Effects of Web Thickness and Flange Thickness on Flexural Crack Evolution and Ductility of H-Shaped UHPC Piles Based on DIC and Finite Element Analysis

Abstract

This study aims to reveal the control mechanism of key geometric parameters (flange thickness and flange edge thickness) of H-shaped cross-section on the bending performance of UHPC piles. Through conducting bending tests, combined with digital image correlation (DIC) technology and finite element simulation, the mechanical behavior was studied, and based on the principal strain field obtained from DIC, a strain field concentration index was proposed. The results show that: as the load ratio increases, the strain field concentration and the peak value of the mid-span principal strain continuously increase, and the crack evolution changes from dispersed development to localized control; near the limit state, the strain field concentration can reach approximately 0.28, and the peak value of the principal strain increases in an increasing trend, approximately 20% or more. Under the specific conditions of this test, in terms of ductility and energy absorption, when the flange thickness is constant, increasing the flange thickness of the web increases the energy absorption of the component by approximately 6% to 10%, while the ductility coefficient decreases by approximately 9% to 15%; when the web thickness is constant, increasing the flange thickness reduces the ductility coefficient by approximately 21% to 25%, and the energy absorption decreases by approximately 27% to 29%. The strain field concentration can effectively reflect the evolution process of the localization of bending cracks in H-shaped UHPC piles and can be used for quantitative analysis of their ductility degradation and energy absorption characteristics. It should be clarified that this study does not claim to isolate the effect of a single parameter.

1. Introduction

Ultra-high performance concrete (UHPC) is a new type of building material, featuring excellent compressive strength, durability, and crack resistance. It is widely used in bridges, super high-rise buildings, and important infrastructure [1,2,3]. Compared with traditional concrete, UHPC not only enhances compressive strength and durability but also can withstand higher loads and harsh environmental conditions, thus having significant application value in modern engineering [4,5]. However, although UHPC improves the structural bearing capacity, the initiation, expansion, and localization of cracks remain key issues affecting its performance and ductility [6].

The generation and development of cracks are the core issues affecting the service life of UHPC materials. Cracks not only reduce their compressive and tensile strength but also affect the ductility and failure mode of the structure. Localized cracks can lead to local damage and cause brittle failure, limiting their application in special projects. Although UHPC has high strength and durability, the evolution process of cracks is complex and has multi-scale characteristics. Therefore, in-depth research on the evolution mechanism of cracks in UHPC components is of great theoretical significance and engineering value for its engineering design, performance optimization, and life prediction.

In recent years, many scholars have conducted extensive research on the compressive strength, flexural performance, and fracture toughness of UHPC, especially in the study of crack evolution. The initiation, expansion, and localization of cracks are considered the key factors determining the service performance of the material. For example, Zong et al. [7] found through four-point bending tests that factors such as the reinforcement ratio of longitudinal bars, hollow ratio, and the content of glass microbeads affect the development of cracks; Huang et al. [8] conducted experimental studies on the flexural performance of UHPC-filled damaged reinforced concrete T-beams. The results showed that UHPC restoration can effectively restore and enhance the bending stiffness, cracking load, and ultimate load of the T-beam, with the ultimate load of the specimen with a 1.0 m repair zone being 34.11% higher than that of the unrestored beam. Moreover, by using chiseling treatment to convert the tensile interface between UHPC and the original concrete into a shear interface, the interface peeling was inhibited, and the crack width of the repaired beam was smaller than that of the control beam. Song et al. [9] studied the influence of fiber content and corrosion degree on the crack evolution of UHPFRC. Increased corrosion will lead to damage localization and brittle failure, changing the crack evolution path: in low corrosion, cracks are dominated by shear, and multiple cracks expand; while in high corrosion, cracks are dominated by tension, and the main crack rapidly loses stability and expands. Al-Obaidi et al. [10] found through experiments that the micro-crack control ability of UHPC is the core of its durability, and nanomaterials improve the dispersion of fibers, the compactness of the matrix, and the self-repair efficiency, enhancing crack stability. Lu et al. [11] studied the influence of the length, volume fraction, diameter, and shape of steel fibers on the initial cracking strength of UHPC through tensile tests. The results showed that steel fibers can enhance the initial cracking strength of UHPC, with the fiber length and volume fraction having a greater influence, and the diameter and shape having a smaller influence; 13 mm long and 3% volume fraction straight steel fibers had the best effect, while deformed fibers caused stress concentration and had a lower initial cracking strength. He et al. [12] compared the effects of glass fibers (GF) and high-performance polypropylene (HPP) fibers on the mechanical properties of UHPC. The results showed that at a 2.0% fiber content, glass fibers improved the compressive, tensile, and flexural strengths of UHPC, which were approximately 20%, 30%, and 40% higher than those of HPP; while HPP fibers had better toughening effects, with the flexural toughness index of HPP fibers being 1.2 times, 2.0 times, and 3.8 times higher than that of GF-UHPC. Birol et al. [13] investigated the influence of different volume contents of macroscopic polypropylene (PP) fibers on the mechanical properties of ultra-high performance concrete (UHPC), and found that the use of macroscopic PP fibers increased the residual bending tensile strength and fracture energy of UHPC by 2.8 times and 2.5 times respectively, and could effectively control cracks. Herbers et al. [14] conducted four-point bending tests on beams and found that the widths of all cracks almost linearly increased with displacement. Although existing studies have provided a theoretical basis for the mechanism of crack evolution [15], H-shaped section members exhibit complex mechanical behavior due to their unique geometric shape under bending conditions. Different from traditional rectangular or circular section members, the flanges of H-shaped members bear tensile and compressive stresses, while the web bears shear stress, resulting in different stress and deformation characteristics during bending. Existing studies have discussed the mechanical behavior of H-shaped sections, but there are few systematic studies on H-shaped UHPC piles, especially considering the combined effect of UHPC’s nonlinear constitutive relationship and geometric effects. The stress–strain distribution of H-shaped UHPC piles is affected by the complex interaction of material properties and geometric shapes, showing mechanical characteristics different from traditional H-shaped piles [16,17]. Moreover, the thickness of the flange and the thickness of the web have significant influences on the bending stiffness and crack distribution pattern of the members, but existing studies have explored this less [18]. Therefore, this study takes these two parameters as key variables to investigate their influence on the mechanical properties of H-shaped UHPC piles and provide a theoretical basis for their optimization design.

