Dynamic Response and Fatigue Life Evaluation of Expansion Joint Anchorage Zones Made with Engineered Cementitious Composites Based on a Vehicle–Expansion Joint Coupled Model

Abstract

Expansion joint anchorage zones are prone to premature cracking and fatigue deterioration under repeated wheel impact and interfacial stress concentration. Engineered cementitious composites (ECCs) are promising anchorage materials because of their tensile strain-hardening behavior, multiple fine cracking, and high deformation capacity. However, how ECC strength–ductility characteristics affect vehicle-induced stress redistribution and fatigue damage accumulation remains unclear. This study develops a material–structure–fatigue framework for ECC anchorage zones. Three PVA-ECC mixtures were tested, and their measured constitutive relationships were incorporated into a three-dimensional vehicle–expansion joint coupled finite element model validated using reported field strain data from a C50 concrete anchorage zone. Critical tensile stress histories were extracted for rainflow counting and Miner-based fatigue assessment. Results show that ECC reduced tensile stress concentration and increased tensile safety margins compared with C50 concrete. Under the defined loading scenario, the estimated fatigue life increased from 9.93 years for C50 concrete to 83.15 years for the best-performing ECC scheme. Ten-year comparative field observations supported the predicted durability trend. By linking ECC strength–ductility characteristics with vehicle-induced stress redistribution and cumulative fatigue damage, the proposed framework provides a quantitative basis for fatigue-resistant material selection and durability-oriented design of expansion joint anchorage zones.

1. Introduction

Bridge expansion joints are critical components connecting adjacent bridge spans or bridge spans and abutments. During service, the anchorage zone of an expansion joint is subjected to repeated vehicle impact, temperature-induced deformation, concrete shrinkage and creep, and complex interfacial load transfer [1,2]. Because of the discontinuity in geometry and stiffness between the pavement, anchorage material, and steel edge beam, stress concentration readily occurs in the anchorage zone. Conventional anchorage zones are commonly constructed using cement-based concrete or fiber-reinforced concrete materials. However, these materials may still suffer from limited tensile deformability, localized cracking, interfacial debonding, spalling, and fatigue deterioration under repeated wheel-impact loading [3,4,5]. Therefore, improving the crack-control and fatigue-resistance performance of expansion joint anchorage materials is important for enhancing the durability of bridge expansion joints.

Engineered cementitious composites (ECCs) have attracted increasing attention because of their tensile strain-hardening behavior, multiple fine cracking, high tensile ductility, and fatigue resistance [6,7,8,9,10]. ECC is a high-performance fiber-reinforced cementitious composite designed based on micromechanics theory [8]. Unlike ordinary concrete, ECC can maintain tensile load-carrying capacity after first cracking through fiber bridging and distributed microcracking [11]. Previous studies have shown that ECC can improve ductility, crack control, energy dissipation, and durability when used in critical structural regions such as bridge piers, beam–column joints, bridge decks, and link slabs [12,13,14,15]. These characteristics indicate that ECC has potential to improve the failure mode of expansion joint anchorage zones from localized brittle cracking to more distributed damage evolution.

Cement-based materials in transport infrastructure are also affected by repeated dynamic loading and aggressive environmental actions. Alternating dynamic impacts and cyclic loading can accelerate crack initiation and damage accumulation, while chloride ingress, sulfate attack, wetting–drying cycles, freeze–thaw cycles, heating–cooling cycles, and their coupled effects can further promote matrix deterioration, reinforcement corrosion, interface degradation, and loss of mechanical performance [16,17,18,19,20]. Although these studies have improved the understanding of material durability and damage mechanisms, most of them focus on material-level deterioration rather than the structural-level stress redistribution and fatigue damage evolution of local bridge components under repeated vehicle impact. For expansion joint anchorage zones, the key issue is not only whether the material has good mechanical or durability properties, but also how these properties influence the local stress response and fatigue damage accumulation under vehicle-induced dynamic loading [21].

Several material modification approaches have been investigated for bridge expansion joint anchorage zones. Mao et al. studied emulsified-asphalt-modified ECC for expansion joint applications and showed that material flexibility and deformation capacity could be improved [22]. Sun et al. investigated fast-hardening polymer cement composite materials for expansion joint anchorage zones and evaluated their mechanical response through experiments and finite element analysis [23]. Wang et al. prepared polyurethane concrete and applied it to bridge expansion joint anchorage zones, demonstrating its potential to improve local mechanical performance [24]. Tian et al. further analyzed the fatigue properties of polyurethane concrete anchorage zones and showed that alternative materials can reduce fatigue damage compared with ordinary cement-based materials [5]. These studies confirm that material replacement is an effective strategy for improving anchorage-zone performance. Nevertheless, polymer-modified cement composites and polyurethane concrete differ fundamentally from strain-hardening ECC in material mechanism. They do not clarify how ECC tensile strength, tensile ductility, elastic modulus, multiple cracking, and post-cracking stress transfer jointly influence stress concentration and fatigue damage accumulation under repeated vehicle impact.

In parallel, vehicle–bridge coupling and expansion joint dynamic-response studies have provided useful methods for analyzing vehicle-induced impact effects. Hou et al. analyzed vehicle–bridge coupling vibration considering expansion joint parameters and demonstrated that expansion joint characteristics can significantly affect vehicle–bridge dynamic response [25]. Ding et al. investigated the dynamic impact generated by vehicles passing over modular bridge expansion joints and clarified its influence on bridge design [26]. Fatigue-life studies of bridge components and expansion joint systems have also provided useful methods for fatigue assessment under traffic loading [27,28]. However, many of these studies focus on the global vehicle–bridge response, the expansion joint device itself, or empirical fatigue evaluation. The material-level tensile behavior of ECC has not been sufficiently connected with the transient stress response and fatigue damage evolution of the expansion joint anchorage zone.

Despite these advances, the material–structure–fatigue mechanism of ECC expansion joint anchorage zones remains insufficiently understood. Previous studies have demonstrated the strain-hardening and crack-control capacity of ECC, but they have not sufficiently clarified how ECC strength–ductility characteristics affect vehicle-induced stress redistribution and fatigue damage accumulation in local anchorage zones. Studies on PCC, PUC, SFC, and other modified anchorage materials have verified the feasibility of material improvement, but most of them focused on specific material performance or engineering applicability rather than the coupling between material constitutive behavior, local dynamic tensile stress history, and cumulative fatigue damage. Vehicle–bridge coupling studies have clarified the dynamic response of bridges and expansion joint systems, but the influence of anchorage-zone material properties on local stress concentration and fatigue life has not been systematically evaluated. Therefore, a quantitative framework that links ECC material properties with vehicle-induced stress response and fatigue damage evolution is still needed.

