the geometric center of the specimen as the origin, and the midpoint coordinates (f) of each fiber were generated within the specimen boundary using a Monte Carlo random function. x ,f y ,f h The fiber orientation angle parameters α and β are randomly generated. Based on the endpoint coordinate formula provided in the document, the spatial orientation and end point positions of each fiber in the specimen can be calculated, and it can be determined which fibers pass through a preset target section (e.g., a transverse section with H=h0). The number of fibers at that section is counted, and the average is taken after multiple repetitions to improve accuracy. This step provides the geometric basis for subsequent random assignment of burial depth and angle, ensuring that the spatial distribution of fibers in the model matches the actual casting conditions.

[0126] According to the document, the burial depth d i The value range is [0, L] f / 2] is [0, 9mm], angle θ i The value range is [0, π / 3]. In Matlab, the rand function is used to generate uniformly distributed random numbers. For example, for a certain fiber, rand=0.3 indicates a burial depth d. i =0.3×9=2.7mm; rand=0.6 then θ i =0.6×π / 3≈0.6283rad (approximately 36°). Taking a 1.0% fiber content and 1,248,993 fiber cross-sections as an example, the embedment depth and angle are generated for each fiber individually, forming a complete set of fiber parameters. This process enables the model to reflect the non-uniform burial depth and tilt distribution of fibers caused by stirring and flow during actual casting, avoiding systematic deviations caused by the assumption of uniformity in traditional models.

[0127] Based on the previous single-fiber pull-out test data, the Weibull distribution was used to fit each characteristic value to obtain the debonding displacement ratio parameter λ. DD Shape parameter k DD De-adhesion proportional parameter λ DF Shape parameter k DF Peak displacement proportional parameter λ PD Shape parameter k PD Peak force proportional parameter λ PF Shape parameter k PFFor example, the fitting result of a certain batch of experiments is λ. DD =0.5mm, k DD =2, λ DF =10N, k DF =3, λ PD =2mm, k PD =1.5, λ PF =50N, k PF =4. These parameters form the basis for random assignment, giving each fiber's pull-out response independent statistical distribution characteristics.

[0128] Based on the inverse transform of the Weibull distribution, the debonding displacement d of each fiber is generated under the control of uniformly distributed random numbers u1, u2, u3, u4 in [0,1]. dep De-adhesion force f dep Peak displacement d peak Peak force f peak For example, when u1=0.3, d dep ≈0.2986mm; when u2=0.5, f dep ≈8.85N; when u3=0.2, d peak ≈0.744mm; when u4=0.4, f peak ≈42.3N. This yields the three-fold linear curve of the fiber: from the origin to (d dep ,f dep ) is the debonding segment, up to (d peak ,f peak The first stage is the elastic rise phase, followed by the softening phase. This process is repeated to assign a unique curve to each fiber, reflecting the random differences in the microscopic pull-out response.

[0129] A fiber truncation algorithm is established to address potential fiber breakage during loading. First, the fiber embedment depth range is divided into several equal-width groups (e.g., 0~2mm, 2~4mm, ...), and within each embedment depth group, subgroups are formed based on angle. , (etc.), forming two-dimensional grouping units. For a certain unit (buried depth 6~8mm, angle, etc.), Using the fracture rate formula Calculate the fracture rate at the boundary points and take the average. avg =0.17, total number of unit fibers N=100, then the number of broken fibers N b =17. Arrange the fibers within the unit in descending order of peak force, select the top 95 fibers as candidates, and determine the minimum peak force F. min =5N is the cutoff threshold. The candidate fiber curves are iterated through, and F is first reached in the rising segment. minThe fiber is truncated at the corresponding displacement point, and the subsequent pull-out force is reduced to zero. This step can effectively simulate the situation where some fibers lose their bridging function prematurely due to stress concentration or bond failure under repeated earthquake action, thus improving the model's ability to predict damage evolution.

