Image Recognition-Based Analysis and Simulation Optimization of Mechanical Performance of Steel Fiber-Reinforced Concrete

Abstract

The traditional analysis of the mechanical performance of steel fiber-reinforced concrete (SFRC) predominantly relies on the assumption of an ideally random fiber distribution. This approach fails to account for the significant distribution inhomogeneity caused by practical construction processes like vibration, creating a discrepancy between simulation and reality. To address this, the main aim of this study was to demonstrate the critical impact of realistic fiber distribution on mechanical behavior by integrating image recognition with meso-mechanical simulation. Multi-factor controlled experiments were conducted to investigate the influence of vibration energy, fiber content, and aggregate volume fraction. An image recognition method was developed to accurately characterize the real spatial distribution of fibers, and these data were used to construct a three-dimensional meso-scale finite element model. Compared with the traditional model assuming random distribution, the proposed model based on the actual distribution showed significantly improved agreement with experimental results in terms of crack propagation paths and reduced the prediction error of the initial cracking load by more than 16.3%. For practitioners, the key takeaway is that modeling based on the actual fiber distribution is crucial for achieving realistic simulations. Our work provides a validated methodology to incorporate real distribution data, thereby improving the reliability of numerical assessments for SFRC structures, rather than relying on idealized random distribution assumptions.

1. Introduction

Steel fiber-reinforced concrete (SFRC) is widely used in civil engineering due to its excellent mechanical properties. Research over the years has primarily focused on areas such as static parameter optimization, characterization of fiber distribution, flexural toughness, and numerical simulation. In parameter optimization, studies often examine the influence of individual factors like fiber content, aspect ratio, and interfacial bond strength. For instance, increasing the fiber aspect ratio has been found to enhance the fracture energy of concrete [1], while experiments have shown a positive correlation between the fracture energy of steel fiber self-compacting concrete and both fiber volume fraction and length [2].

In terms of flexural and fracture performance, static bending and fatigue tests have revealed that the ultimate load of beams increases with higher fiber content [3]. Based on three-point bending tests, a linear model was established between the ductility index and fiber volume parameters, with proposed threshold volume fractions for matrices of different strengths [4]. Other studies [5,6] have shown that steel fibers can significantly increase the fracture energy, but their effect on improving fracture toughness is limited. However, the increase will decrease as the content increases, and it is affected by the sample size and the initial crack depth [7].

Significant progress has been made in fiber distribution characterization techniques. For example, detection technology based on image recognition has been developed to achieve precise extraction of fiber geometric parameters [8]. Research has quantitatively revealed the migration of coarse aggregates and steel fibers during vibration, indicating that non-uniform distribution significantly affects mechanical properties [9]. Meanwhile, methods combining digital imaging and ultrasonic techniques have been employed to observe damage evolution, demonstrating the potential of imaging technology for correlating microstructure with macroscopic performance [10]. In studies on flexural toughness testing and simulation, an optimal toughness was found at a 1.5% fiber dosage, with an ABAQUS 2022 extended finite element model showing good agreement with experimental results [11]. Another study systematically explored the effects of volume fraction, fiber type, and matrix strength, validating the feasibility of numerical simulation through ABAQUS 2022 integral modeling [12].

The advancement of numerical simulation methods relies on a deep understanding of the material’s meso-structure. SFRC has been treated as a three-phase composite of aggregate, mortar, and fiber interface [13]; algorithms for aggregate generation have been improved [14]; and methods for the random distribution of aggregates in three-dimensional concrete have been explored, laying the groundwork for subsequent modeling [15]. Building on this foundation, the development of the random aggregate model provided crucial support for numerical research on concrete [16]. Subsequently, several scholars have developed simulation methods for the SFRC fracture process [17,18,19,20,21]. Furthermore, a three-dimensional meso-scale model of SFRC beams was established using Python 3.9 and ABAQUS 2022 to analyze the influence of parameters such as recycled aggregate replacement rate and reinforcement ratio [22].

However, a critical review of the literature reveals a persistent gap. Although image recognition techniques enable detailed characterization of fiber distribution, and meso-scale modeling has advanced significantly, these two aspects have not been fully integrated. Most existing numerical studies still operate under the assumption of an ideally random fiber distribution within their models. They fail to incorporate the actual, process-induced non-uniformity in fiber distribution—as quantified by modern characterization techniques—directly into the framework for mechanical performance simulation. This disconnect limits the predictive accuracy and representativeness of models when applied to real-world cast elements, where factors such as vibration and flow cause significant fiber segregation and alignment.

To address this research gap, this study aims to directly link quantitatively characterized real fiber distributions with meso-mechanical simulation, with the primary objective of demonstrating the superior accuracy of models based on real distributions compared to those assuming randomness. The structure of this paper is as follows: Section 2 details the materials and experimental methods, including the multi-factor design, mechanical testing, and the developed image recognition workflow for fiber distribution extraction. Section 3 presents the results, analyzing the effects of process parameters on distribution and mechanical properties, and comparing the performance of a finite element model incorporating the real distribution against both experimental data and a traditional random distribution model. Section 4 discusses the underlying mechanisms of the findings and the implications of the proposed approach. Finally, Section 5 concludes the study.

The specific objectives of this research are:

(1)

To quantitatively analyze the effects of key construction process parameters (vibration energy, fiber dosage, aggregate volume fraction) on the actual spatial distribution of steel fibers in cast beams.

(2)

To develop and apply a robust image recognition pipeline to accurately extract and parameterize the real fiber distribution state from cross-sectional specimens.

(3)

To construct a finite element model incorporating the real fiber distribution and verify its superiority over traditional models with ideal random distribution in predicting crack morphology and initial cracking load.

2. Materials and Methods

To clearly present the overall technical approach and logical framework of this study, Figure 1 provides a comprehensive flowchart covering the entire process from multi-factor experiments and image recognition to numerical modeling and validation.