Although various methods for crack development and control have been explored in existing studies, the existing crack monitoring techniques still rely on macroscopic observation and discrete sensors, which are mostly limited to capturing the initial development or local characteristics of cracks. Wang et al. [19] using DIC technology discovered that at the initial stage of cracks, strain concentration occurred at material defects, and cracks expanded along the principal strain direction. DIC could capture the localized strain band at the crack tip; when the cracks reached the critical length, the specimen broke. García et al. [20] quantified the deformation and crack propagation of concrete using DIC and piezoelectric sensors with high precision. Wang et al. [21] used DIC technology to observe the strain cloud map in the three-point bending experiment, finding that cracks expanded with the increase in load and eventually led to specimen failure. DIC technology captures the strain and displacement fields, revealing the initiation and propagation process of cracks [22,23,24].

Numerical simulation techniques play an increasingly important role in crack research. Especially, the concrete damage plasticity (CDP) model based on the finite element method has been widely used for the simulation of crack evolution in UHPC components [25,26]. Faron et al. [27] found that XFEM crack propagation analysis was consistent with the experimental results and could accurately map the crack pattern. Bendezu et al. [28] compared XFEM, the inter-element crack method, and element elimination technology, finding that XFEM could more accurately simulate crack propagation. Patel et al. [29] used XFEM to simulate the three-dimensional crack propagation of high-strength concrete and confirmed the advantages of XFEM in handling crack problems. Chen et al. [30] conducted multi-scale simulations of reinforced concrete columns using XFEM and accurately predicted the crack evolution process. Although existing numerical methods can better predict crack evolution, there are still deficiencies in the quantitative analysis of crack localization and ductility degradation [31,32].

By combining four-point bending tests, digital image correlation (DIC) technology, and finite element simulation, this study investigates the crack evolution mechanism, ductility, and energy absorption characteristics of H-shaped UHPC piles under bending action. Through this study, this paper aims to: (1) based on the full-field strain data obtained by digital image correlation (DIC) technology, construct a strain field concentration index to quantitatively characterize the evolution process of cracks from dispersion to localization in H-shaped UHPC piles under bending, providing a new quantitative characterization method for the analysis of crack localization; (2) introduce the strain field concentration index, combine the crack evolution characteristics with the ductility coefficient and energy absorption, and clarify the control effect of crack localization degree on the degradation of bending performance and energy dissipation ability of H-shaped UHPC piles; (3) provide a quantifiable reference basis for the crack resistance design and ductility optimization of H-shaped UHPC piles.

2. Experimental Program and DIC Measurement Method

2.1. Materials

The mixture proportions of the ultra-high performance concrete (UHPC) used for the specimens are listed in

Table 1. Mix proportions of UHPC matrix.

Cement (kg/m3)	Manufactured Sand (kg/m3)	Silica Fume (kg/m3)	Fly Ash (kg/m3)	GGBS (kg/m3)	Rheology Modifier (kg/m3)	Water (kg/m3)	Superplasticizer (kg/m3)	Steel Fibers (kg/m3)
800	850	250	100	160	131	200	35	155

. The UHPC mixture contained 2% (by volume) straight steel fibers with a diameter of 0.2 mm and a length of 13 mm, Portland cement (P.O 52.5), silica fume, manufactured sand, and a polycarboxylate-based high-range water-reducing admixture. Silica fume, Class I fly ash, and the PCA-HP polycarboxylate superplasticizer were supplied by Henan Jinrun New Materials Co., Ltd. (Zhengzhou, China), Jiangsu Shuangyuan New Materials Co., Ltd. (Nantong, China), and Jiangsu Sobute New Materials Co., Ltd. (Nanjing, China), respectively. The detailed chemical compositions and main physical properties of these materials are provided in

Table 2. Main parameters of silica fume.

SiO2 (%)	Loss on Ignition (%)	Specific Surface Area (m2/g)	Chloride Content (%)
92.4	3.92	19.1	0.07

,

Table 3. Main chemical composition of fly ash.

Chemical Composition	Al2O3	SiO2	SO3	CaO	Others
Mass fraction (%)	24.3	45.1	2.1	5.6	23.0

and

Table 4. Main parameters of ground granulated blast-furnace slag (GGBS).

Density (g/cm3)	Specific Surface Area (m2/g)	7-Day Activity Index (%)	Flowability Ratio (%)	SO3 (%)
2.9	420	420	104	0.11

. Ground granulated blast-furnace slag (GGBS) with a grade of S95 was produced by Jiangsu Shuangyuan New Materials Co., Ltd., and the rheology-modifying admixture for high-performance concrete was supplied by Jiangsu Sobute New Materials Co., Ltd.

2.2. Specimen Preparation

A total of six H-shaped ultra-high performance concrete (UHPC) piles were fabricated for the experimental program. The sectional dimensions and reinforcement details of the specimens are illustrated in Figure 1, and the corresponding design parameters are summarized in

Table 5. Design parameters of H-shaped UHPC pile specimens.

Specimens	Specimen ID	Sectional Dimensions (mm)	Flange Thickness t1/t2 (mm)	Web Thickness f1 (mm)	Flange Width b1/b2 (mm)	Reinforcement Ratio (%)
Group A	Sample1	270 × 300	60	60	120/120	2.05
	Sample2			75	112.5/112.5	1.95
	Sample3			90	105/105	1.87
Group B	Sample1	300 × 300	75	60	120/120	1.71
	Sample2			75	112.5/112.5	1.64
	Sample3			90	105/105	1.57

. The fabrication tolerance of all specimens was controlled within ±1 mm. Two types of H-shaped sections were considered: specimens in Group A had sectional dimensions of 270 mm × 300 mm, while those in Group B had sectional dimensions of 300 mm × 300 mm. The total length of each pile was 3400 mm, with an effective test length of 3000 mm. All specimens were reinforced with six longitudinal HRB400 steel bars with a diameter of 14 mm. Closed stirrups with a diameter of 6 mm were arranged at a spacing of 100 mm along the length of the specimens and were made of HPB350 steel, with a bending angle of 180°.

It should be noted that, due to the geometric coupling between flange width and reinforcement ratio, the term ‘single-variable principle’ should be interpreted with caution. In this experiment, changes in web thickness are associated with corresponding adjustments in flange width and reinforcement ratio. Therefore, the reported results reflect the combined effects of these parameters, rather than the isolated impact of a single variable.

Mechanical property tests were conducted on the two types of reinforcing steel in accordance with GB/T 228.1-2021. Meanwhile, UHPC specimens were prepared following the requirements of GB/T 313832015, including cube specimens (100 mm × 100 mm × 100 mm), prismatic specimens (100 mm × 100 mm × 300 mm), and dog-bone-shaped tensile specimens [33,34]. Compressive strength, Young’s modulus, and tensile strength tests were performed for the corresponding specimens, and the average values were adopted as the final results. The material testing procedures are illustrated in Figure 2.