To address this issue, this study develops a material–structure–fatigue evaluation framework for ECC expansion joint anchorage zones. Three PVA-ECC mixtures with different strength–ductility characteristics were designed and tested. Their measured constitutive parameters were introduced into a three-dimensional vehicle–expansion joint coupled finite element model to obtain local tensile stress histories under vehicle loading. Rainflow counting and Miner’s cumulative damage theory were then used to evaluate fatigue damage and estimated fatigue life. Finally, long-term field performance observations were used to examine whether the predicted durability trend was consistent with engineering performance.

2. Materials and Methods

2.1. Raw Materials

The raw materials used to prepare the ECC mixtures included ordinary Portland cement, fly ash, gold tailings sand (GTS), hydroxypropyl methylcellulose (HPMC), a polycarboxylate-based high-range water-reducing admixture, tap water, and polyvinyl alcohol (PVA) fibers.

P·O 42.5 ordinary Portland cement supplied by Jinan Shanshui Cement Co., Ltd. (Jinan, China) was used. Grade I low-calcium fly ash supplied by Henan Wuhu Environmental Protection Technology Co., Ltd. (Zhengzhou, China) was used. The chemical compositions of the cement and fly ash are listed in

Table 1. Main chemical composition of cement/%.

Chemical Composition	CaO	SiO2	Al2O3	Fe2O3	SO3	MgO	K2O	MnO
Content (%)	63.21	18.48	6.74	3.45	3.16	3.24	0.53	0.27

and

Table 2. Main chemical composition of fly ash/%.

Chemical Composition	SiO2	Al2O3	Fe2O3	CaO	SO3	TiO2
Content (%)	54.28	29.76	8.81	4.21	2.06	1.35

, respectively.

The gold tailings sand was collected from a gold-mine tailings deposit located in Qixia, Yantai, China. Its main chemical component was SiO₂, and it exhibited a hard texture, high wear resistance, and good chemical stability. Its morphology and X-ray diffraction pattern are shown in Figure 1 and Figure 2, respectively. The particle-size distributions of the cementitious materials and gold tailings sand are presented in Figure 3.

HPMC with a viscosity of 150,000 mPa·s, supplied by Henan Qimeng Chemical Technology Co., Ltd. (Zhengzhou, China), was used as a thickener. A polycarboxylate-based high-range water-reducing admixture with a water-reduction rate of approximately 30%, supplied by Jiangsu Sobute New Materials Co., Ltd. (Nanjing, China), was used. Laboratory tap water was used as the mixing water. PVA fibers supplied by Yongan Baohualin Industrial Development Co., Ltd. (Yongan, China) were used, and their physical and mechanical properties are listed in

Table 3. Performance parameters of PVA fibers.

Fiber Type	Length (mm)	Diameter (μm)	Elastic Modulus (GPa)	Tensile Strain (%)	Tensile Strength (MPa)	Density (g/cm3)
PVA	12	40	40	6.5 ± 1	≥1600	1.28

.

2.2. Mix Proportion Design and Specimen Preparation

The experimental program, including the varied factor, specimen preparation, mechanical tests, and parameters used for numerical modeling, is summarized in Figure 4. To investigate the effect of ECC mechanical properties on the dynamic response and fatigue performance of expansion-joint anchorage zones, three water-to-binder ratios of 0.28, 0.29, and 0.30 were selected. Previous studies on expansion-joint anchorage materials have commonly used C40–C50 cement-based concrete or fiber-reinforced concrete as reference materials, while newly developed high-performance anchorage materials can reach compressive strengths above 60 MPa [5]. Therefore, a relatively low water-to-binder ratio range was adopted in this study to maintain a high matrix strength level while improving tensile deformability and crack-control capacity [29]. This design produced a controlled strength–ductility variation within the same gold-tailings-sand PVA-ECC system. The binder composition, gold tailings sand content, PVA fiber dosage, and admixture system were kept constant, and only the water-to-binder ratio was varied. The detailed mix proportions are presented in

Table 4. Mix proportions of ECC (kg/m³).

Sample Number	Cement	Fly Ash	Gold Tailings Sand	Thickener	Water Reducer	Water	Fiber
E1	554	664	438	0.59	5.22	341	26
E2	554	664	438	0.58	5.09	353	26
E3	554	664	438	0.57	4.97	365	26

.

After weighing the raw materials according to the prescribed mix proportions, the dry ingredients (including ordinary Portland cement, fly ash, gold tailings sand, and thickener) were first mixed at low speed for 3 min. Then the water reducer and water were added, followed by low-speed mixing for 2 min and high-speed mixing for another 3 min. Finally, the PVA fibers were uniformly added and mixing continued for 5 min to ensure uniform fiber dispersion.

After casting, the specimens were compacted using a vibrating table, and the surface was finished smooth. After 24 h, the specimens were demolded and then cured for 28 days in a standard curing room at a relative humidity of not less than 95% and a temperature of (20 ± 2) °C.

2.3. Mechanical Properties of ECC

2.3.1. Compressive Test

The compressive test procedure and specimen geometry were determined according to relevant published methods [30]. Cubic specimens with dimensions of 50 mm × 50 mm × 50 mm were used, as shown in Figure 5a. Three specimens were prepared for each mixture. The test was conducted at a loading rate of 0.5 MPa/s until failure, and the average compressive strength was calculated.

The compressive strengths of E1, E2, and E3 were 54.79 MPa, 47.18 MPa, and 41.17 MPa, respectively, as shown in Figure 6. With increasing water-to-binder ratio, the compressive strength decreased gradually. Compared with E1, the compressive strengths of E2 and E3 decreased by 13.89% and 24.86%, respectively. This indicates that a lower water-to-binder ratio is beneficial for improving matrix compactness and compressive load-bearing capacity.

The average compressive stress–strain curves are shown in Figure 7. All mixtures exhibited a typical nonlinear compressive response, including an initial linear stage, a nonlinear ascending stage, and a post-peak softening stage. E1 showed the highest peak stress and the steepest ascending branch, indicating higher compressive stiffness. These measured compressive properties were used to define the ECC compressive constitutive parameters in the finite element model.