2.1. Experimental Materials and Multi-Factor Design

To systematically investigate the influence of construction process parameters on steel fiber distribution and mechanical performance, this experiment adopted the orthogonal experimental design method. Four independent variables were selected: vibration energy, fiber dosage, aggregate volume fraction, and model validation method. Each variable was set with multiple gradient levels. A total of 30 sets of specimens (including control groups) were cast. The experimental data were cross-validated using three-point bending tests, visual strain gauges, and numerical simulation.

Multiple gradient levels were established for each variable. As shown in

Table 1. Experimental Group Design.

Comparative Group for Parameter Influence
Group	Vibration Level		Steel Fiber Dosage	Aggregate Volume Fraction
A1	Low Energy (Vibration Time 10 s)		1.5%	40%
A2	Medium Energy (Vibration Time 30 s)		1.5%	40%
A3	High Energy (Vibration Time 50 s)		1.5%	40%
B1	Medium Energy (Vibration Time 30 s)		1.0%	40%
B2	Medium Energy (Vibration Time 30 s)		1.5%	40%
B3	Medium Energy (Vibration Time 30 s)		2.0%	40%
C1	Medium Energy (Vibration Time 30 s)		1.5%	30%
C2	Medium Energy (Vibration Time 30 s)		1.5%	40%
C3	Medium Energy (Vibration Time 30 s)		1.5%	50%
Numerical Model Validation Group
Group	Model Type	Parameter Setting	Test Sample Source	Cross-Section Comparison
D1	Traditional Random Model	Assumed Uniform Fiber Distribution	Numerical Simulation Data	Compared with D3
D2	Image Recognition Distribution Model	Actual Distribution via Image Recognition	Numerical Simulation Data	Compared with D3
D3	Actual Test Sample	Parameters of Group A2	Laboratory Cast Specimen	Reference Sample

Note: The selection of parameter levels is based on the following standards and typical ranges: Vibration energy levels represent insufficient, standard, and excessive compaction in common practice. Steel fiber dosage covers the common effective range in SFRC applications. Coarse aggregate volume fraction spans the typical range in conventional concrete mix design. The concrete matrix used in this study was designed to have a strength grade of C35. The matrix mix design utilized PO42.5 ordinary Portland cement, with a water-cement ratio (w/c) of 0.42.

, nine key parameter combinations were designed in this study, with three replicate specimens prepared for each combination to assess the experimental variability. Among these, the benchmark parameter combinations (A2, B2, and C2)—serving as key reference controls—were supplemented with one additional specimen each, intended for more detailed image analysis and model validation. Consequently, the total number of specimens amounts to 30 (9 combinations × 3 specimens + 3 additional specimens = 30). In this study, the term “control group” primarily refers to those benchmark parameter combinations in which the other variables are maintained at their medium levels when examining the effect of a specific parameter (e.g., A2, B2, and C2). All specimens were fabricated following identical dimensional standards and preparation procedures to ensure comparability.

2.2. Mechanical Property Testing of Specimens

Through three-point bending tests (Figure 2 and Figure 3), the typical failure process of SFRC specimens was observed and can be divided into three stages:

• Initial cracking stage: Micro-cracks appeared at the bottom mid-span of all specimens, indicating the initiation of fiber-matrix interface debonding.
• Stable propagation stage: Characterized by “multi-crack propagation,” where 3–5 secondary cracks with widths less than 0.1 mm were generated around the main crack.
• Final failure stage: Specimen failure occurred when the mid-span deflection reached approximately 2.8 mm. To quantitatively analyze the failure mode, the pull-out lengths of all observable steel fibers on the fracture surface were systematically measured. Statistical results indicated that the pull-out length exhibited a distinct bimodal distribution. This bimodal distribution carries clear physical significance: the shorter pull-out peak (4 mm) primarily corresponds to fibers with strong bonding to the matrix, which either fractured or were only partially pulled out during failure, whereas the longer peak (8 mm) mainly corresponds to fibers that were nearly completely pulled out due to weaker interfacial bonding or unfavorable orientation. This distribution characteristic directly confirms that different vibration energies, by influencing fiber orientation and spatial distribution, lead to inhomogeneity in the fiber-matrix interfacial bonding state, ultimately manifesting as differentiated fiber failure mechanisms at the macroscopic level.

2.3. Fiber Distribution Image Recognition Method

2.3.1. Specimen Cutting and Image Acquisition

To systematically analyze the fiber distribution within all specimens, this study conducted standardized longitudinal sectioning on all three-point bending beam specimens. The cutting scheme was as follows: along the height direction of each specimen (650 mm), sections were made along the central axis of its 150 mm × 650 mm side surface to obtain a longitudinal cross-section spanning the full length of the specimen (approximately 150 mm × 650 mm). This cross-sectional orientation was parallel to the load direction, effectively revealing the fiber distribution status in the core stress zone of the beam. Subsequently, high-resolution images were acquired of the obtained longitudinal cross-sections. Figure 4 displays selected representative cross-sectional images that clearly demonstrate the actual spatial distribution of steel fibers within the concrete matrix, providing a unified, high-quality visual data foundation for subsequent image recognition and quantitative statistical analysis.

2.3.2. Image Grayscale Conversion

Image grayscale conversion is a crucial preprocessing step that transforms the collected RGB color fiber source images into grayscale images. Its purpose is to minimize the volume of image data processing while maximally preserving the effective contrast information between the fibers and the matrix. This study employs the weighted average method [23], which is based on human visual perception characteristics, for the grayscale conversion. The calculation formula is shown in Equation (1). This algorithm can retain the color contrast of the original color image to the greatest extent.

$${\mathit{Gray}}_{(x,y)}=0.299\times R_{(x,y)}+0.587\times G_{(x,y)}+0.114\times B_{(x,y)}$$

(1)

In the equation, ${\mathrm{Gray}}_{(\mathrm{x},\mathrm{y})}$ represents the grayscale value at pixel (x,y) in the grayscale image; ${\mathrm{R}}_{(\mathrm{x},\mathrm{y})}$, ${\mathrm{G}}_{(\mathrm{x},\mathrm{y})}$ and ${\mathrm{B}}_{(\mathrm{x},\mathrm{y})}$ represent the red, green, and blue component values, respectively, of the corresponding pixel in the original color image. The setting of the weight coefficients conforms to human visual characteristics, accurately reflecting the brightness and darkness levels. After grayscale processing, the corroded steel fibers exhibit higher grayscale values due to their reddish-brown characteristics, forming a significant contrast with the gray concrete matrix, as shown in Figure 5.

