Study on the bending deformation properties of microcracked R-ECC road–bridge link slabs

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Preliminary research has shown that R-ECC road-bridge link slabs possess superior deformation absorption capacity, tensile strength, and crack control capabilities. However, micro-cracks developed on the surface of these slabs due to seasonal temperature fluctuations. While R-ECCs demonstrate improved bending ability compared to conventional ECCs, they exhibit lower compressive strength. Further research is necessary to investigate the crack development and bending deflection of microcracked R-ECC road-bridge link slabs under vehicle loads, which will help determine the suitability of R-ECCs for this application.The microcracked R-ECC slab has a great crack control capacity, and the rebound deflection measured in the experiment is less than the allowable value, indicating that the microcracked R-ECC slab meets the durability and strength standard. A sensitivity parameter finite element analysis was conducted considering the effects of slab thickness and equivalent elasticity modulus of the foundation on the R-ECC road-bridge link slab. Two evaluation indexes ‘ C t ’ and ‘ C e ’ are proposed to evaluate the performance and construction cost of the R-ECC slab. To improve performance and minimize construction costs, a design thickness of 180 mm and an equivalent elasticity modulus of the foundation of 800 MPa were recommended for the R-ECC road-bridge link slab. Physical sciences/Engineering Physical sciences/Materials science Fully jointless bridges Microcracked R-ECC road-bridge link slabs Seasonal temperature variation Traffic loads Crack development Rebound deflection Sensitive parameter finite element analysis Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 1 Introduction A jointless bridge is defined by the International Association of Jointless Bridges (IAJBs) as a bridge structure with a continuous superstructure without installing any expansion equipment within the whole bridge structure. This definition emphasizes the absence of expansion joints throughout the entire superstructure of a bridge [ 1 – 2 ]. One novel design of the fully jointless bridges (FJBs) utilizes a road-bridge link slab further to eliminate the gaps between the continuous bridge ends and the approach road[ 3 ]. Currently, FJBs are suitable for the construction of medium and small bridges to improve ride comfort at road-bridge connections [ 4 – 5 ]. In preview research, an innovative road-bridge link slab made from engineered cementitious composites (ECCs), referred to as ECC road-bridge link slabs, as shown in Fig. 1 , effectively utilizes the high-strain hardening characteristics of the ECC material, including its multiple cracking characteristics[ 6 – 8 ] and strong crack width control capability[ 9 – 11 ], thereby significantly enhancing the performance of FJBs[ 12 – 13 ]. Zhan XF, et al.[ 4 – 5 ] studied the tensile performance of the ECC road-bridge link slab, and the results demonstrated its substantial ability to absorb longitudinal deformations, which aligns with the requirements for FJBs to accommodate the deformations of bridge structures. However, ECC is quite expensive because of the use of silica sand. Zhang ZG, et al.[ 14 – 16 ] and Zhan XF, et al.[ 12 ] developed a rubberized engineered cementitious composite (R-ECC) by using river fine sand and rubber crumb to completely substitute for silica sand and reduce its cost. The experimental results validated the suitability of the R-ECC material used in the road-bridge link slab to absorb longitudinal deformations caused by system temperature loads[ 13 ]. Seasonal temperature loads is a key factor influence the performance of FJBs. Under seasonal temperature loads, micro-cracks developed on the surface of the R-ECC road-bridge link slabs of FJBs. But previous research proved that the microcracked R-ECC slabs exhibit strong crack control capabilities and meet the strength criteria for FJBs[ 13 ]. Compared to ECCs, R-ECCs have improved bending ability but lower compressive strength. At this point, whether the road-bridge link slab with micro-cracks can bear the vehicle load is worth studying. In order to demonstrate the successful application R-ECC in road-bridge link slabs for FJBs and establish a design theory for R-ECC road-bridge link slabs, further research is needed. This research should focus on the rebound