2.3.2. Uniaxial Tensile Test

Uniaxial tensile tests were performed on dog-bone specimens according to JSCE recommendations [31], as shown in Figure 5b. Three specimens were prepared for each mixture. The tests were conducted under displacement control at a loading rate of 0.5 mm/min until tensile failure.

The first cracking strengths of E1, E2, and E3 were 2.51 MPa, 2.18 MPa, and 1.85 MPa, respectively, while their tensile strengths were 4.10 MPa, 3.58 MPa, and 3.09 MPa, as shown in Figure 8 and Figure 9. Both first cracking strength and tensile strength decreased with increasing water-to-binder ratio, indicating a reduction in matrix cracking resistance and tensile load-bearing capacity.

The peak tensile strains of E1, E2, and E3 were 2.51%, 3.86%, and 5.32%, respectively, as shown in Figure 10. In contrast to strength, the tensile deformation capacity increased with increasing water-to-binder ratio. The tensile stress–strain curves in Figure 11 show that all three ECC mixtures exhibited strain-hardening behavior after first cracking. These tensile properties were used to define the ECC tensile constitutive parameters in the subsequent finite element model.

3. Theoretical Estimation of Fatigue Damage Life of Expansion Joints

In the fatigue-life analysis of expansion joints, the time history of the maximum principal stress at vulnerable locations of the expansion joint under wheel loading is first obtained either through finite element simulation or by installing sensors on the bridge. The stress history is then simplified into stress cycles, and the number of cycles corresponding to each stress level is determined using the rainflow counting method, thereby obtaining the fatigue stress spectrum [32]. Subsequently, the fatigue life is determined using the material S-N curve [33]. However, since the S-N curve only considers fatigue life under constant-amplitude loading, whereas the fatigue problem of expansion joint structures involves variable-amplitude fatigue under wheel-impact loading, the present study adopts Miner’s linear cumulative fatigue damage theory [34] to linearly accumulate fatigue damage under different stress cycles and obtain the total fatigue damage, denoted by D. When nD = 1, the modular expansion joint is considered to have failed, where n is the fatigue life of the modular expansion joint, in years. The calculation procedure for the fatigue life of concrete in the expansion joint anchorage zone is shown in Figure 12. Rainflow counting and Miner-based cumulative fatigue-damage calculations were performed using MATLAB R2023b (The MathWorks, Inc., Natick, MA, USA).

According to Miner’s theory, the total fatigue damage D is calculated using Equation (1):

$$D={\displaystyle \sum _k{D}_k}={\displaystyle \sum _k\frac{N_k}{N_{fk}}}$$

(1)

where N_fk is the fatigue life corresponding to the stress amplitude △σ_k on the S-N curve, k = 1, 2, 3, …; N_k is the number of cycles of the stress amplitude △σ_k within one year, with N_k = 365 N_dk, and N_dk is the number of cycles of the stress amplitude △σ_k within one day.

For the fatigue-life calculation of C50 concrete in the expansion joint anchorage zone, the concrete axial tensile fatigue equation proposed in Ref. [35] is used:

$$f_{t\max }/f_t=0.9873-0.04\lg N$$

(2)

where N is the fatigue life of concrete, and f_t and f_tmax are the axial tensile strength and the maximum tensile stress of the concrete, respectively.

For the fatigue-life calculation of ECC in the expansion joint anchorage zone, the ECC axial tensile fatigue equation proposed in Ref. [36] is used:

$$S=1.22405-0.09542\lg N$$

(3)

where N is the fatigue life of ECC, and S is the stress level, i.e., the ratio of the maximum tensile stress of ECC to its tensile strength.

The ECC fatigue relationship in Ref. [36] was selected because it was established from constant-amplitude uniaxial tensile fatigue tests on PVA-ECC specimens and expressed fatigue life in terms of the tensile stress level (S), which is consistent with the fatigue evaluation framework adopted in this study. The ECC specimens in Ref. [36] contained 2 vol.% PVA fibers with a length of 12 mm, a diameter of 0.04 mm, a tensile strength of 1600 MPa, and an elastic modulus of 40 GPa, and were cured for 28 days at 20 ± 2 °C and relative humidity greater than 95%. The material parameters and curing conditions reported in Ref. [36] are comparable to those adopted in the present study, providing a relevant reference for the fatigue evaluation of PVA-ECC materials. Ref. [36] established ECC tensile fatigue relationships under five stress levels (Smax = 0.90, 0.85, 0.80, 0.75, 0.70; Smin = 0.10), providing a suitable basis for estimating tensile fatigue damage of PVA-ECC materials. Since the objective of this analysis is to compare the relative fatigue resistance of different anchorage materials under the same vehicle-loading and cumulative-damage framework, the calculated fatigue lives are considered estimated values under the defined loading scenario.

The above procedure provides the basis for evaluating fatigue damage accumulation in the anchorage zone. Since stress histories at critical locations are required as input, a vehicle–expansion joint coupled finite element model is established in the following section to obtain the transient tensile stress responses of different anchorage-zone materials during vehicle passage. These stress histories are then used for rainflow counting and Miner-based fatigue damage evaluation.

4. Finite Element Model

4.1. Expansion Joint Modeling

4.1.1. Establishment of the Expansion Joint Finite Element Model

The three-dimensional vehicle–expansion joint coupled finite element model was established using Abaqus 2025 (Dassault Systèmes SIMULIA Corp., Johnston, RI, USA). In this study, a D80 single-gap steel expansion joint with special-shaped steel sections was adopted. Its structural components include the anchorage-zone concrete, bridge deck pavement layer, and F-shaped steel edge beams [37]. Steel plates are welded to the lower flange of the F-shaped steel section and are reliably connected to the anchorage reinforcement through these plates. A schematic of the structure is shown in Figure 13.

The steel edge beam, as the main load-bearing component of the expansion device, is generally made of low-carbon steel with good corrosion resistance. In this study, corrosion-resistant Q345 steel was selected as the material for the steel edge beam. The anchorage zone materials included three types of ECC (E1, E2, and E3) as well as C50 ordinary concrete. HRB400 reinforcing bars with a diameter of 16 mm were used as anchorage reinforcement. Bituminous concrete was used for the bridge deck pavement layer, and C50 concrete was used for the girder. The material properties are listed in

Table 5. Material properties.