2.3.3. Image Binarization

This study employs the OTSU algorithm [24] to automatically determine the optimal segmentation threshold. This method, based on the statistical characteristics of the image grayscale histogram, can adaptively identify the threshold point that maximizes the distinction between the foreground and background, achieving precise separation of steel fibers from the concrete matrix. The mathematical expression is shown in Equation (2).

$$G_{(x,y)}=\{\begin{array}{c}1, \mathit{when} g_{(x,y)}>T\\ 0, \mathit{when} g_{(x,y)}\le T\end{array}$$

(2)

Here, ${\mathrm{G}}_{(\mathrm{x},\mathrm{y})}$ represents the value of pixel (x,y) after binarization, ${\mathrm{g}}_{(\mathrm{x},\mathrm{y})}$ is the grayscale value of the corresponding point, and T is the optimal segmentation threshold determined by the OTSU algorithm. When the grayscale value of a pixel is greater than the threshold T, it is identified as the steel fiber region and assigned a value of 1 (white); otherwise, it is identified as the background region and assigned a value of 0 (black).

The core principle of the OTSU algorithm is to determine the optimal threshold by maximizing the inter-class variance, which effectively handles interference factors such as color differences and texture variations in the matrix. After binarization, the original image is converted into a black-and-white binary image with distinct contrast, as shown in Figure 6.

2.3.4. Initial Detection Region Extraction Method

The core principle of initial detection region extraction is based on the spatial distribution characteristics of fiber pixels (i.e., foreground pixels) in the binary image. By locating the coordinate extremes of all foreground pixels, an axis-aligned bounding box that completely encompasses all fiber regions is determined. Let the coordinates of fiber pixels in the binary image be the set S = {(x_i, y_i)|G(x_i, y_i) = 1}. The boundaries of the initial detection region are then defined as shown in Equation (3).

$$\{\begin{array}{c}{x}_{\mathit{min}}=\mathit{min}\left\{x_i\right\}, x_{\mathit{max}}=\mathit{max}\left\{x_i\right\}\\ y_{\mathit{min}}=\mathit{min}\left\{y_i\right\}, y_{\mathit{max}}=\mathit{max}\left\{y_i\right\}\end{array}$$

(3)

In the equation, (${\mathrm{x}}_{\min }$,${\mathrm{y}}_{\min }$) and (${\mathrm{x}}_{\max }$,${\mathrm{y}}_{\max }$) represent the coordinates of the top-left corner and bottom-right corner of the minimum bounding rectangle, respectively. The rectangular region R = [${\mathrm{x}}_{\min }$,${\mathrm{x}}_{\max }$] × [${\mathrm{y}}_{\min }$,${\mathrm{y}}_{\max }$] determined in this way is the initial detection region. This rectangular area serves as the effective analysis scope for subsequent extraction of fiber characteristic parameters, effectively excluding interference from invalid background regions at the image edges.

2.3.5. Visual Annotation of Detection Results

Visual annotation first establishes a mathematical foundation through coordinate system transformation. The fiber pixel coordinates obtained by the recognition algorithm originate from a matrix coordinate system with the top-left corner of the image as the origin. Precise conversion to the display coordinate system is achieved via a linear mapping relationship, ensuring consistency between the annotation positions and the actual spatial distribution of the fibers. After determining the spatial locations, the fiber centroid coordinates obtained from the aforementioned image recognition serve as the core positioning points. The centroid coordinates are calculated using the image moment method as shown in Equation (4).

$$\{\begin{array}{c}{x}_c={\displaystyle \frac{M_{10}}{M_{00}}} \\ y_c={\displaystyle \frac{M_{01}}{M_{00}}} \end{array}$$

(4)

In the equation,${ \mathrm{M}}_{\mathrm{pq}}$ represents the (p + q)th-order geometric moment of the fiber-connected region.

During the marker generation phase, a circular shape is employed as the basic marking unit, with pure red (255,0,0) selected in the RGB color space. The marker size is determined through an adaptive mechanism, and its radius is calculated using the formula shown in Equation (5).

$$r=k·\sqrt{{\displaystyle \frac{A}{\pi }}}$$

(5)

Here, A represents the fiber pixel area, and k is a scaling factor set after testing and validation (with a value of 1.2). This design ensures that the marker size maintains a proportional relationship with the actual fiber dimensions while avoiding significant overlap issues caused by oversized markers. Finally, using image compositing techniques, the generated markers are merged with the original background image, producing the complete visualization results as shown in Figure 7.

2.3.6. Output of Steel Fiber Characteristic Parameters

The standardized output of characteristic parameters is a crucial link connecting image recognition with subsequent statistical modeling. The parameter output system established in this study aims to transform the recognition results into two types of quantitative data: stratified quantitative statistics and spatial position information, providing a comprehensive data foundation for studying fiber distribution characteristics and their impact on mechanical performance.

• Stratified Quantitative Statistics aims to quantify the distribution pattern of fibers across the specimen cross-section. The beam specimen with a total height of 65 cm is divided into 5 cm segments, and the number of fibers in each layer is counted. Representative data are shown in

  Table 2. Segmental Quantity Statistics of Steel Fibers in Beams (Partial Data).