deflection test of the microcracked R-ECC road-bridge link slab under vehicle loads. The objective was to evaluate whether the crack development and the bending deformation capacity of the R-ECC road-bridge link slabs with microcracks under vehicle load meet the durability and strength criteria of FJBs. 2 Rebound deflection test 2.1 Objective and Overview In practical projects, the road-bridge link slabs often develop microcracks due to seasonal temperature variations, particularly in winter. These slabs are subjected to pressure, impact, shear, and wear from vehicle loads, creating complex stress conditions that make it challenging to ensure the durability of microcracked slabs under these conditions. The rebound deflection is directly related to the design strength of the pavement. It serves as one of the standards to check whether the construction of the pavement meets the design strength requirements. To explore the applicability of R-ECC road-bridge link slabs for FJBs, a vehicle load that directly acts on the most unfavourable cracking position of the R-ECC slab is used to test its rebound deflection. The contact pressure, contact shape, and contact area between the vehicles and surface course are difficult to simulate in the laboratory. In accordance with the Specifications for the Design of Highway Asphalt Pavement in China, a dual wheel with one single-axle load of 100 kN is designed as the standard axle load, denoted as BZZ-100. The tire contact pressure is calculated to be 0.7 MPa, and the diameter of a single-wheel contact area equivalent circle is 21.3 cm[ 17 ]. Then, the diameter of the steel bearing plate used to simulate the wheel effect is determined to be 21.3 cm, with a thickness of 2 cm. 2.2 Model Design 2.2.1 General description The test model consists of an R-ECC slab measuring 5 m in length, 0.5 m in width, and 0.15 m in thickness, as shown in Fig. 2 (a,b)[ 13 ].There are three layers: a 15cm R-ECC road-bridge link slab layer, a 25cm 5% cement-stabilized gravel base layer, and a 20cm grade gravel base layer, as shown in Fig. 2 (a). To prevent overflow of the base materials under vertical loading, the base materials are contained within a wooden box, as illustrated in Fig. 2 (c). As shown in Fig. 2 (d), a 2 mm thick emulsified asphalt sealing (EAS) layer is poured as a sliding layer between the 5% cement-stabilized gravel base layer and the R-ECC slab layer. Additionally, the detailed model design, casting process and reinforcement arrangement of the R-ECC slab are illustrated in Fig. 2 (c to h). 2.2.2 Model parameters Based on previous research findings[ 13 ], the R-ECC mix ratio for the design of the R-ECC road-bridge link slab is shown in Table 1 . Table 1 Material mix ratio of R-ECC Portland Cement (kg/m³) Fly Ash (kg/m³) Fine Sand (kg/m³) Water (kg/m³) Rubber crumb replace ratio (Vol%) PVA fibers (Vol%) High-range water reducing admixture (Vol%) 390 780 448 363 15 2 1 The detailed material parameters for the R-ECC slab test specimen are shown in Table 2 . Table 2 Detailed material parameters for the R-ECC slab Numbers of longitudinal steel bars The diameter of the longitudinal steel bars (mm) Longitudinal reinforcement ratio of R-ECC slab (%) Tensile strength of steel bars (MPa) Tensile strength of R-ECC (MPa) Compressive strength of R-ECC (MPa) Elasticity modulus of R-ECC (GPa) 3 16 0.804% 335 3.7 26.7 17.3 2.3 Loading location Before conducting the rebound deflection test, a low-cycle tensile/compression test of the R-ECC slab must be performed to simulate the cracking that occurs in the slab due to seasonal temperature fluctuations[ 18 ]. In this case, a low two-and-a-half cycle tensile/compression test was simulated[ 13 ]. At the end of the two-and-a-half tensile test, lots of microcracks appeared on the surface of the R-ECC slab and the larger cracks are primarily concentrated near the tension end. The crack distribution within the slab are shown in Fig. 3(a). To prevent a significant change in slab stiffness and to facilitate the placement of the bearing plate for vehicle load simulation, a position 50 cm away from the tension end is selected as the loading location, as shown in Fig. 3(b). 