Material Type	Elastic Modulus/MPa	Poisson’s Ratio	Density/kg·m−3
Section steel	206,000	0.3	7850
Bolting steel	210,000	0.3	7850
Bituminous concrete	1421	0.25	2400
C50 concrete	38,000	0.2	2500
E1	22,000	0.2	1910
E2	21,000	0.2	1890
E3	19,500	0.2	1870

.

In establishing the finite element model, the anchorage reinforcement was modeled using two-node linear three-dimensional truss elements, while the remainder of the model was represented using eight-node linear hexahedral elements with relatively high accuracy. Reduced integration was adopted in the analysis to balance computational efficiency and result accuracy. To make the stress analysis results more consistent with actual engineering conditions, mesh refinement was applied to the steel edge beam and the anchorage-zone concrete region, thereby improving simulation accuracy.

The interaction properties in the model were set as follows: a tie constraint was used between the bridge deck pavement layer and the girder, while for all other contact interfaces, the tangential behavior was defined as “rough” and the normal behavior as “hard” contact, so as to realistically simulate force transfer between components.

The boundary conditions of the expansion joint model were set with reference to the local expansion joint model analysis of relevant scholars [23] and adjusted reasonably according to the actual size effect of the present local model. Specifically, the bottom surface of the expansion joint structure (Y-direction) was fully fixed, with constraints of U1 = U2 = U3 = UR1 = UR2 = UR3 = 0. The back face of the model (Z-direction) was set as rotationally fixed, with constraints of U1 = UR1 = UR2 = UR3 = 0. The left and right sides of the model (X-direction) were assigned symmetry constraints, with U3 = UR1 = UR2 = 0. The established finite element model of the expansion joint is shown in Figure 14.

4.1.2. Material Constitutive Models

Both C50 concrete and ECC were modeled using the concrete damage plasticity (CDP) model, which can describe the different tensile and compressive responses of cementitious materials and the stiffness degradation caused by damage development [38]. The constitutive relationship of C50 concrete was determined according to the Code for Design of Concrete Structures [39].

For ECC, the constitutive parameters were determined from the material tests in Section 2.3 and relevant constitutive models in the literature. The elastic modulus of each ECC mixture was obtained from the initial linear segment of the measured compressive stress–strain curve, and Poisson’s ratio was taken as 0.20. The compressive strength, peak compressive strain, and ultimate compressive strain were obtained from the compression tests and are listed in

Table 6. Compressive parameters of the ECC.

Sample Number	${\mathit{\sigma }}_{\mathit{cp}}$ (MPa)	${\mathit{\epsilon }}_{\mathit{cp}}$ (%)	${\mathit{\epsilon }}_{\mathit{cu}}$ (%)
E1	54.79	0.30	1.22
E2	47.18	0.31	1.12
E3	41.17	0.32	1.22

. Based on these parameters, the compressive stress–strain relationship of ECC was generated using the model proposed by Zhou et al. [40] as expressed by Equation (4). For tensile behavior, a trilinear constitutive model was adopted according to Ref. [41], as expressed by Equation (5). The initial cracking strength, peak tensile strength, initial cracking strain, peak tensile strain, and ultimate tensile strain were extracted from the direct tensile test curves and are listed in

Table 7. Tensile parameters of the ECC.

Sample Number	${\mathit{\sigma }}_{\mathit{t}0}$ (MPa)	${\mathit{\epsilon }}_{\mathit{t}0}$ (%)	${\mathit{\sigma }}_{\mathit{tp}}$ (MPa)	${\mathit{\epsilon }}_{\mathit{tp}}$ (%)	${\mathit{\epsilon }}_{\mathit{tu}}$
E1	2.51	0.15	4.10	2.51	3.07
E2	2.18	0.19	3.58	3.86	4.23
E3	1.85	0.23	3.09	5.32	5.41

. Therefore, the tensile constitutive curves used in the numerical model were directly linked to the measured tensile strength and deformation capacity of each ECC mixture.

The tensile and compressive damage factors of C50 concrete and ECC were calculated separately based on the energy-equivalence method [42], as expressed by Equation (6). The constitutive curves of C50 concrete and ECC are shown in Figure 15 and Figure 16, respectively.

The same CDP parameters were used for all cementitious materials, whereas the stress–strain and damage evolution curves were defined separately according to the experimentally determined properties of C50 concrete and each ECC mixture. In this way, the numerical model reflected the differences between ordinary concrete and ECC in tensile ductility, post-cracking load-carrying capacity, compressive nonlinearity, and damage evolution. The anchorage reinforcement was modeled using an ideal elastic–plastic constitutive law.

$${\sigma }_c=\{\begin{array}{cc}\frac{2{\sigma }_{c0}{\epsilon }_c}{{\epsilon }_{c0}}& \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}0\le {\epsilon }_c\le \frac{{\epsilon }_{c0}}{3}\\ \frac{{\sigma }_{c0}{\epsilon }_c}{2{\epsilon }_{c0}}+\frac{{\sigma }_{c0}}{2}& \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\frac{{\epsilon }_{c0}}{3}<{\epsilon }_c\le {\epsilon }_{c0}\\ 2{\sigma }_{c0}-\frac{{\sigma }_{c0}{\epsilon }_c}{{\epsilon }_{c0}}& \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}{\epsilon }_{c0}<{\epsilon }_c\le \frac{3{\epsilon }_{c0}}{2}\\ \frac{f_{c0}\left({\epsilon }_c-{\epsilon }_{cu}\right)}{3{\epsilon }_{c0}-2{\epsilon }_{cu}}& \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\frac{3{\epsilon }_{c0}}{2}<{\epsilon }_c\le {\epsilon }_{cu}\end{array}$$

(4)

where ${\sigma }_c$ is the compressive stress; ${\sigma }_{c0}$ is the axial compressive strength; ${\epsilon }_{c0}$ is the peak axial compressive strain; ${\epsilon }_{cu}$ is the ultimate compressive strain; and ${\epsilon }_c$ is the compressive strain.

$${\sigma }_t=\{\begin{array}{cc}\frac{{\sigma }_{t0}{\epsilon }_t}{{\epsilon }_{t0}}& \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}{\epsilon }_t\le {\epsilon }_{t0}\\ {\sigma }_{t0}+\left({\sigma }_{tp}-{\sigma }_{t0}\right)\frac{{\epsilon }_t-{\epsilon }_{t0}}{{\epsilon }_{tp}-{\epsilon }_{t0}}& \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}{\epsilon }_{t0}<{\epsilon }_t\le {\epsilon }_{tp}\\ {\sigma }_{tp}\left(\frac{{\epsilon }_{tu}-{\epsilon }_t}{{\epsilon }_{tu}-{\epsilon }_{tp}}\right)& \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}{\epsilon }_{tp}<{\epsilon }_t\le {\epsilon }_{tu}\end{array}$$