  Number	Quantity	Location	≥60 cm	55~60 cm	50~55 cm	45~50 cm	40~45 cm	35~40 cm	30~35 cm	25~30 cm	20~25 cm	15~20 cm	10~15 cm	5~10 cm	0~5 cm
  A1			2	8	6	10	10	12	12	9	8	6	11	14	7
  A2			1	2	7	6	6	10	9	8	6	9	9	11	7
  A3			1	1	3	6	9	9	6	12	11	12	13	15	5
  ⋯			⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯

  .
• Spatial position information outputs the centroid coordinates (x_c, y_c) of each fiber in a Cartesian coordinate system. The origin of the coordinate system is set at the top-left vertex of the detection region, with the X-axis extending to the right and the Y-axis extending downward. This is consistent with the pixel matrix of the digital image, ensuring the direct usability of the data. This coordinate data records the precise position of all identified fibers within the cross-section. Representative data are shown in

  Table 3. Coordinates of Steel Fibers in Beam Cross-Sections (Partial Data; Unit: Pixel).

  Steel Fiber Coordinate Data Sheet
  A1	X	17.58377239	10.36150235	6.609195402	5.396907216	7.845070423	24.47572816	30.28787879	44.33	41.7063197	43.78983834	⋯
  	Y	304.2286617	2100.328638	2189.126437	3493.953608	5062.147887	1594.543689	2510.590909	276.91	2959.973978	1243.605081	⋯
  A2	X	14.42430704	15.26808511	6.927536232	10.30508475	17.40273038	30.33802817	20.32	20.38271605	26.78571429	26.31147541	⋯
  	Y	2553.52452	5592.710638	2110.130435	1120.728814	2854.59727	5037.988732	2150.07	4340.876543	4074.972527	5692.016393	⋯
  A3	X	3.880434783	3.333333333	6.441558442	7.078534031	14.75695461	10.65443425	11.02083333	16.72727273	10.19148936	21.88842975	⋯
  	Y	1602.554348	2203.666667	2699.74026	2814.596859	4801.38653	5246.201835	5332.145833	4890.755245	2043.042553	858.464876	⋯
  ⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯

  .

2.3.7. Verification and Error Analysis of Image Recognition Algorithm

In order to ensure the reliability of fiber distribution data extracted from two-dimensional images and provide a solid foundation for subsequent quantitative analysis and modeling, this study conducted systematic accuracy verification and error evaluation of the image recognition algorithm used.

• Verification by comparison with manual counting. Two independent researchers manually annotated and counted the fibers as the true values. Subsequently, the automatic recognition results were compared with the manual count results to calculate the detection accuracy, false positive rate, and false negative rate. The partial comparison results are shown in

  Table 4. Comparison of Artificial Recognition and Image Recognition Results (Partial Data).

  Image Number	Manual Count	Image Recognition Count	Absolute Error	Recognition Accuracy	False Positive Count	Number of Missed Tests
  A1	119	119	4	96.6%	3	7
  A2	94	91	3	96.8%	2	5
  A3	112	103	9	92.0%	4	5
  ⋯	⋯	⋯	⋯	⋯	⋯	⋯

  .

2.

Analysis of main error sources

(1)

Fiber overlap and adhesion. In two-dimensional projections, spatially adjacent or crossing fibers may be algorithmically identified as a single connected domain due to pixel connectivity, resulting in undercounting compared to the actual number. This is the primary source of missed detection.

(2)

Boundary and partial fibers. Fibers located at the cutting edge of the sample may appear as fragmented due to incomplete inclusion in the image, resulting in incomplete geometric features, which can easily lead to missed detection or errors in geometric parameter extraction.

(3)

Matrix background interference. Dark aggregates, pores, or fine cracks in the concrete matrix may exhibit grayscale values similar to fibers under specific lighting conditions. Although the OTSU global threshold method can effectively segment the fibers, it may still cause a small number of false-positive detections in localized areas.

(4)

Low-contrast fibers. Fibers completely enveloped by cement paste or severely corroded, exhibiting markedly reduced contrast with the surrounding matrix, may be excluded during binarization.

3. Results

3.1. The Influence of Process Parameters on Fiber Distribution and Mechanical Properties

3.1.1. Statistical Analysis of Flexural Tensile Strength

Based on the experimental data, this study employed a normal distribution model to evaluate the flexural tensile strength and residual strength, in accordance with the requirements specified in Appendix A of the Chinese industry standard Technical Specification for Application of Fiber Reinforced Concrete (JGJ/T 221-2010) [25]. The calculation formulas used are shown in Equations (6) and (7) below.

$$f_{\mathit{ftmk}}=f_{\mathit{ftmm}}(1-k_s{\mathsf{\delta }}_c)$$

(6)

$$f_{\mathit{Rjk}}=f_{\mathit{Rjm}}(1-k_s{\mathsf{\delta }}_c)$$

(7)

In the equations, ${\mathrm{f}}_{\mathrm{ftmk}}$ is the characteristic value of the ultimate flexural tensile strength (MPa); ${\mathrm{f}}_{\mathrm{Rjk}}$ is the characteristic value of the residual flexural strength corresponding to COMDj (MPa); ${\mathrm{f}}_{\mathrm{ftmm}}$ is the average value of the ultimate flexural tensile strength from tests (MPa); ${\mathrm{f}}_{\mathrm{Rjm}}$ is the average value of the residual flexural tensile strength from tests (MPa); and ${\mathrm{k}}_{\mathrm{s}}$ is the fractile factor.

For each process parameter group, we align the load–displacement data of all parallel specimens with displacement as the reference, calculate the average load, and then fit an “average load–displacement curve” to represent the typical mechanical response of the group. The load–displacement curve and the mechanical performance evaluation table obtained from the calculations are shown in Figure 8. The obtained Young’s modulus and flexural strength are shown in

Table 5. Table of Yang’s Modulus and Bending Strength.

Group	Young’s Modulus (GPa)	Flexural Strength(MPa)
A1	31.5	4.2
A2	36.8	5.9
A3	33.1	5.0
B1	29.7	4.8
B2	36.8	5.9
B3	34.2	5.3
C1	32.4	5.3
C2	36.8	5.9
C3	34.5	6.2

.

3.1.2. Analysis of Experimental Results

• Influence of Vibration Energy Gradient

(1)

Low Energy (Group A1): The fiber distribution was closest to a random state. However, due to insufficient vibration, the fiber sedimentation rate was only 12%, failing to form an effective gradient-enhanced structure. This resulted in the lowest tensile strength, with a failure mode characterized by a single penetrating crack.