2.4Layout of Measuring Instrument Two bearing plates are used for vehicle load application, One is marked as 'B', located 0.5 meters away from the tension end, as shown in Fig. 4 (a,b). Four dial gauges are arranged along the bearing plate 'B' and labeled as 'B1' to 'B4'. The other bearing plate is labeled as 'D' and is positioned approximately 319.5 mm away from bearing plate 'B', at a distance of 1.5 times the radius (r) of the bearing plate. Additionally, four dial gauges are arranged along the bearing plate 'D' and labeled as 'D1' to 'D4', as shown in Fig. 4 (a,c). These gauges are used to measure the vertical displacement of the bearing plates under vertical load. In addition, a dial gauge labeled as 'A' is positioned at the centre of the two bearing plates to measure the rebound deflection. 2.5Loading process The vertical load applied to the center of the bearing plate is divided into two levels, with each level carrying a load of 50 kN. After loading, the model rests for 5 minutes and the data is recorded. When unloading vertical loads, the process is completed all at once. 2.6 Results and discussion 2.6.1Crack development The largest crack width of the microcracks near the tension end is 65 µm, as shown in Fig. 5 (a). As the load increases, the crack width grows slightly, but remains constant beyond 100 µm, as shown in Fig. 5 (b). When the vertical loads reaches 100kN, the maximum crack width( w max )reaches 90 µm and after unloading, the crack width decreases to 85 µm. It indicates that the microcracked R-ECC slab possesses strong crack control capabilities and durability resistance under vehicle loads. 2.6.2 Rebound deflection The recorded vertical deflections are shown in Table 3 . The vertical deflection results of bearing plate 'B' and 'D' are obtained by averaging the deflection measured from 'B1' to 'B4' and 'D1' to 'D4', respectively. The maximum vertical deflection at 'B' and 'D' is 0.279 mm and 0.282 mm, respectively, and the vertical residual deflection is 0.011 mm and 0.012 mm after unloading, respectively. Then the rebound deflection at 'B' and 'D' are 0.268mm and 0.270mm, respectively. While the rebound deflection at 'A' is 0.235 mm. Table 3 The recorded vertical deflections(mm) F/kN B1 B2 B3 B4 B A D1 D2 D3 D4 D 0 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 50 0.139 0.137 0.136 0.138 0.137 0.110 0.138 0.140 0.141 0.140 0.140 100 0.280 0.279 0.278 0.279 0.279 0.243 0.281 0.280 0.283 0.282 0.282 0(unload) 0.012 0.011 0.011 0.009 0.011 0.008 0.013 0.012 0.014 0.009 0.012 Rebound deflection 0.268 0.235 0.270 The standard value for the rebound deflection of a 5% cement-stabilized gravel base is given in Table 4 , and the acceptance rebound deflection can be calculated via the following equation [ 19 ]: where P is the tire contact pressure under the standard axle load, which is 0.7 MPa; is the equivalent circular radius of the dual wheels, which is 16 cm; is the theoretical deflection; and is the rebound modulus of the base course. Table 4 Standard values for the rebound deflection [19] Theoretical rebound deflection /mm Acceptance rebound deflection /mm Calculated acceptable rebound deflection /mm 5% cement-stabilized gravel base 0.170 0.371 0.345 Therefore, the rebound deflection of the microcracked R-ECC road–bridge link slab is 0.235 mm, less than the acceptable rebound deflection of 0.345 mm. This indicates that the microcracked R-ECC road-bridge link slab meets the strength requirements under vehicle loads. 3 Sensitivity parameter analysis An investigation of the sensitive influencing parameters (such as the slab thickness and the equivalent elasticity modulus of foundation) on the performance of the R-ECC road-bridge link slab was performed to obtain the design parameters for the R-ECC road-bridge link slab. In this paper, a finite element analysis model of R-ECC road-bridge link slab is established based on the experimental results[ 13 ].The mechanical properties of the R-ECC road-bridge link slabs were simulated via the concrete damaged plasticity (CDP) plasticity damage failure criterion. 