The material test results indicate that the average compressive strength of UHPC cubes was 107.72 MPa, the elastic modulus was approximately 35.81 GPa, and the axial tensile strength was 8.71 MPa. For the reinforcing steel, HRB400 exhibited a yield strength of 400 MPa and an ultimate strength of 600 MPa, corresponding to a yield strain of approximately 0.002. The HPB350 steel showed a yield strength of 350 MPa, an ultimate strength of 500 MPa, and a yield strain of 0.00175.

2.3. DIC Measurement System and Loading Protocol

The digital image correlation (DIC) testing system employed in this study is illustrated in Figure 3. The measurement system mainly consists of an image acquisition system and an image processing and computation system. The image acquisition system includes a high-resolution digital camera mounted on a rigid support frame and a lighting source to ensure uniform illumination. The speckle images captured by the camera are imported into the image analysis system (DIC-3D system) for subsequent processing, enabling the determination of full-field displacement and strain distributions on the specimen surface throughout the entire loading process [35,36].

Prior to DIC measurements, surface preparation of the specimens was carried out to ensure adequate speckle quality, as shown in Figure 4. The main parameters of the DIC system used in the tests are summarized in

Table 6. DIC testing parameters for crack propagation analysis of H-shaped UHPC piles.

Test objective:	Based on digital image correlation (DIC) technology, the flexural crack evolution and ductility behavior of H-shaped UHPC piles were investigated. By monitoring the crack development process, a strain field localization index was proposed, and its quantitative relationship with ductility was analyzed. The findings provide a reference for evaluating the flexural performance of H-shaped UHPC piles and for optimizing their structural design.
Type	Parameters	Equipment
Basic information	Camera resolution	4000 × 3000 pixels
	Acquisition frequency	Dynamic loading: 5 Hz; Static loading: 1–2 Hz
Measurement accuracy	Standard accuracy	±0.1 mm
	Subset size	25 × 25 pixels
	Step size	5 pixels
Image quality	Image contrast quality	High contrast
Lighting conditions	Illumination uniformity	Uniform light source
Technical features:
①	Digital image correlation (DIC) technology enables dynamic monitoring of crack evolution and provides accurate strain and displacement data, offering a reliable basis for crack localization analysis.
②	Under varying loading conditions, DIC is capable of capturing crack development trends, which aids in analyzing the influence of different parameters on the performance of H-shaped UHPC piles.

.

A four-point bending loading scheme was adopted in the tests. The load was applied using a hydraulic actuator with a capacity of 500 kN and was monitored and controlled in a closed-loop manner through a load cell. The loading setup is shown in Figure 5. The loading protocol strictly followed the provisions of the Standard for Test Methods of Concrete Structures [37] and employed a combined loading strategy consisting of force control followed by displacement control.

Prior to formal loading, a preload was applied to ensure proper seating of the specimen and to eliminate possible contact gaps. The preload level was set to approximately 5–10% of the estimated peak load and was maintained for about 2–3 min for zero calibration. Subsequently, stepwise loading was conducted under force-control mode until the applied load approached the peak value, with an increment of 10 kN at each loading step. Each load level was held until the readings became stable. When the applied load reached approximately 80–90% of the theoretically estimated peak load and visible cracking accompanied by stiffness degradation was observed, or when a decreasing trend in load-carrying capacity was detected, the loading mode was switched to displacement control. At this stage, closed-loop control based on mid-span deflection was adopted, with a loading rate of 0.1–0.2 mm/min, in order to capture crack propagation and the post-peak softening behavior. The yield displacement was determined by using the displacement value corresponding to the load reaching 85% of the peak load in the load–displacement curve.

3. Results and Discussion

3.1. Load–Deflection Curve Analysis

As illustrated by the vertical displacement contours in Figure 6, the overall vertical displacement of all specimens increases monotonically with the progression of loading stages. During the initial loading stage (0–0.2$F_p$), the mid-span vertical displacement remains relatively small, and the deformation is mainly governed by elastic bending. The maximum vertical displacement is generally less than approximately 5 mm, indicating that the specimens are still in a relatively uniform stress state. As the load increases to 0.4$F_p$ and 0.6$F_p$, the mid-span vertical displacement increases markedly, and the displacement gradient becomes more pronounced. At this stage, the specimens enter the crack development phase, and flexural deformation gradually becomes dominant.

When the load approaches the ultimate state (0.8$F_p$–1.0$F_p$), the mid-span vertical displacement of all specimens reaches its peak value, and the displacement distribution becomes increasingly concentrated at the mid-span and crack-localized regions. This phenomenon indicates a transition of the deformation mode from global bending to localized deformation control. For specimens with the same web thickness, those with a flange thickness of 75 mm exhibit maximum vertical displacements of approximately 35–40 mm at the ultimate state, whereas the corresponding specimens with smaller sectional dimensions show lower maximum vertical displacements of about 25–30 mm.

Figure 7 shows the load–displacement curves for different specimens. Under the same cross-sectional dimensions, specimens with different web thicknesses exhibit differences in bearing capacity and deformation capacity. As the web thickness increases, the bearing capacity of the specimens improves. For example, for specimens with a cross-sectional size of 270 mm × 300 mm, the maximum load of the specimen with a web thickness of 90 mm is approximately 4.3% higher than that of the specimen with a web thickness of 60 mm. The deformation capacity also increases with the increase in web thickness. Specifically, for specimens with a 300 mm × 300 mm cross-section, the cross-sectional displacement of the specimen with a web thickness of 75 mm is approximately 9.5% higher than that of the specimen with a web thickness of 60 mm. When the web thickness is further increased to 90 mm, it shows an increase compared to the specimen with a web thickness of 60 mm, with an increase of approximately 10.8%.

Increasing the web thickness can effectively enhance the bearing capacity and deformation capacity of the specimens, indicating that a thicker web design can not only improve the bearing capacity but also provide greater deformation capacity, demonstrating better ductility performance. Increasing the thickness of the web plate can enhance the bending and shear stiffness of the cross-section, thereby improving the peak bearing capacity of the specimen. However, the increase in stiffness will inhibit the plastic rotational capacity of the cross-section and intensify the localized effect of the bending cracks, ultimately resulting in a decrease in the ductility coefficient rather than a reduction in the absolute value of non-ductility.

When the web plate is relatively thin, the cross-sectional stiffness is smaller, the bending deformation is more uniform, the cracks are dispersed, and the stress can be effectively transferred and released. The component can generate more sufficient plastic rotation, thus having a higher ductility coefficient.

As the thickness of the web plate increases, the bending stiffness of the cross-section improves, the cracks rapidly concentrate in the pure bending zone and form the main crack, the strain localization effect is enhanced; the concentrated development of cracks weakens the multi-crack collaborative energy dissipation mechanism, resulting in a decrease in the post-peak deformation capacity of the component, manifested as a decrease in the ductility coefficient and a more brittle failure mode.