(2)

Medium Energy (Group A2): The fiber sedimentation rate increased to 20%, with the fiber density at the bottom being approximately 1.3 times that at the top. The flexural tensile strength reached its peak. The moderate vibration energy optimized fiber orientation, leading to an ideal crack propagation path featuring multiple cracks.

(3)

High Energy (Group A3): The fiber sedimentation rate further increased to 28%, but local aggregation occurred (aggregated area accounted for about 8%). This caused the flexural tensile strength to be slightly lower than that of Group A2, although its residual strength was the highest. This indicates that excessive vibration energy can lead to uneven fiber distribution, resulting in stress concentration.

In the above results, the fiber sedimentation rate is calculated as (total number of fibers in the dense bottom zone (e.g., 50–65 cm) − total number of fibers in the sparse top zone (e.g., 0–15 cm))/total number of fibers × 100%. The fiber aggregation rate is defined as the percentage of the total fiber pixel area in all connected domains (i.e., domains with a connected domain area > 2.5 times the average area of a single fiber) relative to the total fiber pixel area in the image.

• Influence of Steel Fiber Dosage

(1)

Low Dosage (Group B1): The fiber spacing was too large, and the fiber bridging effect was weak. Cracks propagated rapidly, leading to the lowest flexural tensile strength.

(2)

Medium Dosage (Group B2): The fiber spacing was moderate, and the distribution was uniform. The porosity in the interfacial transition zone was minimized, resulting in a significant improvement in flexural tensile strength.

(3)

High Dosage (Group B3): The fiber agglomeration rate was as high as 12%. The excessive fibers disrupted the continuity of the matrix, causing the flexural tensile strength to be lower than that of Group B2.

• Influence of Aggregate Volume Fraction

(1)

Low Aggregate Fraction (Group C1): The obstruction effect of aggregates on fibers was insufficient, leading to inadequate fiber participation in load transfer. The probability of fiber bending was low (0.15), resulting in the lowest tensile strength.

(2)

Medium Aggregate Fraction (Group C2): The skeleton structure was effective, with a fiber bending probability of 0.25. The crack propagation path was extended, yielding the highest flexural tensile strength.

(3)

High Aggregate Fraction (Group C3): The fiber bending probability increased to 0.32, the mortar layer became thinner, and the interface zone was weakened, increasing the risk of early cracking.

3.2. Image Recognition Results of the Actual Distribution Characteristics of Steel Fibers

3.2.1. Steel Fiber Distribution

Based on the image recognition results, the fiber count was counted in segments of 5 cm, and the distribution diagrams of steel fibers in each group of specimens were drawn as shown in Figure 9.

3.2.2. Gradient Distribution Characteristics

The overall trend of steel fiber distribution shows an apparent gradient change in the number of fibers along the length of the beam. The distribution exhibits a general characteristic of “higher fiber density at the bottom than at the top,” but with fluctuations in the middle section.

(1)

Gradient Features of Quantitative Distribution

① Overall Quantitative Distribution Pattern

Top Sparse Zone (0–20 cm): The fiber count is the lowest, reaching a minimum in the 0–5 cm interval (average 2.45 fibers). A secondary peak appears in the 15–20 cm interval (average 8.05 fibers), possibly due to local clustering of fibers or flow disturbance during the casting process.

Middle Transition Zone (20–50 cm): The fiber count increases significantly and remains at a relatively high level in the intervals from 30–35 cm to 45–50 cm (average 9.50–10.80 fibers). The distribution is relatively stable but still shows fluctuations, reflecting the influence of fiber flow and vibration within the concrete.

Bottom Dense Zone (50–60 cm): The fiber count reaches its peak, being most concentrated in the 55–60 cm interval (average 12.05 fibers). This indicates that fibers settle and aggregate towards the bottom end of the beam under the combined effects of vibration and fluidity.

Lowest End (≥60 cm): The fiber count slightly decreases compared to the 55–60 cm interval (average 8.35 fibers), which may be influenced by mold boundary effects or fiber accumulation morphology.

② Quantifying Distribution Non-uniformity

To quantitatively characterize the non-uniformity of fiber distribution along the beam length, this study defines the gradient distribution coefficient G. This coefficient physically measures the maximum relative gradient of fiber density in spatial distribution. A higher value indicates more uneven distribution, enabling direct capture of unidirectional gradient characteristics formed by gravity sedimentation or vibration. This approach provides more targeted analysis of process effects on distribution, with its calculation method as shown in Equation (8).

$$G={\displaystyle \frac{{\mathit{\rho }}_{\max }-{\mathit{\rho }}_{\min }}{{\mathit{\rho }}_{\mathrm{avg}}}}$$

(8)

where ${\mathsf{\rho }}_{\max }$ is the maximum layer density, ${\mathsf{\rho }}_{\min }$ is the minimum layer density, and ${\mathsf{\rho }}_{\mathrm{avg}}$ is the average density. To provide intuitive reference, we classify G < 0.5 as relatively uniform distribution, 0.5 ≤ G < 1.0 as moderately uneven, and G ≥ 1.0 as significantly uneven. Based on the analysis of all specimen cross-sections in this study, the calculated G values ranged from 0.8 to 1.5. The results indicate that the fiber distribution exhibits significant unevenness, with the maximum layer density approximately four times the minimum layer density and a notable average density deviation. These quantitative findings clearly reflect potential fiber settlement or rheological segregation phenomena during construction. Optimizing construction parameters is therefore recommended to enhance distribution uniformity.

(2)

Spatial Coordinate Distribution Characteristics

In the vertical direction, fibers are primarily concentrated in the Y = 1000–3000 pixel range (corresponding to an actual height of 15–45 cm), with 1500–3000 pixels forming a dense band. The distribution spans from Y = 142 to 5783, covering the entire cross-section.

In the horizontal direction, the X coordinates are uniformly distributed from 10 to 636. The fiber quantities on the left and right sides are basically balanced. In the central region (X = 200–400), the fiber distribution is relatively concentrated, with no apparent segregation.