(5)

where ${\sigma }_t$ is the tensile stress; ${\sigma }_{t0}$ is the initial cracking strength; ${\sigma }_{tp}$ is the peak tensile strength; ${\epsilon }_{t0}$ is the initial cracking strain; ${\epsilon }_{tp}$ is the ECC peak strain corresponding to the peak tensile strength; ${\epsilon }_{tu}$ is the ultimate tensile strain; and ${\epsilon }_t$ is the tensile strain.

$$d_{\left(c,t\right)}=1-\sqrt{{\displaystyle \frac{{\sigma }_{\left(c,t\right)}}{E_0{\epsilon }_{\left(c,t\right)}}}}$$

(6)

where d(c,t) is the damage factor of ECC, denoted as dc under compression and dt under tension; E₀ is the initial elastic modulus; and σ(c,t) and ε(c,t) are the stress and strain under compression or tension, respectively.

4.2. Vehicle Modeling

To accurately reproduce the vibration and impact effects when a vehicle passes over a bridge expansion joint, a three-dimensional vehicle dynamics model was established based on multibody dynamics theory [43]. In Abaqus, the entire vehicle was simplified into a multirigid-body system connected by rigid beams, in which the vehicle body and tires were defined as rigid bodies, while the damping and stiffness characteristics of the suspension system and tires were equivalently simulated using spring–damper elements.

The constructed vehicle model mainly consisted of a vehicle body, front axle, rear axle, and four wheels, with force and motion transmitted among the components through the suspension system. The model fully considered key dynamic degrees of freedom during vehicle travel, including vertical vibration, pitching motion, and rolling motion, and was thus able to accurately reflect the complex stress response characteristics of the vehicle in the expansion joint region. The geometry of the vehicle finite element model is shown in Figure 17, and the mechanical parameters are listed in

Table 8. Vehicle properties.

Name	Properties
Mass of vehicle body (M)	24,808.00 kg
Moment of inertia of the vehicle body about xy (Ixy)	172,160.00 kg·m2
Moment of inertia of the vehicle body about xz (Ixz)	172,160.00 kg·m2
Moment of inertia of the vehicle body about zy (Izy)	31,496.00 kg·m2
Mass of front tire and suspension system (mf)	725.40 kg
Mass of rear tire and suspension system (mr)	1160.00 kg
Stiffness of primary suspension system (front axle, Kf)	727,812.00 N/m
Stiffness of primary suspension system (rear axle, Kr)	1,969,034.00 N/m
Stiffness of secondary suspension system (front axle, Ktf)	1,972,900.00 N/m
Stiffness of secondary suspension system (rear axle, Ktr)	4,735,000.00 N/m
Damping of primary suspension system (front axle, Cf)	2189.60 Ns/m
Damping of primary suspension system (rear axle, Cr)	7181.80 Ns/m
Damping of secondary suspension system (front axle, Ctf)	0.00 Ns/m
Damping of secondary suspension system (rear axle, Ctr)	0.00 Ns/m

[44].

4.3. Mesh Sensitivity Analysis

To ensure that the numerical response was not significantly affected by mesh discretization, a mesh sensitivity analysis was conducted before model validation and subsequent dynamic-response analysis. All solid components, including the steel edge beam, anchorage-zone material, asphalt pavement layer, and main girder concrete, were modeled using eight-node linear hexahedral reduced-integration elements (C3D8R). The anchorage reinforcement was represented using two-node linear three-dimensional truss elements (T3D2).

A non-uniform meshing strategy was adopted according to the expected stress gradients in different structural regions. The anchorage zone, F-shaped steel edge beam, anchorage reinforcement, and adjacent interface regions were treated as critical regions because local stress concentration was expected in these areas. The adopted local mesh size for these regions was 25 mm. The asphalt pavement layer and main girder concrete, which were located away from the critical load-transfer path, were meshed using a coarser nominal element size of 50 mm to reduce the computational cost. The overall mesh configuration of the finite element model is shown in Figure 14.

The EJ-C50 model was selected as the representative case for the mesh sensitivity analysis. The vehicle-passing condition was set to 20 km/h, which was identical to the condition used in the subsequent field-based model validation. All material properties, contact definitions, boundary conditions, vehicle parameters, and analysis settings were kept unchanged among the mesh schemes. Three local mesh sizes, namely 50 mm, 25 mm, and 12.5 mm, were considered for the anchorage zone, steel edge beam, anchorage reinforcement, and adjacent interface regions, whereas the mesh density of the pavement layer and main girder concrete was kept unchanged.

A fixed numerical monitoring point was defined within the C50 anchorage zone at the same geometric location as the strain-measurement position used in the subsequent validation case. The axial strain component in the sensor direction was extracted from this point for all mesh schemes. Only numerical results were used in this section to assess mesh convergence, whereas the field-measured strain was used separately in Section 4.4 for model validation.

As summarized in

Table 9. Mesh sensitivity analysis results of the anchorage-zone local mesh.

Mesh Scheme	Nominal Local Mesh Size of Anchorage Zone /mm	Peak Strain at Numerical Monitoring Point /με	Relative Deviation Relative to Finest Mesh /%	Calculation Time /h
Coarse mesh	50.0	40.85	19.54	3.2
Adopted mesh	25.0	35.84	4.87	7.5
Finest tested mesh	12.5	34.18	-	16.9

, the peak compressive strain gradually converged as the local mesh was refined. The peak compressive strain decreased from 40.85 με for the 50 mm mesh to 35.84 με and 34.18 με for the 25 mm and 12.5 mm meshes, respectively. Taking the 12.5 mm mesh as the reference, the relative deviations of the 50 mm and 25 mm mesh schemes were 19.54% and 4.87%, respectively. The 50 mm mesh was therefore considered insufficient for accurately capturing the local dynamic response of the anchorage zone. In contrast, further refinement from 25 mm to 12.5 mm resulted in only a limited change in the peak strain, whereas the calculation time increased from 7.5 h to 16.9 h. Therefore, the 25 mm local mesh was adopted for the subsequent model-validation, dynamic-response, and fatigue-life analyses because it satisfied the adopted 5% convergence criterion while maintaining reasonable computational efficiency.