The crack propagation paths shown in Figure 6 exhibit a high degree of consistency with the load–mid-span displacement responses presented in Figure 7. For the specimen with a sectional dimension of 300 mm × 300 mm and a web thickness of 90 mm, more pronounced crack propagation is observed; however, both the load-carrying capacity and deformation capacity are simultaneously enhanced. This indicates that a larger sectional size combined with a thicker web not only provides higher structural strength but also allows greater deformation prior to failure.

In contrast, the specimen with a sectional dimension of 270 mm × 300 mm and a web thickness of 60 mm exhibits relatively limited crack propagation, while both the load-carrying capacity and deformation capacity remain comparatively low. This suggests that specimens with smaller sectional dimensions and thinner webs possess insufficient load resistance and limited deformation capacity.

As shown in Figure 7, with the increase in the thickness of the web plate, the number of cracks gradually decreases and gradually concentrates in the mid-span area; especially when the web plate thickness is 90 mm, the crack width increases and the spacing decreases, showing a clear localized trend. This phenomenon is consistent with the research conclusion of Niu Y et al. [38]. Their research pointed out that an increase in web plate thickness would enhance the structural bending stiffness, leading to an intensified stress concentration effect and promoting the localized development of cracks. This study further verified and supplemented this conclusion through quantitative analysis of the strain localization index—as the web plate thickness increases, the strain localization index increases, clearly quantifying the evolution law of the crack concentration effect, and compensating for the lack of quantitative characterization in previous studies.

Although an increase in web plate thickness can enhance the structural bearing capacity, it will lead to a decrease in the ductility coefficient. The main reason is that crack localization dominates the deformation process of the component, inhibiting the coordinated energy dissipation of multiple cracks. This law is consistent with the viewpoint proposed by Qasem A et al. [39] in the study of the mechanical properties of UHPC components, which states that an increase in component stiffness is prone to causing stress concentration, restricting the uniform expansion of cracks, and thereby exacerbating brittle failure. This study further clarifies that this restrictive relationship is more obvious in H-shaped UHPC piles, due to their synergistic load-bearing characteristics of the flange and web plate, which is a supplement and extension of previous studies.

Energy absorption is a key indicator for evaluating the ability of a component to resist brittle failure, especially applicable in dynamic load scenarios such as earthquakes. This study found that with the increase in web plate thickness, the energy absorption capacity shows a “first increase then sharp decline” trend, which is consistent with the research conclusion of Luo J et al. [40]. Their research indicates that crack localization limits the energy dissipation capacity of the structure, and this limiting effect becomes more obvious after the web plate thickness exceeds 75 mm. This is mainly due to the thick web plate accelerating the formation of the main crack, weakening the bridging effect of steel fibers, resulting in a single energy dissipation path and rapid attenuation.

3.2. Principal Strain Contours and Crack Propagation Trajectories

Figure 8 illustrates the evolution of principal strain distributions and the corresponding crack propagation trajectories of H-shaped piles subjected to four-point bending. At the initial loading stage, the principal strain contours of all specimens indicate that deformation is mainly concentrated near the specimen edges and the web region, with relatively low strain levels and no visible cracking. During this stage, the principal strain values generally range from 0 to approximately 0.3%, suggesting that the specimens remain in the elastic regime and that crack development is negligible.

With increasing load, the strain levels gradually increase, particularly for specimens with larger sectional dimensions (e.g., 300 mm × 300 mm), where the principal strain reaches approximately 0.6–1.0%. At this stage, crack propagation paths begin to emerge and are mainly concentrated in the mid-span region and the web, indicating the onset of nonlinear behavior. The larger sectional specimens exhibit more pronounced strain localization and crack development, and their load-carrying capacity approaches the ultimate level. As the load approaches the ultimate state, the strain values increase further. For example, the maximum principal strain of the specimen with a sectional dimension of 300 mm × 300 mm and a web thickness of 90 mm reaches nearly 2.0%, whereas that of the specimen with a sectional dimension of 270 mm × 300 mm and the same web thickness is approximately 1.5%.

3.3. Failure Modes and Crack Localization Characteristics

Figure 9 presents the final failure patterns of specimens with different sectional dimensions under various loading levels. With increasing sectional size and web thickness, more pronounced crack propagation is observed, accompanied by an increase in crack density and propagation rate. For specimens with sectional dimensions of 270 mm × 300 mm, the number of cracks and their degree of localization gradually increase as the web thickness increases. In particular, the specimen with a web thickness of 90 mm exhibits the largest number of cracks with a relatively wide distribution, indicating rapid crack propagation near the ultimate load and the occurrence of localized damage.

In comparison, specimens with larger sectional dimensions of 300 mm × 300 mm show more evident crack development. Especially for the specimen with a web thickness of 90 mm, the crack density and propagation rate are the highest, suggesting that the combination of a larger sectional size and a thicker web enhances the load-carrying capacity while allowing greater deformation and more extensive crack development.

More specifically, the failure modes of the specimens can be classified as follows. For the 270 mm × 300 mm specimens:

(A1) The specimen with a web thickness of 60 mm exhibits initial crack development with a limited number of cracks that are relatively uniformly distributed, and the failure mode is dominated by flexural behavior, with slight bending deformation and a small number of cracks appearing near the mid-span.

(B1) The specimen with a web thickness of 75 mm shows an increased number of cracks with a tendency toward localization, characterized by a combination of flexural failure and localized compression crushing, with relatively rapid crack propagation and visible crushing traces in local regions.

(C1) The specimen with a web thickness of 90 mm presents the largest number of cracks with a wider distribution, and crack propagation occurs rapidly, indicating localized damage dominated by flexural failure as the specimen approaches the ultimate load.

For the 300 mm × 300 mm specimens:

(A2) The specimen with a web thickness of 60 mm exhibits a limited number of cracks with relatively slow propagation, and the failure mode is mainly flexural, with cracks concentrated near the mid-span.

(B2) The specimen with a web thickness of 75 mm shows a larger number of cracks with a higher propagation rate, and the failure behavior is dominated by flexural failure accompanied by localized compression crushing in certain regions, with cracks propagating along the width direction of the specimen.

(C2) The specimen with a web thickness of 90 mm exhibits the highest crack density and the fastest crack propagation. The cracks are mainly vertical flexural cracks propagating along the height of the member, and the failure mode is characterized by flexural failure with localized compression crushing.