(3)

Analysis of Gradient Formation Mechanism

The fiber aggregation in the central region (35–55 cm) conforms to the law of vibration-induced redistribution. The lower quantities at the top (<5 cm) and bottom (≥60 cm) may be related to mold boundary effects. The gradient formation is primarily controlled by the combined effects of vibration energy and fiber-matrix flow characteristics.

3.3. Simulation Comparison Between Actual and Random Distributions

To verify the superiority of the image recognition-based fiber distribution modeling method, this chapter constructs a three-dimensional meso-scale finite element model that incorporates the statistical characteristics of the actual fiber distribution derived from the aforementioned recognition results. Crucially, the transition from 2D image data to 3D model parameters was achieved through a “statistical-feature-constrained” modeling approach. Specifically, the layered fiber counts quantified from the cross-sectional images—which capture the macroscopic distribution gradient along the beam height—were used as key input parameters. During 3D model generation, the beam was divided into corresponding layers along its height, and the number of fibers randomly generated within each layer was strictly controlled to match the statistically obtained count for that layer. This method ensures that the constructed 3D model realistically reproduces the primary inhomogeneity in fiber distribution induced by the construction process (vibration), while assuming a uniform random distribution within each horizontal layer. A comprehensive validation is then conducted using the experimental data as a benchmark. Through multi-dimensional comparisons, including prediction errors of mechanical performance and similarity of crack morphology, the accuracy and reliability of this actual-distribution-informed model are revealed in contrast to the traditional assumption of a fully random and uniform fiber distribution.

3.3.1. Model Parameters and Material Constitutive Laws

① Matrix and Aggregate: A three-dimensional solid model of the concrete matrix was created in ABAQUS 2022 according to the actual dimensions of the specimen. Using an in-house developed Python 3.9 script, spherical coarse aggregates with a particle size range of 4–9 mm were generated and randomly distributed and placed within the matrix, with the volume fraction constrained between 30% and 50%, thus ensuring the randomness and representativeness of the aggregate spatial distribution.

② Fiber Modeling: Steel fibers are simulated using truss elements. The fiber length and orientation are controlled via a Python 3.9 script to achieve a parametric definition of fiber aspect ratio and volume fraction.

③ Component Assembly: All components (aggregate, fibers, mortar) are assembled in the global coordinate system to form a complete analysis model. A geometric interference detection algorithm is employed to avoid overlap between fibers and aggregate particles, ensuring the geometric authenticity of the model.

(1)

Material Property Definition

① Mortar Matrix: The quasi-brittle mechanical behavior of the mortar was simulated using the Concrete Damage Plasticity (CDP) model in ABAQUS 2022. The model parameters defining the yield surface, flow rule, and damage evolution were set as follows: dilation angle (ψ) = 30°; eccentricity (ϵ) = 0.1; the ratio of biaxial to uniaxial compressive strength (fb0/fc0) = 1.16; the coefficient (Kc) defining the shape of the deviatoric cross-section = 0.667; and viscosity parameter (μ) = 0.0001. These values, in conjunction with the defined elastic modulus (Ec) and Poisson’s ratio (ν), are standard for modeling the inelastic behavior of ordinary concrete and ensure reasonable convergence in the damage simulation.

② Steel Fibers: The steel fibers were defined as a linear elastic material with an elastic modulus of 200 GPa and a Poisson’s ratio of 0.3. The interaction between the fibers and the surrounding mortar matrix was modeled using an embedded element technique combined with a simplified bond-slip constitutive law. This law consisted of two stages: a perfect bond stage up to a maximum interfacial shear stress of 2 MPa (corresponding to a slip of 0.02 mm), followed by a friction stage governed by a Coulomb friction model with a coefficient of 0.1.

③ Coarse Aggregate: The coarse aggregates were simplified as linear elastic, isotropic particles with an elastic modulus of 70 GPa and a Poisson’s ratio of 0.2. A “Tie” constraint was applied at the interface between the aggregates and the mortar matrix, assuming a perfect bond, as the primary failure mechanisms were considered to be within the mortar and at the fiber-mortar interface.

The established fiber random distribution model is shown in Figure 10.

3.3.2. Simulation Process and Alignment with Experimental Tests

To accurately reproduce and compare with physical test results, a three-point bending simulation environment consistent with laboratory conditions was constructed in the finite element model.

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Boundary Conditions and Support Settings

Simply supported constraints are applied at the locations of the two support rollers at the bottom of the model, i.e., constraining vertical displacement (U2) and lateral displacement (U1), to simulate actual support conditions. No displacement constraints are applied at the mid-span loading point to allow for free deformation.

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Load Application and Loading Protocol

A discrete rigid body is created at the mid-span to simulate the loading head of the testing machine. Surface-to-surface contact is defined between the loading head and the specimen surface, with tangential behavior set as Coulomb friction with a coefficient of 0.1. The load is applied in a displacement-controlled manner, by imposing a vertical downward displacement on the reference point of the loading head. The loading rate is set at 0.1 mm/s to simulate a quasi-static loading process. Throughout the analysis, the reaction force-displacement data at the loading head are automatically recorded, thereby generating load–displacement curves for comparative analysis.

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Incorporation of Fiber Distribution

The core of this model lies in abandoning the traditional assumption of ideally random fiber distribution. Instead, the actual spatial distribution data of steel fibers (including position and orientation) obtained in Chapter 3 via image recognition technology are directly parameterized and embedded into the finite element mesh. This constructs an “image recognition-actual distribution model” capable of reflecting the true meso-structure of the component.

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Method for Extracting Mechanical Parameters

To accurately obtain key mechanical performance parameters in the finite element analysis, corresponding history output requests were set in the Step module of this study. By monitoring the damage evolution variables in the Concrete Damage Plasticity (CDP) model and simultaneously recording the reaction force-displacement data at the loading point, the load corresponding to the first clear inflection point in the load–displacement curve, where the damage variable shows a sudden change, is identified as the initial crack load. Concurrently, by outputting the sectional forces at the mid-span cross-section, a moment-displacement curve is plotted, and the moment value corresponding to its peak point is determined as the ultimate moment. For solid elements, the Free Body Cut function is additionally used to verify the accuracy of the resultant moment at the cross-section. This systematically achieves quantitative characterization of the material’s cracking and ultimate bearing behavior.