[0130] A bridging force model for the randomness of single-fiber pull-out was established. To ensure the balance of burial depth and angle distribution, the number of fibers at burial depths of 0mm, 3mm, 6mm, and 9mm was allocated in a 1:2:2:1 ratio, and the number of fibers at angles from 0° to 60° was allocated in a 1:2:2:2:1 ratio at the same burial depth, resulting in an average burial depth of 4.5mm and an average angle of 30°. Then, the displacement coordinates of all fiber pull-out curves were normalized to 0.01mm intervals, and resampling was performed based on the nearest available interval. For example, if the original data for a certain fiber was a time series of stress values, after converting it to displacement based on the pull-out speed, the force values ​​at displacement points such as 0.10mm, 0.20mm, and 0.30mm were extracted and incorporated into the normalized grid. The data from different burial depth and angle groups were superimposed and averaged to obtain representative curves for each group. These curves were then weighted and synthesized according to the number of fibers in each group in the actual cross-section to obtain the complete bridging force-opening displacement curve for a single cross-section. Figure 3 The model curves for doping levels of 0.5% to 2.0% are shown, indicating that the bridging stress first increases and then decreases with increasing doping level.

[0131] In this case study of strengthening key nodes in a frame structure, bridging force models generated by different admixture schemes were embedded into the concrete damage plasticity model or bond-slip constitutive model in finite element software to perform nonlinear time history analysis on the crack opening and closing process of the nodes under seismic action. Comparison of experimental and model results revealed the following: at a 0.5% admixture, the experimental bridging stress was 3.64 MPa, the model predicted 2.52 MPa, and the opening displacement was 0.56 mm; at a 1.0% admixture, the experimental stress was 5.30 MPa, the model predicted 4.98 MPa, and the opening displacement was 0.62 mm in the experiment and 0.53 mm in the model; at a 1.5% admixture, the experimental stress was 8.05 MPa, the model predicted 7.45 MPa, and the opening displacement was 0.53 mm in the experiment and 0.52 mm in the model; at a 2.0% admixture, the experimental stress was 7.26 MPa, the model predicted 6.81 MPa, and the opening displacement was 0.55 mm in the experiment and 0.50 mm in the model. The model trends are consistent with the experimental results, effectively capturing the relationship between admixture and bridging performance, and demonstrating high accuracy in predicting opening displacement. Accordingly, the designers selected a dosage of 1.0% as the optimal solution, which ensures improved ductility while avoiding the increased construction difficulty and cost caused by excessive dosage.

[0132] The application of this model construction method in this scenario not only realizes the entire process from fiber-level random parameter generation and fracture simulation to macroscopic bridging force prediction, but also verifies the reliability of the model through comparison with experimental data, providing a scientific basis for the material selection and performance evaluation of UHDC in the seismic strengthening of important structures. Its advantage lies in organically combining microscopic randomness with macroscopic mechanical response, overcoming the limitations of traditional deterministic models. It can provide more realistic material behavior predictions under complex stress paths and multi-crack collaborative propagation, thus making it suitable for engineering fields with extremely high requirements for crack control and toughness, such as high-rise building core tubes, subway tunnel segments, airport runways, and nuclear power plant containment structures, promoting the leap of ultra-high ductility concrete from material research and development to refined engineering design.

[0133] In the description of this specification, references to terms such as "an embodiment," "example," "specific example," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0134] The preferred embodiments of the present invention disclosed above are merely illustrative of the invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the invention to any specific implementation. Clearly, many modifications and variations can be made based on the content of this specification. This specification selects and specifically describes these embodiments to better explain the principles and practical applications of the invention, thereby enabling those skilled in the art to better understand and utilize the invention. The invention is limited only by the claims and their full scope and equivalents.

Claims

1. A method for constructing a ductile concrete bridge splice model considering the randomness of fiber pull-out, characterized in that: The construction method includes the following steps: Modeling and calculating the number of fibers in the cross-section; Randomly assign burial depth and angle to each fiber; Obtain the random distribution parameters of the characteristic values ​​of each fiber; Generate a pull-out curve for each fiber; Establish a fiber truncation algorithm; By superimposing the pull-out curves of single fibers, a bridging force model based on the randomness of single fiber pull-out is established. The fiber truncation algorithm is established, including the following steps: Obtain two-dimensional grouping units; The fiber breakage rate at the boundary points of two-dimensional grouped units is calculated using the cutoff rate calculation formula. The arithmetic mean of the fracture rates at the boundary points is taken as the average fracture rate φ of the two-dimensional grouped unit. Calculate the number N of broken fibers in this two-dimensional grouping unit. b The expression is: N b =φ·N, where N is the total number of fibers in the two-dimensional grouping unit; Within each two-dimensional grouping unit, the top N fibers are selected by sorting them from largest to smallest single-fiber pull-out peak force. b Root fibers are considered as candidates for fracture. Determine the minimum peak force F among candidate fibers min and the minimum peak force F min Set as the cutoff threshold; Traversing the pull-out curves of candidate fibers, the minimum peak force F is first reached in the rising segment of the pull-out curve. min The force is cut off at the corresponding displacement point, and the subsequent pull-out force is reduced to zero.