This indicator is based on the method used in references [40,41,42] to characterize the unevenness of the strain field. This paper is the first to apply it to the analysis of the bending crack evolution of H-shaped UHPC piles, and establishes a quantitative relationship with ductility and energy absorption. To quantitatively characterize the evolution process of cracks in H-shaped UHPC piles from dispersion to localization concentration under bending action, this paper introduces the strain field concentration index [38,39]. This indicator is calculated based on the principal strain field data obtained by digital image correlation (DIC) technology, aiming to reflect the unevenness of cracks and strains in spatial distribution. The definition of strain field concentration is as follows:

$$C={\displaystyle \frac{{\sum }_{i=1}^n{\left({\epsilon }_i−\bar{\epsilon }\right)}^2}{{\sum }_{i=1}^n{\epsilon }_i^2}}$$

(1)

$$\bar{\epsilon }={\displaystyle \frac{1}{n}}{\sum }_{i=1}^n{\epsilon }_i$$

(2)

where ${\epsilon }_i$ denotes the principal strain value at the $i$-th measurement point, $\bar{\epsilon }$ represents the average principal strain over the analyzed region, and $n$ is the total number of measurement points.

The concentration index of the strain field is a dimensionless parameter that reflects the degree of spatial dispersion of the strain. When the cracks develop in a dispersed manner, and the strain is relatively uniform in space, the concentration is small; while when the cracks gradually concentrate in a local area and the main crack dominates the deformation process, the concentration increases, indicating that the structure has entered the brittle failure stage dominated by crack localization.

The change in the concentration of the strain field can quantitatively describe the spatial distribution characteristics of the strain during the evolution of cracks. During the loading process of the structure, the initial development of cracks is usually accompanied by a uniform distribution of strain, and at this time, the concentration of the strain field is low. As the cracks expand, especially the development of the main crack, the strain gradually becomes concentrated, resulting in an increase in the concentration of the strain field, and ultimately indicating that the structure has entered the failure stage dominated by localization. This method can provide a precise quantitative basis for the localization analysis of cracks, especially for the study of crack behavior of UHPC materials under complex loading.

Traditional methods (such as crack width measurement) can only be evaluated after the visible cracks appear. However, the strain concentration index in this paper can detect the uneven distribution of strain during the elastic stage (approximately 0.2 times the peak load) and achieve early monitoring of the initial stage of crack evolution. The current crack assessment methods are mostly qualitative descriptions and lack a quantitative relationship with the macroscopic performance of the structure (such as ductility, energy absorption). This paper establishes a quantitative relationship between the strain concentration value and the ductility coefficient and energy absorption through regression analysis, improving the predictive ability of the crack localization index in engineering. The traditional strain gradient method or strain concentration coefficient relies on the absolute size of the strain, making it impossible to directly compare different specimens. This paper normalizes the denominator to eliminate the influence of the overall level of strain on the results, allowing different specimen sizes and different load levels to be directly compared. The comparison of existing methods with the strain concentration index of this paper is shown in

Table 7. Concentration of stress field compared with traditional methods.

Method/ Literature	Principle	Data Type	Applicable Stage	The Association with Ductility/Energy Absorption	Limitations
Traditional measurement of a crack width/spacing (empirical method)	Manual or semi-automatic measurement of the geometric parameters of cracks	Discrete point data	Once the cracks appeared	No direct connection	Due to relying on visual recognition, it is impossible to detect early damage.
Strain gradient method	Calculate the spatial gradient of the strain field	Overall Response (DIC)	Linear elasticity to localization	No quantitative relationship has been established.	Sensitive to noise, and the physical meaning is not intuitive enough.
Localized crack model	Based on the statistics of the crack area/density	Binaryized crack image	The stage of stable expansion of cracks	No quantitative relationship has been established.	Image segmentation is required, but it is difficult to achieve automation.
Concentration of the strain field	Ratio of variance to the sum of squares	Overall Response (DIC)	From the stage of elasticity to the stage of destruction	Preliminary quantitative correlation observed	Due to the precision of DIC, the threshold needs to be further calibrated.

.

Figure 10 shows the variations in the strain field localization index and the peak principal strain at mid-span with respect to the load ratio for specimens with different flange thicknesses and web thicknesses. The load ratio is defined as the ratio of the applied load to the peak load of the specimen. Overall, during the initial loading stage, both the strain field localization index and the peak principal strain at mid-span increase gradually with increasing load ratio, indicating that cracks mainly develop in a dispersed manner and that the specimens remain in a relatively uniform stress state. As the load ratio increases further, the strain field localization index and the peak principal strain continue to rise, suggesting that cracks begin to concentrate in localized regions and that strain localization gradually becomes apparent.

When the load ratio approaches 1.0 (i.e., close to the peak load), the growth rates of the strain field localization index and the peak principal strain at mid-span become more pronounced. At this stage, crack development transitions from a relatively stable propagation phase to a localization-dominated phase. The further mobilization of load-carrying capacity is primarily governed by strain concentration in localized regions, whereas the increase in global deformation capacity becomes limited, indicating that the failure process is increasingly controlled by localized damage.

A comparison among specimens with different flange thicknesses shows that, under the same load ratio, specimens with larger flange thickness generally exhibit higher strain field localization indices and higher peak principal strains at mid-span. For example, at a load ratio of 1.0, the specimen with a sectional dimension of 300 mm × 300 mm and a web thickness of 90 mm exhibits a strain field localization index of 0.28 and a peak principal strain of 21.5%, which are approximately 47% and 23% higher, respectively, than those of the specimen with a sectional dimension of 270 mm × 300 mm and a web thickness of 60 mm. Although the differences in mid-span displacement between these specimens are relatively limited, the pronounced differences in strain field localization indicate that increasing flange thickness does not significantly enhance the global deformation capacity. Instead, it promotes the concentration of strain and cracking in localized regions, causing crack localization to occur earlier as the specimen approaches the ultimate state.

3.4. Ductility and Energy Absorption Characteristics

In the investigation of the flexural behavior of H-shaped ultra-high performance concrete (UHPC) piles, ductility and energy absorption characteristics are important performance indicators. By means of digital image correlation (DIC) technology, full-field displacement and strain data on the specimen surface can be obtained. The ductility coefficient ${\mu }_{\mathrm{\Delta }}$ is adopted to evaluate the deformation capacity of the specimens. As defined in Equation (3), ${\mu }_{\mathrm{\Delta }}$ is expressed as the ratio of the ultimate deflection ${\mathrm{\Delta }}_u$ to the yield deflection ${\mathrm{\Delta }}_y$.