The three-point bending crack propagation model established based on the above methods, which accounts for the true fiber distribution, is shown in Figure 11.

3.4. Quantitative Mechanical Property Analysis

3.4.1. Model Validation and Error Analysis of Mechanical Parameters

After the simulation was completed, key mechanical performance parameters such as the initial cracking load and ultimate bending moment were output through the post-processing module, as shown in

Table 6. Comparison of mechanical performance parameters.

Performance Parameter	Experimental Measurement Values (Mean ± Standard Deviation)	Traditional Random Model (D1) (Absolute Error, Relative Error)	Actual Distribution Model (D2) (Absolute Error, Relative Error)
Initial cracking load (kN)	15.8 ± 0.9	11.2 (−4.6 kN, −28.9%)	13.8 (−2.0 kN, −12.6%)
Limit bending moment (kN·m)	4.25 ± 0.21	2.83 (−1.42 kN·m, −33.4%)	3.58 (−0.67 kN·m, −15.8%)

.

(1)

Initial Crack Load: The error of the traditional model (Group D1) was 28.9%, while the error of this model (Group D2) was reduced to 12.6%, a reduction of 16.3%. The significant improvement in the prediction accuracy of the initial cracking load is mainly attributed to the fact that the actual distribution model can realistically reflect the fiber gradient distribution effect caused by the vibration process, thereby more accurately predicting the initial cracking behavior.

(2)

Ultimate Bending Moment: The error of the traditional model was 33.4%, while the error of this model was only 15.8%. The error of the D1 model mainly stems from its assumption of ideal random distribution, which fails to reflect the non-uniformity of fiber spatial distribution caused by rheological properties and vibration processes in actual construction. By incorporating actual fiber data obtained through image recognition, this model more realistically reproduces the spatial distribution characteristics of fibers during the modeling process, thereby improving the prediction accuracy of the component’s ultimate bearing capacity.

The comparison of the above mechanical performance parameters proves that the actual distribution model (D2) based on image recognition proposed in this study is significantly superior to traditional methods in predicting the mechanical performance of steel fiber-reinforced concrete, highlighting the importance of considering the actual fiber distribution in numerical simulations.

3.4.2. Comparison of Crack Path Similarity

To compare the consistency between the simulation and the experiment in terms of failure morphology, this study adopts the Hausdorff distance as an evaluation index for crack path similarity, calculating the geometric similarity between the final crack patterns observed in the numerical simulation and physical tests. The definition of the Hausdorff distance is based on two directed Hausdorff distances. By calculating the maximum degree of mismatch between two point sets, it can effectively capture the maximum local deviation in spatial distribution between the simulated and experimental cracks.

Let the discrete point set of the crack path observed in the physical test be A = {${\mathrm{a}}_1, {\mathrm{a}}_2, \dots , {\mathrm{a}}_{\mathrm{m}}$}, and the discrete point set of the crack path obtained from the numerical simulation be B = {${\mathrm{b}}_1, {\mathrm{b}}_2, \dots , {\mathrm{b}}_{\mathrm{m}}$}, where ${\mathrm{a}}_{\mathrm{i}}$, ${\mathrm{b}}_{\mathrm{j}}$ ∈ ${\mathrm{R}}^2$ are two-dimensional coordinate points.

The calculation of the Hausdorff distance is divided into two steps:

First, define the directed Hausdorff distance from set A to set B, ${\mathrm{h}}_{(\mathrm{A},\mathrm{B})}$. The calculation formula is shown in Equation (9).

$$h_{\left(A, B\right)}=\underset{a\in A}{\mathit{max}}\left(\underset{b\in B}{\mathit{min}}\Vert a-b\Vert \right)$$

(9)

In the equation, $\Vert \mathrm{a}-\mathrm{b}\Vert$ represents the Euclidean distance between points $a$ and $b$. The directed distance indicates that for each point in the experimental crack set $A$, we identify the point in the simulated crack set $B$ that is closest to it, and then take the maximum value among these minimum distances. This reflects the maximum of the minimum distances from the experimental crack to the simulated crack, as viewed from the perspective of the experimental crack.

Similarly, the directed Hausdorff distance from set B to set A, denoted as ${\mathrm{h}}_{(\mathrm{B},\mathrm{A})}$, is defined as shown in Equation (10):

$$h_{\left(B, A\right)}=\underset{b\in B}{\mathit{max}}\left(\underset{a\in A}{\mathit{min}}\Vert b-a\Vert \right)$$

(10)

The final (undirected) Hausdorff distance ${\mathrm{H}}_{(\mathrm{A},\mathrm{B})}$ is defined as the maximum of the two directed distances, as shown in Equation (11):

$$H_{\left(A, B\right)}=max\left(h_{\left(A, B\right)},h_{\left(B, A\right)}\right)$$

(11)

To enhance the statistical power of the analysis, this study performed the aforementioned analysis on the final crack paths of parallel specimens. To provide a more physical interpretation of the Hausdorff distance, it was normalized by dividing by the specimen’s cross-sectional height (H = 150 mm), yielding a dimensionless relative distance, ${\mathrm{HD}1}_{\mathrm{n}\mathrm{o}\mathrm{r}\mathrm{m}}$ = H/150 mm.

Table 7. Comparative Analysis of Hausdorff Distance of Crack Path (Partial Data).

Image Number	Manual Count	Image Recognition Count	Absolute Error	Recognition Accuracy	False Positive Count	Number of Missed Tests
A1	119	119	4	96.6%	3	7
A2	94	91	3	96.8%	2	5
A3	112	103	9	92.0%	4	5
⋯	⋯	⋯	⋯	⋯	⋯	⋯

presents partial comparative results of the Hausdorff distance between the crack paths predicted by the traditional stochastic model (D1) and the actual distribution model (D2) and their corresponding experimental paths.