3.1 Model specifications A finite element model of the R-ECC slab was established via the discrete simulation method. In this model, the R-ECC slab, tension end, anchor end, and base course were simulated with C3D8R solid elements, whereas the steel bars were simulated with T3D2 truss elements. To ensure computational accuracy, different parts of the model were divided into different grids. Therefore, the R-ECC slab and steel bars used a finer mesh, whereas the base course used a coarser mesh, as shown in Fig. 6(a). The effect of slipping between the steel bars and the R-ECC slab was not considered. The anchor end and the base course of the R-ECC slab were fully constrained, as shown in Fig. 6(b). The interaction between the R-ECC slab and the 5% cement-stabilized gravel base was simulated through surface-to-surface contact, allowing for separation after contact. The tangential interaction was modeled via Coulomb friction, with a friction coefficient of 1.15[ 13 ]. The base course at a depth of 20 m was treated as an isotropic elastic material with a Poisson's ratio of 0.3, and variations in the Young's modulus were used to simulate changes in the ERM of the base course. The PVA fibers were modeled by inputting their three-dimensional parameters with a fixed volume fraction of 2%. The steel bars were modeled via an ideal elastic-plastic material model. 3.2 traffic loads simulation As we mentioned before, the most unfavorable position (0.5 m away from the tensile end) was selected as the control point to apply the vertical vehicle load, as shown in Fig. 7 and the vehicle load for each bearing plate is 100kN. 3.3 Results and discussion 3.3.1Influence of the slab thickness The mechanical performance of R-ECC road–bridge link slabs with five different thicknesses ( t = 100 mm, 120 mm, 150 mm, 180 mm, and 200 mm) was investigated. The influence of slab thickness on the maximum stress and tensile damage of R-ECC slabs was evaluated and the results are shown in Fig. 8. From Fig. 8(a), it can be seen that the maximum stress decreased with the increase in the thickness of the R-ECC slab. But when the thickness of the R-ECC slab increased from 120 mm to 150 mm, the maximum internal force decreased rapidly, it decreased by 18.9%. From Fig. 8(b), it can be seen that the tensile damage also decreased with the increase in the thickness of the R-ECC slab. But when the thickness of the R-ECC slab increased from 150 mm to 180 mm, the tensile damage decreased rapidly, it decreased by 91.2%. 3.3.2 Influence of the equivalent elasticity modulus of the foundation The effects of six different equivalent elasticity modulus of the foundation ( E = 200 MPa, 400 MPa, 600 MPa, 800 MPa, 1000 MPa, and 1200 MPa) on the maximum stress and tensile damage of the R-ECC slab were investigated and the results are shown in Fig. 9 . As seen in Fig. 9 (a), as the equivalent elasticity modulus of the foundation increases, the maximum decreases consistently. Meantime, the tensile damage in the R-ECC slab diminishes as the equivalent elasticity modulus of the foundation rises. Once the equivalent elasticity modulus of the foundation exceeds 800 MPa, there are minimal changes observed in the results. 3.3.3 discussion Based on the results of sensitive parameter calculations, a relationship between the slab thickness and the maximum stress and tensile damage of the R-ECC slab were established. It was found that the thicker the slab thickness, the better the performance. However, increasing the slab thickness also raises construction costs. We introduce the evaluation parameter " C t " to quantify the relationship between the decrement of maximum stress/tensile damage and the increment of the constrution cost. Here, the construction cost is calculated in units of 1,000 USD. A larger value of " C t " indicates a greater stress/tensile damage reduction for the same increment of the construction cost, suggesting that this structural type is a more cost-effective option. The calculation for this parameter is as follows: $$\:{C}_{t}=\frac{\text{D}\text{e}\text{c}\text{r}\text{e}\text{m}\text{e}\text{n}\text{t}\:\text{o}\text{f}\:\text{m}\text{a}\text{x}\text{i}\text{m}\text{u}\text{m}\:\text{s}\text{t}\text{r}\text{e}\text{s}\text{s}（\text{M}\text{P}\text{a}）/\text{t}\text{e}\text{n}\text{s}\text{i}\text{l}\text{e}\:\text{d}\text{a}\text{m}\text{a}\text{g}\text{e}\:}{\text{I}\text{n}\text{c}\text{r}\text{e}\text{m}\text{e}\text{n}\text{t}\:\text{o}\text{f}\:\text{c}\text{o}\text{n}\text{s}\text{t}\text{r}\text{u}\text{c}\text{t}\text{i}\text{o}\text{n}\:\text{c}\text{o}\text{s}\text{t}\:（\text{\$}1000）}$$ 1 The value of " C t " can be determined using Eq. ( 1 ), and the results are presented in Table 5 . Table 5 C t with different slab thicknesses( t ) t (mm) Maximum stress(MPa) Tensile damage Increment of construction cost( $ 1000) C ti C tt 100 4.198 0.538 - - - 120 3.746 0.494 0.020 2.262 0.220 150 3.037 0.424 0.030 2.362 0.231 180 2.918 0.037 0.030 0.400 1.290 200 2.868 0.005 0.020 0.249 0.162 pl : C ti represents the relationship between the decrement of maximum stress and