In addition, the energy absorption $E_d$ is indirectly calculated based on strain field data, which is defined as the difference between the external work and the strain energy, as given in Equations (4)–(8) [43,44]. In the DIC measurement process, the displacement of marked points in the recorded images is tracked, and the strain field is obtained through numerical differentiation or finite difference methods. The resulting strain field data contain the principal strain values at each grid point of the specimen surface. Please note that the energy absorption values provided are approximate, and the assumption of linear elastic behavior (σ = Eε) becomes less accurate as damage progresses, particularly after cracking of UHPC and yielding of the reinforcement.

$$\begin{array}{cccc}& {\mu }_{\mathrm{\Delta }}={\displaystyle \frac{{\mathrm{\Delta }}_u}{{\mathrm{\Delta }}_y}}& & \end{array}$$

(3)

The strain energy $U_{\mathrm{strain}}$ represents the energy stored in the material during the loading process and constitutes a core component of the energy dissipation analysis. According to the fundamental assumptions of elasticity theory, the strain energy of a specimen can be calculated as

$$U_{strain}={\int }_v{\displaystyle \frac{1}{2}}\sigma ϵdV$$

(4)

where $\sigma$ denotes the stress, $\epsilon$ represents the strain, and $V$ is the volume of the specimen. Under the assumption of linear elasticity, the stress–strain relationship can be expressed as

$$\sigma =E\epsilon$$

(5)

where $E$ is the elastic modulus of the material. By substituting this relationship into the above equation, the strain energy can be further expressed as

$$U_{strain}={\int }_V{\displaystyle \frac{1}{2}}E{\epsilon }^2\hspace{0.17em}dV$$

(6)

The external work $W_{\mathrm{ext}}$ can be obtained by integrating the product of the applied load $F$ and the corresponding displacement $\delta$, which can be expressed as

$$W_{ext}=\int F\delta$$

(7)

Accordingly, the energy absorption capacity $E_d$ of the specimen is defined as the difference between the external work and the strain energy stored in the material, which can be written as

$$E_d=W_{ext}-U_{strain}$$

(8)

This definition enables a quantitative evaluation of the energy dissipation behavior of H-shaped UHPC piles by incorporating both the global load–displacement response and the internal strain energy evolution derived from DIC measurements.

As shown in

Table 8. Ductility and energy absorption.

Specimens		Load (kN)		Deflection (mm)			${\mathit{E}}_{\mathit{d}}$ (kN⋅mm)	${\mathit{\mu }}_{∆}$
		${\mathit{p}}_{\mathit{y}}$	${\mathit{p}}_{\mathit{p}}$	${∆}_{\mathit{y}}$	${∆}_{\mathit{p}}$	${∆}_{\mathit{u}}$
Group A	Sample1	96.7	128.5	10	25	45.1	6400.9	4.5
	Sample2	110	132.4	12	28	49.4	6657.2	4.11
	Sample3	107.7	134.1	13	30	51.7	6830.3	3.98
Group B	Sample1	130	150.1	13	32	44.3	4524.4	3.41
	Sample2	134	152.2	15	35	48.5	4786.6	3.23
	Sample3	137	152.8	16	37	49.1	4938.7	3.07

Note: The data in this table represent the results of a single test, and no repeated tests were conducted. The fiber distribution and orientation of UHPC materials have inherent variability.

, under the changes in web thickness and flange thickness, the ductility and energy absorption of the components have opposite trends. Increasing the web thickness is beneficial for enhancing the energy absorption of the component, but it reduces the ductility; while increasing the flange thickness reduces the energy absorption, but the decline in ductility is smaller.

The increase in web thickness enhances the stiffness of the component, resulting in a more concentrated crack extension. Specifically, a thicker web restricts the uniform distribution of cracks in the structure, causing the cracks to gradually concentrate in specific areas, thereby triggering localized phenomena. The intensification of this localized effect causes the structure to lose its overall deformation ability, resulting in a decrease in the ductility coefficient. For the Group A section, the ductility coefficient decreased from 4.50 to 3.98, showing a downward trend of approximately 11.56%; for the Group B section, it decreased from 3.41 to 3.07, showing a downward trend of approximately 9.97%. This indicates that the negative impact of increasing the web thickness on ductility is mainly due to the strain concentration caused by localization and the decline in energy dissipation capacity.

Although the ductility coefficient decreases, the energy absorption shows an upward trend. With the increase in web thickness, the crack distribution gradually concentrates in local areas. During the process of localization, the structure’s resistance to external forces increases, and it can absorb more energy. Especially in the Group A section, the energy absorption increased from 45.

When the flange thickness is fixed, an increase in the web thickness is beneficial for enhancing the energy absorption of the component; however, under the condition where the web thickness is constant, an increase in the flange thickness will reduce the energy absorption of the component. In both cases, the ductility coefficient of the component shows a downward trend.

Based on the regression analysis, a quantitative relationship was established among the strain field concentration index (C), the ductility coefficient (μ_Δ), and the energy absorption (E_d), and the specific expression is (9):

$$C=0.4248-0.0593\cdot {\mu }_{\mathrm{\Delta }}+5.86\times {10}^{-6}\cdot E_d$$

(9)

Among them, C represents the concentration index of the strain field, μΔ is the ductility coefficient, and Ed is the energy absorption. The goodness of fit (R²) of this regression equation is 0.854, indicating that this equation can accurately describe the relationship between the concentration index of the strain field, ductility, and energy absorption.

Equation (9) provides a preliminary empirical correlation between the strain field concentration index and ductility/energy absorption. It is based on limited data (n = 6, single specimens) and should be interpreted with caution. The R² value of 0.854 reflects the preliminary nature of this correlation and does not imply a validated predictive model.

In this study, only one specimen was tested for each configuration, and no duplicate samples were set up. Considering the inherent variability of the material properties of UHPC (especially the distribution and orientation of fibers) during the manufacturing process, the quantitative values (such as the percentage increase in bearing capacity, the change in ductility coefficient, the increase in energy absorption, etc.) in this paper should be regarded as specific observations under the current test conditions, rather than statistical conclusions.

4. Finite Element Simulation and Experimental Validation

4.1. Model Development and Material Parameters

To verify the accuracy of the experimental results, a three-dimensional finite element model was established using ABAQUS (2021 version). The geometric parameters of the model were defined according to the design specifications of the six H-shaped UHPC pile specimens listed in Table 5. The UHPC matrix was simulated using eight-node linear reduced-integration hexahedral elements (C3D8R), while the longitudinal reinforcing bars were modeled using two-node three-dimensional truss elements (T3D2) [45]. The total number of elements in the finite element model was 54,720.

The boundary conditions are illustrated in Figure 11. At the fixed end, all degrees of freedom were restrained (UX = UY = UZ = 0), whereas at the free end, the transverse and vertical displacements were constrained (UY = UZ = 0). The external load was applied in the form of uniformly distributed pressure on the top surface of the specimen along the predefined loading lines, so as to adequately reproduce the mechanical conditions of the four-point bending test.