4.4. Model Validation

After the mesh sensitivity analysis, the finite element model with the selected 25 mm local mesh was validated against the field-test results reported by Zhao [45]. In that test, a truck passed over an expansion joint with a C50 concrete anchorage zone at a speed of 20 km/h, and embedded resistance-type concrete strain sensors were installed in the anchorage zone to record the strain response in real time. The test arrangement is shown in Figure 18.

Following the above test scheme strictly, a three-dimensional truck model was established in Abaqus to simulate the truck passing over the expansion joint at the same speed (20 km/h). For convenient comparison, a parameter D was introduced to represent the relative wheel position: D was defined as the distance between the wheel centerline and the interface between the expansion joint anchorage zone and the bridge deck pavement layer (see Figure 19). D takes a negative value before the wheel centerline crosses the interface and a positive value after crossing.

The time–history curve of concrete strain in the anchorage zone at travel distance D was extracted and compared with the reported field test data (see Figure 20). The results show that throughout the process of the vehicle passing over the expansion joint, the strain time–history curve obtained from the finite element simulation agrees well with the field test curve in overall trend. The maximum compressive strains obtained from the simulation and field test were 35.84 με and 37.70 με, respectively, with a relative error of 4.93%, indicating acceptable agreement for engineering comparison.

The above comparison validates the vehicle–expansion joint coupled dynamic framework used in this study, including the vehicle-passing process, contact definition, boundary condition, mesh scheme, and local dynamic strain response of the anchorage zone. After validation, the same geometric model, boundary conditions, contact settings, vehicle model, loading process, and stress extraction method were adopted for all material schemes. Therefore, under identical structural and loading conditions, the differences in the dynamic response of C50 concrete and ECC anchorage zones are governed primarily by their material constitutive behavior. As described in Section 4.1.2, the ECC material models were defined using the experimentally determined compressive and tensile constitutive relationships and damage parameters. Thus, the validated coupled framework provides a reasonable basis for comparing the stress response and fatigue damage tendency of anchorage zones made of different materials.

Based on the mesh convergence analysis and model validation, the established model was used in the following section to analyze the spatial distribution and peak values of the principal tensile and compressive stresses in C50 concrete and ECC anchorage zones. The extracted critical tensile stress histories were further combined with the fatigue-life evaluation procedure introduced in Section 3 to estimate fatigue damage accumulation.

The following assumptions and limitations should be noted. First, the bridge expansion joint was modeled as a local structural system, and equivalent boundary constraints were applied to represent the restraint effect of the surrounding bridge structure. Therefore, full-bridge vibration and long-distance wave propagation were not explicitly considered. Second, the vehicle was simplified as a multirigid-body system, and the suspension and tire effects were represented using spring–damper elements. Complex tire deformation, braking or acceleration, wheel-path deviation, and random pavement roughness were not included. Third, the contact conditions between different structural components were idealized using predefined contact settings, and long-term interface degradation, debonding, material wear, and environmental deterioration were not explicitly simulated. Finally, the fatigue lives obtained in this study should be interpreted as comparative estimates under the defined vehicle-loading scenario, rather than as absolute service lives for all field conditions.

5. Results and Discussion

Based on the fatigue-life calculation framework established in Section 3 and the validated vehicle–expansion joint coupled model described in Section 4, the dynamic response and fatigue performance of different anchorage-zone materials were analyzed in this section. Four working conditions were considered, corresponding to anchorage zones made of E1, E2, E3, and C50 concrete, denoted as EJ-E1, EJ-E2, EJ-E3, and EJ-C50, respectively. The principal stress response was first analyzed to identify critical stress regions, and the extracted tensile stress histories were then used for fatigue-damage and fatigue-life evaluation.

5.1. Principal Stress Response Analysis of the Anchorage Zone

Figure 21 shows the variation in the maximum principal compressive and tensile stresses in the anchorage zone along the driving direction under different material schemes. The stress responses exhibit a clear multi-peak fluctuation pattern. The peak locations are generally consistent among different materials, while the peak magnitudes vary with the anchorage-zone material. This indicates that the spatial distribution of principal stress is mainly governed by the wheel-load position and structural configuration, whereas the material properties primarily affect the stress level.

The main stress peaks occur near the pavement–anchorage-zone interface ((D = 0) − 100 mm and (D = 900) − 1000 mm) and the steel-edge-beam–anchorage-zone interface ((D = 300) − 400 mm and (D = 600) − 700 mm). These regions correspond to abrupt changes in stiffness, geometry, and boundary restraint, which disturb the load-transfer path and produce local stress concentration when the wheel load passes through the expansion joint.

Figure 22 and Figure 23 show the principal compressive and tensile stress contours at representative wheel positions under the EJ-E1 condition. The high-stress regions are mainly located beneath the wheel contact area and near the above-mentioned interfaces, confirming the localized nature of the stress response. Therefore, the pavement–anchorage-zone interface and the steel-edge-beam–anchorage-zone interface are identified as the critical regions for subsequent compressive stress, tensile stress, and fatigue-damage analyses.

5.2. Analysis of Maximum Principal Compressive Stress in the Anchorage Zone

Figure 24 shows the variation in the maximum principal compressive stress in the anchorage zone with travel distance (D) for different materials. The compressive stress response presents a clear multi-peak fluctuation pattern, with stress peaks mainly concentrated near the pavement–anchorage-zone interface and the steel-edge-beam–anchorage-zone interface. This indicates that the compressive stress distribution is strongly affected by the wheel-load position, interface stiffness difference, and local boundary restraint.

Figure 25 compares the peak values of the maximum principal compressive stress and their ratios to the corresponding compressive strengths. The peak compressive stresses of EJ-E1, EJ-E2, EJ-E3, and EJ-C50 were 7.82 MPa, 7.63 MPa, 6.86 MPa, and 6.78 MPa, respectively, and the corresponding stress-to-strength ratios were 0.14, 0.16, 0.17, and 0.14. Although the peak values varied among different materials, all ratios remained far below 1.0, indicating that all anchorage-zone materials had sufficient compressive capacity reserve under the defined vehicle-loading condition.

Therefore, compressive failure is not the controlling failure mode of the anchorage zone in this study. The subsequent analysis focuses mainly on the principal tensile stress response and tensile fatigue damage, which are more directly related to cracking and long-term deterioration of expansion joint anchorage zones.