The original Hausdorff distance values (approximately 3.5–5.1 mm) correspond to 2.3–3.4% of the specimen height and exceed the typical macro crack width (typically <2 mm), indicating several millimeter-level local deviations in geometric position between the crack paths predicted by the two models and the experimental paths. The actual distribution model (D2) demonstrated smaller Hausdorff distances than the conventional model (D1) across all three specimens, with an average reduction of 1.33 mm (normalized distance decreased by 0.0088) and an average improvement rate of 27.4%, showing stable enhancement effects.

Therefore, through the comparative analysis of numerical simulation and three-point bending test results, the practical distribution model based on image recognition (Group D2) proposed in this study significantly outperforms the traditional random distribution model (Group D1) in both aspects: the overall mechanical response (load and bending moment) and the local failure mode (crack path) of the simulated SFRC beam.

4. Discussion

4.1. Mechanism of Process Parameters Affecting Fiber Distribution and Properties

• An optimal performance was achieved under moderate vibration energy (30 s), revealing the dual role of vibration. Insufficient energy (Group A1) leaves fibers largely immobilized by the yield stress of the paste, resulting in a random yet inefficient distribution with poor bridging. Excessive energy (Group A3), while enhancing settlement, also induces significant fiber agglomeration due to inertial forces, creating stress concentration points. The moderate energy strikes a balance, promoting favorable fiber orientation along the principal stress and a beneficial bottom-enriched gradient, thereby maximizing crack resistance and toughness.
• A distinct “saturation threshold” was identified at 1.5% volume fraction. Below this threshold (Group B1), excessive fiber spacing fails to bridge crack-tip stress fields, leading to brittle failure. Exceeding it (Group B3) promotes fiber clustering, which not only wastes material but critically disrupts matrix continuity, creating preferential paths for crack propagation. This underscores that increasing fiber content alone is counterproductive beyond its dispersibility limit within the matrix.
• Aggregate Fraction: An aggregate volume fraction of 40% (Group C2) formed an optimal skeletal structure. This structure physically hinders fiber settling, increasing the likelihood of fiber bending and reorientation for better load transfer, while maintaining sufficient mortar thickness to ensure the integrity of the fiber-matrix interfacial transition zone (ITZ). Lower fractions (Group C1) reduce this beneficial hindrance, while higher fractions (Group C3) thin the mortar layer and weaken the ITZ, both compromising performance. This highlights the active role of aggregates in controlling fiber distribution and interfacial quality in SFRC mix design.

4.2. Advantages and Significance of Image Recognition and Numerical Simulation

• Traditional numerical models typically rely on the idealized assumption of completely random fiber distribution in space (Group D1). However, the image recognition results and the influence patterns of processing parameters obtained in this study confirm that the actual distribution exhibits significant non-uniformity and process dependency. By utilizing image recognition technology, this study achieves precise mapping of reality and parametrically embeds this mapping into the numerical model, thereby shifting the starting point of simulation from idealized assumptions to realistic mapping.
• Mechanism analysis improved prediction accuracy. The comprehensive enhancement in prediction accuracy of the actual distribution model (Group D2) can be explained from a meso-mechanical perspective. The significant reduction in the error of predicting the initial cracking load is primarily attributed to the model’s accurate representation of the fiber gradient distribution induced by vibration.

4.3. Limitations and Future Outlook

• Scale and Dimensional Limitations. This study was conducted using standard laboratory-scale beam specimens. In real-world engineering structures, the dimensions are significantly larger and involve more complex boundary conditions. The distribution of internal fibers may be influenced by multiple factors such as the template effect, resulting in more intricate patterns. When extrapolating the findings to large-scale engineering applications, it is crucial to carefully consider dimensional effects. Additionally, current image recognition technologies rely on two-dimensional cross-sectional analysis to infer three-dimensional distribution characteristics, assuming uniform distribution within horizontal layers. Future research should focus on developing CT scanning combined with three-dimensional image processing techniques to achieve in situ quantitative characterization of spatial fiber networks, thereby enabling more precise studies.
• Expansion of Parameter Range. This study primarily focused on three key process parameters. However, in practical engineering, fiber type (hooked-end, straight, etc.), matrix rheology (self-compacting concrete vs. ordinary concrete), environmental conditions, and other factors may interactively influence fiber distribution. Future research could further expand the parameter space and establish a more comprehensive database and predictive model.

5. Conclusions

This study has successfully addressed its predefined objectives through an integrated methodology that combines multi-factor experimentation, image recognition, and meso-scale numerical simulation. The findings are presented in direct correspondence with the three research aims outlined in the Introduction.

In relation to the first objective, which focused on quantifying the effects of process parameters, the experimental results elucidate the quantitative relationships among vibration energy, fiber dosage, aggregate volume fraction, fiber distribution, and macroscopic mechanical performance. An optimal parameter combination was identified, consisting of moderate vibration energy (30 s), a fiber dosage of 1.5%, and an aggregate volume fraction of 40%. This combination promoted favorable fiber orientation and a graded distribution, leading to the highest flexural strength and a multi-crack failure mode.

Regarding the second objective of establishing an image recognition pipeline, a comprehensive and reliable workflow was developed and implemented. This process includes specimen sectioning, grayscale conversion, Otsu binarization, and feature extraction, enabling precise localization and parametric description of the actual steel fiber distribution within cross-sectional images.

Concerning the third objective, a finite element model that explicitly incorporates image-recognized fiber distribution characteristics was developed and validated. Comparative analysis against experimental data and conventional random-distribution models demonstrated its clear advantages: the model reduced prediction errors for the initial cracking load and ultimate bending moment by 16.3% and 17.6%, respectively, while improving the geometric similarity of simulated crack paths by approximately 27.3%.

In summary, this work offers a validated methodology that bridges the gap between idealized modeling assumptions and the process-influenced material reality of SFRC. The results emphasize the essential role of accounting for actual, non-uniform fiber distribution—as shaped by construction processes—in achieving reliable numerical simulations of SFRC structural behavior.