2. The method for constructing a ductile concrete bridge splice model considering the randomness of fiber pull-out according to claim 1, characterized in that: The logic for obtaining two-dimensional grouping units is as follows: Based on the fiber burial depth range, it is divided into N g There are three equal-width groups, each with a width of w. For each burial depth group, it is further divided into M angle subgroups according to the range of extraction angles, forming an M×N group. g Two-dimensional grouping unit.

3. The method for constructing a ductile concrete bridge splice model considering the randomness of fiber pull-out according to claim 1, characterized in that: For each fiber, a random burial depth and angle are assigned, including the following steps: Input the total number of fibers N and the fiber length L. f and the fiber burial depth d distribution range [0, L] f The distribution range of [π / 2] and angle θ is [0, π / 3]; In Matlab software, the rand function is used to generate the fiber burial depth d for each fiber. i and angle θ i ; A set of fiber parameters is formed based on the generation results. .

4. The method for constructing a ductile concrete bridge splice model considering the randomness of fiber pull-out according to claim 3, characterized in that: In Matlab software, use the rand function to generate the fiber burial depth d for each fiber according to the following rules. i and angle θ i The expression is: , where L f Where θ is the fiber length, and π / 3 is the maximum value of the angle θ distribution range.

5. The method for constructing a ductile concrete bridge splice model considering the randomness of fiber pull-out according to claim 1, characterized in that: For each fiber, a pull-out curve is generated by randomly assigning values ​​to the debonding force, debonding displacement, peak force, and peak displacement of each fiber during pull-out using random numbers from the corresponding distribution parameters of the fiber characteristic values. This results in a three-segmented pull-out curve for each fiber.

6. The method for constructing a ductile concrete bridge splice model considering the randomness of fiber pull-out according to claim 1, characterized in that: Modeling and calculating the number of fibers in a cross-section includes the following steps: Obtain the specimen dimensions, fiber volume fraction, and fiber length; Matlab software was used for modeling and calculation to obtain the total number of fibers N in the specimen. A three-dimensional rectangular coordinate system OXYH is constructed with the geometric center of the specimen as the origin, where the X and Y axes are parallel to the cross-section of the specimen, and the H axis is perpendicular to the cross-section. The Monte Carlo random function is used to generate the midpoint coordinates of each fiber within the specimen boundary range, and the fiber orientation angle parameters α and β are randomly generated. The fiber endpoint extends beyond the side boundary perpendicular to the XOY plane, with the boundary intersection as the reflection point, maintaining the original direction of the fiber's angular reflection extension; Set the target cross-section position H=h0. If the two ends of the fiber satisfy dh1≤h0≤dh2 or dh2≤h0≤dh1, then it is determined that the fiber passes through the cross-section. Count the fibers that pass through the cross-section, repeat the count S times, and take the average value as the number of fibers in the cross-section.

7. The method for constructing a ductile concrete bridge splice model considering the randomness of fiber pull-out according to claim 6, characterized in that: The total number of fibers N in the specimen was obtained by modeling and calculation using Matlab software. The expression is as follows: In the formula: N is the total number of fibers within a given specimen size at the corresponding fiber content; V f The total fiber volume is represented by X, H, and Y, which represent the length, width, and height of the specimen, respectively; L represents the total fiber volume. f denoted as 'F', where 'D' is the fiber length and 'D' is the fiber diameter.

8. The method for constructing a ductile concrete bridge splice model considering the randomness of fiber pull-out according to claim 7, characterized in that: Calculate the coordinates of the two ends of the fiber based on the coordinates of the fiber midpoint, the orientation angle, and the fiber length: Where (dx1, dy1, dh1) and (dx2, dy2, dh2) are the three-dimensional coordinates of the two ends of the fiber, α and β are the fiber orientation angle parameters, and L f f is the fiber length. x f h f y This represents the coordinate components of the midpoint of the fiber.

9. The method for constructing a ductile concrete bridge splice model considering the randomness of fiber pull-out according to claim 8, characterized in that: The pull-out curves of superimposed single fibers include the following steps: Determine the minimum step size for data acquisition; The pull-out curves of all fibers on the cross section are superimposed point by point in sequence; The fiber bridging force-opening displacement curve of a single cross section is obtained, which is the fiber bridging force model.

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