5.3. Analysis of Maximum Principal Tensile Stress in the Anchorage Zone

Figure 26 shows the variation in the maximum principal tensile stress in the anchorage zone with travel distance (D) for different materials. Similar to the compressive stress response, the tensile stress also exhibits a multi-peak fluctuation pattern along the driving direction. The stress peaks are mainly concentrated near the pavement–anchorage-zone interface and the steel-edge-beam–anchorage-zone interface, indicating that these regions are the most critical locations for tensile cracking under wheel-impact loading.

Compared with the C50 concrete anchorage zone, the ECC anchorage zones showed lower principal tensile stress peaks and smoother stress fluctuations. This indicates that replacing ordinary concrete with ECC can improve tensile stress redistribution in the anchorage zone and reduce local tensile stress concentration. Among the ECC schemes, EJ-E3 exhibited the lowest peak tensile stress because of its lower elastic modulus and stronger deformation adaptability. However, the tensile safety margin should also consider the tensile strength of the material.

Figure 27 compares the peak principal tensile stress and its ratio to the corresponding tensile strength. The peak tensile stresses of EJ-E1, EJ-E2, EJ-E3, and EJ-C50 were 2.43 MPa, 2.00 MPa, 1.83 MPa, and 2.58 MPa, respectively. The corresponding stress-to-strength ratios were 0.59, 0.56, 0.59, and 0.98. The ratio for EJ-C50 was close to 1.0, indicating that the C50 anchorage zone was close to its tensile strength limit under the defined vehicle-loading condition. In contrast, the stress-to-strength ratios of all ECC anchorage zones remained below 0.60, showing a larger tensile safety margin. These results indicate that ECC can effectively reduce tensile stress concentration and improve the cracking resistance of expansion joint anchorage zones.

5.4. Estimated Fatigue Damage Life of Anchorage Zones with Different Materials

Based on the tensile stress analysis, the critical tensile stress histories in the anchorage zone were extracted from the finite element model, as shown in Figure 28. The stress cycles were then counted using the rainflow method to obtain the fatigue stress spectra of different materials, as shown in Figure 29. Based on the fatigue-life calculation procedure described in Section 3, the fatigue damage and estimated fatigue lives were obtained, as listed in

Table 10. Fatigue-damage under different working conditions.

Specimen Number	Stress Amplitude/MPa	Ndk	Nk	Nfk	ΔDk	D
EJ-E1-80	1.81	5000	1.83 × 106	1.59 × 108	1.15 × 10−2	1.21 × 10−2
	1.32	4100	1.50 × 106	2.84 × 109	5.26 × 10−4
	0.69	6650	2.43 × 106	1.16 × 1011	2.09 × 10−5
	0.32	9900	3.61 × 106	1.02 × 1012	3.53 × 10−6
EJ-E2-80	1.65	5000	1.83 × 106	9.95 × 107	1.83 × 10−2	1.92 × 10−2
	1.20	5000	1.83 × 106	2.07 × 109	8.83 × 10−4
	0.71	7000	2.56 × 106	5.62 × 1010	4.55 × 10−5
	0.32	9950	3.63 × 106	7.79 × 1011	4.66 × 10−6
EJ-E3-80	1.53	5000	1.83 × 106	4.35 × 107	4.19 × 10−2	4.27 × 10−2
	1.02	4500	1.64 × 106	2.34 × 109	7.03 × 10−4
	0.64	7500	2.74 × 106	4.54 × 1010	6.02 × 10−5
	0.25	9000	3.29 × 106	9.55 × 1011	3.44 × 10−6
EJ-C50-80	1.84	5000	1.83 × 106	1.81 × 107	1.01 × 10−1	1.01 × 10−1
	1.43	6050	2.21 × 106	1.38 × 1011	1.60 × 10−5
	0.92	8800	3.21 × 106	9.34 × 1015	3.44 × 10−10
	0.31	9600	3.50 × 106	5.58 × 1021	6.28 × 10−16

and Figure 30.

The estimated fatigue life of the C50 concrete anchorage zone was 9.93 years. In comparison, the estimated fatigue lives of EJ-E3, EJ-E2, and EJ-E1 were 23.43, 51.89, and 83.15 years, respectively. This indicates that all ECC anchorage zones showed lower fatigue damage accumulation than C50 concrete under the same vehicle-loading condition and fatigue evaluation framework. Among them, EJ-E1 exhibited the longest estimated fatigue life, mainly because it maintained the highest tensile strength reserve and the lowest fatigue stress level.

The fatigue damage results further explain this difference. The maximum fatigue damage increment of EJ-C50 reached 0.101, whereas those of EJ-E1, EJ-E2, and EJ-E3 were 0.012, 0.018, and 0.042, respectively. The faster damage accumulation of C50 concrete is related to its low tensile strength reserve and high tensile stress-to-strength ratio. In contrast, ECC can maintain tensile load-carrying capacity after first cracking through strain-hardening and multiple fine cracking, which helps redistribute stress at the pavement–anchorage-zone and steel-edge-beam–anchorage-zone interfaces and delays localized crack development.

The comparison among the ECC mixtures shows that fatigue resistance is not governed by tensile ductility alone. Although EJ-E3 had the largest tensile deformation capacity and the lowest tensile stress peak, its lower tensile strength resulted in a higher fatigue stress level and a shorter estimated fatigue life than EJ-E1 and EJ-E2. Therefore, the fatigue performance of ECC anchorage zones depends on the combined effects of tensile strength reserve, tensile ductility, elastic modulus, and dynamic stress response. Under the defined loading scenario, E1 provided the most favorable balance among these factors.

It should be emphasized that the fatigue lives reported in this section are estimated values under the defined vehicle-loading scenario. They are mainly used to compare the relative fatigue resistance of different anchorage-zone materials within the same stress-extraction, rainflow-counting, and Miner-based damage framework.

5.5. Fatigue Damage Comparison of Anchorage Zones with Different Materials

To further evaluate the fatigue-resistance advantage of ECC anchorage zones, fast-hardening polymer cement composite (PCC), polyurethane concrete (PUC), and steel fiber-reinforced concrete (SFC) were introduced for comparison based on recent studies [5,23,46]. The material parameters used in the finite element analysis are listed in

Table 11. Material parameters.