To ensure the accuracy of the finite element analysis, the mesh size was adjusted, and recalculations were conducted under different mesh accuracies, as shown in Figure 12. Specifically, three different mesh accuracies were adopted, with the number of meshes being 14,557 (Finite Element 1), 29,480 (Finite Element 2), and 54,720 (Finite Element 3). Through comparative analysis, it was found that the finite element simulation errors under the three mesh accuracies were not significantly different. Therefore, the mesh accuracy with 54,720 meshes was finally selected for the analysis.

The constitutive behavior of the reinforcing steel was modeled using a five-stage elastoplastic model [46], as illustrated in Figure 13, and its mathematical expressions are given in Equations (10)–(14). Key parameters, including the yield strength ($f_y$), ultimate strength ($f_u$), and elastic modulus ($E_s$), were determined based on the material test results summarized in the preceding tables.

To simulate the interaction between the reinforcing steel and ultra-high performance concrete (UHPC), perfect bond behavior between steel and concrete was assumed, considering the relatively short reinforcement length and the confinement provided by the surrounding concrete. To further improve the model accuracy and to account for possible slip effects under practical conditions, an embedded bond–slip constitutive law will be introduced in future studies to evaluate the influence of bond–slip behavior on the numerical results.

$$\sigma =E_S·\epsilon$$

(10)

$$\sigma =-\mathrm{A}·{\epsilon }^2+\mathrm{B}·\epsilon +C$$

(11)

$$\sigma =f_y({\epsilon }_2<\epsilon \le {\epsilon }_3)$$

(12)

$$\sigma =f_y·[1+0.6·{\displaystyle \frac{\epsilon -{\epsilon }_3}{{\epsilon }_4-{\epsilon }_3}}]({\epsilon }_3<\epsilon \le {\epsilon }_4)$$

(13)

$$\sigma =1.6·f_y(\epsilon >{\epsilon }_4)$$

(14)

where $E_s$ denotes the elastic modulus of the reinforcing steel, and $f_y$ represents the yield strength of the steel reinforcement. The characteristic strain parameters are defined as follows:

$${\epsilon }_1=0.8{\displaystyle \raisebox{1ex}{$f_y$}\!\left/ \!\raisebox{-1ex}{$E_s$}\right.}, {\epsilon }_2=1.5{\epsilon }_1, {\epsilon }_3=10{\epsilon }_2, {\epsilon }_4=100{\epsilon }_2$$

The constitutive behavior of UHPC in both compression and tension was described using the stress–strain models proposed by Hoang–Le Minh et al. [47], as given in Equations (15)–(20), to represent the mechanical response of UHPC during loading. In the finite element analysis, the concrete damage plasticity (CDP) model was adopted to capture the nonlinear mechanical behavior of UHPC. The key parameters of the CDP model were set as follows: dilation angle φ = 30°, shape factor $K=0.6667$, eccentricity $e=0.1$, ratio of biaxial to uniaxial compressive strength $f_{b0}/f_{c0}=1.16$, and viscosity coefficient $\mu =0.005$ [7]. In terms of the material constitutive parameters, the elastic modulus E of UHPC is 35.8 GPa, and the Poisson’s ratio ν is 0.2, the compressive stress–strain relationship and damage factor are calibrated according to the test curve, the tensile stress–displacement curve adopts a softening constitutive model based on fracture energy, the yield strength of the steel bar fy is 400 MPa, and the elastic modulus Es is 200 GPa.

In addition, a damage evolution mechanism was incorporated within the CDP framework. The tensile damage variable $d_t$ and the compressive damage variable $d_c$ were calculated using the corresponding formulations [48,49] to account for stiffness degradation induced by cracking and crushing. This modeling approach enables a reliable representation of the plastic deformation and damage evolution of UHPC throughout the entire loading process.

$$x={\displaystyle \frac{{\epsilon }_C}{{\epsilon }_{C0}}}$$

(15)

$${\displaystyle \frac{{\sigma }_c}{f_{c0}}}=\left\{\begin{array}{c}1.2x-{0.2x}^2,0<x<1\\ {\displaystyle \frac{10}{{(x-1)}^2}}+x, x\ge 1\end{array}\right.$$

(16)

$$Y={\displaystyle \frac{{\epsilon }_t}{{\epsilon }_{t0}}}$$

(17)

$${\displaystyle \frac{{\sigma }_t}{f_{t0}}}=\left\{\begin{array}{c}1.09y+0.82y^2-{0.91y}^3,0<y<1\\ {\displaystyle \frac{5}{{5.5(y-1)}^2}}+y,y\ge 1\end{array}\right.$$

(18)

$$d_c=1-{\displaystyle \frac{\raisebox{1ex}{${\sigma }_C$}\!\left/ \!\raisebox{-1ex}{$E_0$}\right.}{(1-d_c)({\epsilon }_c-{\epsilon }_c^{pl})}}$$

(19)

$$d_t=1-{\displaystyle \frac{\raisebox{1ex}{${\sigma }_t$}\!\left/ \!\raisebox{-1ex}{$E_0$}\right.}{(1-d_t)({\epsilon }_t-{\epsilon }_t^{pl})}}$$

(20)

4.2. Comparison of Load–Mid-Span Displacement Curves Between Simulation and Experiment

Figure 14 presents the comparison between the experimental and numerical load–mid-span displacement curves, while

Table 9. Comparison between experimental and numerical results of H-shaped UHPC piles.

Sectional Parameters (mm × mm)	Experimental Peak Load (kN)	Numerical Peak Load (kN)	Peak Load Error (kN)	Experimental Midspan Displacement (mm)	Numerical Midspan Displacement (mm)	Displacement Error (mm)
270 × 300-60	128.5	124.8	−3.7	45.1	46.8	+1.7 mm
270 × 300-75	132.4	130.1	−2.3	49.4	51.2	+1.8 mm
270 × 300-90	134.1	127.8	−6.3	51.7	50.1	−1.6 mm
300 × 300-60	150.1	146.1	−4.0	44.3	47.6	+3.3 mm
300 × 300-75	152.2	148.7	−3.5	48.5	50.8	+2.3 mm
300 × 300-90	152.8	151.9	−0.9	49.1	48.7	−0.4 mm

summarizes the comparison of peak loads obtained from experiments and simulations for specimens with different sectional parameters. The numerical results indicate that the differences between the simulated and experimental peak loads remain within a reasonable range, with errors generally less than 5%. For example, the error for the specimen with a sectional dimension of 270 mm × 300 mm and a web thickness of 60 mm is −3.7 kN (2.9%), while that for the specimen with a sectional dimension of 300 mm × 300 mm and a web thickness of 90 mm is −0.9 kN (0.6%).

The numerical predictions of mid-span displacement also show good agreement with the experimental results, with discrepancies generally within 3.5 mm. Specifically, the displacement error for the 270 mm × 300 mm specimen with a 60 mm web thickness is 1.7 mm (3.8%), whereas that for the 300 mm × 300 mm specimen with a 90 mm web thickness is −0.4 mm (0.8%).

From the perspectives of load-carrying capacity and ductility, increasing the web thickness contributes to improvements in flexural resistance and deformation capacity to a certain extent. The good consistency between the numerical simulations and experimental observations confirms the reliability of the finite element model in predicting both load-carrying capacity and ductility. Although some discrepancies exist, the errors remain within acceptable limits, indicating that the numerical model is capable of reasonably reproducing the mechanical behavior of the specimens with different web thicknesses.

By extracting the initial stiffness values (obtained as the slope of the load–displacement curve within the first 20% of the linear segment) from the experiments and numerical simulations of the typical specimen (Group B, with a flange thickness of 75 mm), the results are presented in

Table 10. Comparison and error analysis of initial stiffness between experimental values of typical specimens and finite element values.

Response Indicators	Experimental Value	Finite Element Value	Absolute Error	Relative Error
Initial stiffness (kN/mm)	12.8	13.9	+1.1	+8.6%
Peak load (kN)	152.2	148.7	−3.5	−2.3%
Limit displacement (mm)	48.5	50.8	+2.3	+4.7%

.

The finite element simulation can accurately capture the overall load–displacement response, peak load (error < 5%) and ultimate displacement (error < 5%). However, the initial stiffness was overestimated by approximately 8.6%, which is attributed to the assumption of material homogeneity and the idealized boundary conditions. Despite this discrepancy, this numerical model can reliably predict the behavior after crack propagation, the location pattern of the crack, and the influence of the thickness of the web/flange on ductility and energy absorption, as all of these are controlled by the non-linear stage rather than the initial elastic response.

4.3. Comparison of Crack Propagation Between Simulation and Experiment

Figure 15 compares the crack patterns of different specimens after loading, including the experimental observations, DIC-derived strain fields, and finite element simulation results. The experimental results show that, with increasing flange thickness and web thickness, both the number of cracks and their propagation range increase. This trend is particularly evident in specimens with larger flange and web thicknesses, where crack development becomes more pronounced. As the load-carrying capacity approaches the ultimate state, the specimens exhibit larger deformations and localized damage, and cracks gradually propagate from the mid-span region toward both ends of the specimens.

The analysis of DIC strain fields indicates that, with increasing web thickness, the strain level in the mid-span region increases progressively, and cracks tend to concentrate in regions with higher strain values. For specimens with a web thickness of 60 mm, cracks are mainly concentrated in the mid-span region and propagate gradually along the loading direction. As the web thickness increases to 75 mm and 90 mm, the number of cracks increases significantly, and the propagation rate becomes faster. In particular, specimens with a web thickness of 90 mm exhibit the most pronounced crack development. Both the DIC strain fields and finite element results consistently capture the process of crack propagation from the mid-span toward the specimen ends.

The finite element simulations show good agreement with the experimental observations, demonstrating that crack localization becomes more evident with increasing web thickness. In specimens with smaller web thicknesses, crack propagation is relatively slow and large-scale damage does not occur. In contrast, specimens with larger web thicknesses exhibit faster crack propagation and gradually form more extensive damage zones. The numerical results confirm the significant influence of web thickness on crack propagation patterns, indicating that cracks in specimens with thicker webs develop more rapidly and in a more localized manner.

Overall, increasing web thickness enhances the stiffness and load-carrying capacity of the specimens. However, specimens with larger web thicknesses exhibit relatively limited plastic deformation capacity, and more pronounced localized damage is observed during crack propagation. These observations suggest that a trade-off exists between stiffness and ductility: while increased stiffness contributes to higher load-carrying capacity, it also tends to restrict plastic deformation and promote crack localization.

5. Conclusions

Based on four-point bending tests, digital image correlation (DIC) measurements, and finite element simulations, this study investigated the effects of flange thickness and web thickness on crack evolution, ductility, and energy absorption performance of H-shaped UHPC piles under flexural loading. The main conclusions are summarized as follows:

(1)

Under the condition of a constant flange thickness, as the web thickness increases, the energy absorption of the specimen increases, while the ductility coefficient decreases. Within the section parameter combination range set in this paper (with the flange thickness fixed and the web thickness varying but the flange width and reinforcement ratio being adjusted in tandem), it was observed that the energy absorption increased by approximately 6% to 10%, and the ductility coefficient decreased by approximately 9% to 15%. This change reflects the combined influence of multiple parameters and should not be attributed solely to the web thickness. Specifically, the energy absorption increased by about 6% to 10%, and the ductility coefficient decreased by about 9% to 15%. The results indicate that increasing the web thickness is beneficial for enhancing the energy absorption of the component, but it will reduce its relative ductility level.

(2)

Under the condition of a constant web plate thickness, when the flange thickness increases from 60 mm to 75 mm, the ductility coefficient and energy absorption capacity of the specimen significantly decrease. Under the parameter combination of the test specimens in this paper, the ductility coefficient shows a trend of approximately a 21% to 25% reduction. Specifically, the ductility coefficient decreases by about 21% to 25%, and the energy absorption decreases by about 27% to 29%. This indicates that an increase in flange thickness is not conducive to the deformation capacity and energy absorption of the component.

(3)

With increasing load ratio, both the strain field localization index and the peak principal strain at mid-span exhibit an overall increasing trend, and crack evolution gradually transitions from dispersed development to localization-dominated behavior. When the load ratio approaches 1.0, the strain field localization index and the peak principal strain increase markedly. Specimens with larger sectional dimensions exhibit superior load-carrying capacity, while differences in mid-span deformation remain within a reasonable range. Increasing flange thickness further promotes the concentration of strain and cracking in localized regions, but contributes limited improvement to the global deformation capacity.

(4)

The finite element simulation captures the overall load–displacement response reasonably well, with peak load and ultimate displacement errors within 5%.

(5)

The strain field localization index proposed in this study can effectively quantify the degree of crack localization during the flexural process of H-shaped UHPC piles. It provides a quantitative tool for evaluating ductility degradation and failure modes from the perspective of strain fields, and offers useful references for crack control and ductility-oriented design optimization of such members.

This study aims to preliminarily reveal the influence of the thickness trends of the web and the flange on the bending performance of H-shaped UHPC piles. Since only one specimen was tested for each configuration, subsequent studies should set at least three replicate samples under the same parameters to quantify the impact of material variability on the results and verify whether the numerical changes observed in this study have statistical significance.