Materials	Elastic Modulus /MPa	Poisson Ratio	S-N Curve
PCC	3800	0.2	lgN = 13.8781 − 3.2253σ
PUC	2551	0.3	lgS = 0.27866 − 0.12565 lgN
SFC	30,800	0.2	lgσ = 0.5659 − 0.0504 lgN

.

Figure 31 shows the maximum principal tensile stress histories of anchorage zones made with different materials. The C50 and SFC anchorage zones exhibited relatively high tensile stress peaks, indicating stronger tensile stress concentration under wheel-impact loading. In comparison, the ECC, PCC, and PUC anchorage zones showed lower tensile stress responses. Among the polymer-modified materials, PUC produced a slightly lower tensile stress response than PCC, which is consistent with previous findings that PUC can reduce stress response through its lower modulus and higher deformation capacity.

Table 12. Fatigue-damage calculation results.

Materials	Maximum Principal Tensile Stress /Mpa	D
E1	2.43	1.21 × 10−2
E2	2.00	1.92 × 10−2
E3	1.83	4.27 × 10−2
C50	2.58	1.01 × 10−1
PCC	2.31	3.25 × 10−2
PUC	2.18	1.95 × 10−2
SFC	2.53	7.54 × 10−2

compares the calculated fatigue damage values of different anchorage materials. C50 showed the highest fatigue damage, followed by SFC, indicating that ordinary concrete and steel-fiber-reinforced concrete had relatively limited fatigue-damage control under the present loading condition. Among the ECC mixtures, E1 exhibited the lowest fatigue damage of all compared materials, while E2 showed a damage level close to PUC and lower than PCC and SFC. Although E3 reduced fatigue damage compared with C50 and SFC, its lower tensile strength resulted in higher fatigue damage than E1 and E2.

These results indicate that the fatigue advantage of ECC depends on the balance between tensile strength reserve and deformation capacity, and that E1 and E2 provide more favorable fatigue-damage control for expansion joint anchorage zones. This comparison also shows that the fatigue performance of an anchorage material cannot be evaluated only from its material type or deformation capacity. Instead, it should be assessed by combining its tensile strength reserve, deformation capacity, elastic modulus, and vehicle-induced tensile stress response. Compared with previous studies that mainly focused on modified anchorage materials, polymer-based repair materials, or the dynamic response of expansion joint systems, the present study further connects the measured strength–ductility characteristics of ECC with local tensile stress histories and cumulative fatigue damage. This provides a more direct basis for evaluating strain-hardening cementitious composites as fatigue-resistant anchorage materials for bridge expansion joints.

5.6. Engineering Application of ECC in Expansion Joint Anchorage Zones

In October 2016, the E1-ECC mixture was applied to the anchorage zone of an expansion joint in a bridge reconstruction and expansion project in Shandong Province, replacing ordinary concrete in a short-span bridge. The ECC was prepared according to the designed mix proportion, and the bridge was opened to traffic after casting, curing, and performance confirmation. The construction procedure is shown in Figure 32.

Long-term comparative field performance observations were conducted on the same road section from 2016 to 2026. Three anchorage materials were compared: ordinary concrete, fiber-reinforced concrete, and E1-ECC. These anchorage zones adopted the same type of expansion joint system and were exposed to similar traffic loading, climatic conditions, temperature–moisture variations, drainage conditions, and maintenance environment. The service states of the different anchorage zones are shown in Figure 33.

The ordinary concrete anchorage zone exhibited visible cracking, spalling, and joint damage after approximately 3–5 years of service. The fiber-reinforced concrete anchorage zone showed improved early-stage performance, but visible cracks appeared after approximately 3–5 years and developed into relatively extensive through-cracks after approximately 10 years. In contrast, the E1-ECC anchorage zone maintained good surface integrity after nearly 10 years of service, with no obvious visible cracking, spalling, or interfacial damage.

These observations were based on service-condition inspection rather than continuous sensor-based monitoring. Therefore, they were used as comparative engineering evidence supporting the predicted durability trend of ECC, rather than as direct calibration of the absolute fatigue-life values obtained from the Miner-based model.

From the perspective of practical application, ECC can be prepared, cast, and cured using procedures similar to those for conventional cementitious repair materials, with additional attention to workability control and fiber dispersion. Although the unit material cost of ECC is higher than that of ordinary concrete, the anchorage zone of an expansion joint is a local high-risk region with a relatively small repair volume. Therefore, the increase in initial material cost may be partly offset by the reduction in cracking, spalling, repeated repair, lane closure, and traffic-interruption costs. The nearly ten-year field performance of the E1-ECC anchorage zone further indicates its practical applicability. However, a quantitative life-cycle cost analysis was not included in this study and should be addressed in future work.

6. Conclusions

This study evaluated the dynamic response and fatigue performance of ECC expansion joint anchorage zones through material testing, vehicle–expansion joint coupled finite element analysis, Miner-based fatigue assessment, and long-term field performance observations. The main conclusions are as follows:

(1)

The three ECC mixtures exhibited a clear strength–ductility variation. As the water-to-binder ratio increased, compressive and tensile strengths decreased, while tensile deformation capacity increased. This provided a suitable material basis for evaluating the influence of ECC strength, stiffness, and ductility on anchorage-zone response.

(2)

The principal stress response of the anchorage zone was mainly concentrated near the pavement–anchorage-zone interface and the steel-edge-beam–anchorage-zone interface. These regions are the critical locations for stress concentration, cracking risk, and fatigue damage under vehicle impact.

(3)

Compared with C50 concrete, ECC anchorage zones showed lower principal tensile stress and larger tensile safety margins. The improvement was mainly related to the combined effects of tensile strength reserve, lower elastic modulus, tensile ductility, and post-cracking stress redistribution.

(4)

Under the defined vehicle-loading scenario, the estimated fatigue life increased from 9.93 years for the C50 anchorage zone to 83.15 years for the best-performing ECC anchorage zone. The ECC schemes also showed lower fatigue damage than C50 concrete and steel fiber-reinforced concrete, indicating their advantage in fatigue-damage control.

(5)

Long-term field performance observations from 2016 to 2026 showed that the E1-ECC anchorage zone maintained good surface integrity after nearly ten years of service, while ordinary concrete and fiber-reinforced concrete anchorage zones developed visible cracking or spalling. These observations support the practical applicability and predicted durability advantage of ECC in expansion joint anchorage zones. Future studies should incorporate measured traffic spectra, wheel-path distribution, environmental actions, and long-term in-situ stress monitoring to refine absolute fatigue-life prediction.