the increment of construction cost. C tt represents the relationship between the decrement of tensile damage and the increment of construction cost. It can be seen from Table 5 that the value of C ti decreases with the increase of slab thickness. Especially when the thickness of the slab increases from 150 mm to 180 mm, the value of C ti reduction decreases. This shows that when the slab thickness is greater than 150 mm, increasing the slab thickness can only slightly reduce the reduction of the maximum stress. And when the slab thickness reaches 180 mm, the value of C tt is the largest. Therefore, this paper recommends a slab thickness of 180 mm to minimize the slab's performance and construction cost. Meantime, the relationship between the equivalent elasticity modulus of the foundation and the performance of the R-ECC slab also has been examined. It was found that a higher equivalent elasticity modulus of the foundation corresponds to improved mechanical properties of the slab. However, increasing the equivalent elasticity modulus of the foundation will also lead to higher construction costs. However, no research results have been found on the relationship between cost and the equivalent elastic modulus of the foundations. In this paper, we propose an evaluation parameter " C e " to assess the relationship between the mechanical properties and the equivalent elasticity modulus of the foundation of R-ECC slabs. A larger value of " C e " indicates a greater stress/tensile damage reduction for the same increment of the equivalent elasticity modulus of the foundation, suggesting that this structural type is a more cost-effective option.The calculation for this parameter is as follows: $$\:{C}_{e}=\frac{\text{D}\text{e}\text{c}\text{r}\text{e}\text{m}\text{e}\text{n}\text{t}\:\text{o}\text{f}\:\text{m}\text{a}\text{x}\text{i}\text{m}\text{u}\text{m}\:\text{s}\text{t}\text{r}\text{e}\text{s}\text{s}（\text{M}\text{P}\text{a}）/\text{t}\text{e}\text{n}\text{s}\text{i}\text{l}\text{e}\:\text{d}\text{a}\text{m}\text{a}\text{g}\text{e}\:}{\begin{array}{c}Increment\:of\:equivalent\:elasicity\:modulus\:of\:the\:foundation\:（GPa\end{array}）}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:$$ 2 The value of " C e " can be determined using Eq. ( 2 ), and the results are presented in Table 6 . Table 6 C e with the different equivalent elasticity modulus of the foundation Equivalent elasticity modulus of the foundation(MPa) Maximum stress(MPa) Tensile damage Increment of equivalent elasticity modulus of the foundation(GPa) C ei C et 200 2.747 0.175 - - - 400 2.424 0.122 0.2 1.614 0.264 600 2.214 0.081 0.2 1.054 0.203 800 2.073 0.040 0.2 0.703 0.162 1000 1.966 0.043 0.2 0.535 0.032 1200 1.879 0.045 0.2 0.435 -0.010 pl : C ei represents the relationship between the decrement of maximum stress and the increment of equivalent elasticity modulus of the foundation. C et represents the relationship between the decrement of tensile damage and the increment of equivalent elasticity modulus of the foundation. It can be seen from Table 6 that the value of C ei decreases with the increase of equivalent elasticity modulus of the foundation. Especially when the equivalent elasticity modulus of the foundation is greater than 800 MPa, the value of C ei reduction decreases. This shows that when the equivalent elasticity modulus of the foundation is greater than 800 MPa, the increase of equivalent elasticity modulus of the foundation can only slightly reduce the reduction of the maximum stress. And when the equivalent elasticity modulus of the foundation reaches 1000 MPa, the value of C tt is drops the most. Therefore, in order to minimize the performance and construction cost of the slab, this paper recommends an equivalent elasticity modulus of the foundation of 800 MPa. In conclusion, in light of the mechanical properties and cost constraints of the R-ECC road-bridge link slab, this paper proposes that the design specifications for the R-ECC road-bridge link slab should be as follows: a thickness of 180 mm and an equivalent elasticity modulus of the foundation of 800 MPa. 4 Conclusions Based on the results of this study, the following conclusions can be drawn: (1) Through the vertical bearing plate test, it is found that microcracked R-ECC road-bridge link slab has strong crack control capabilities and durability resistance. The vertical deformation of the microcracked R-ECC road-bridge link slab increased with increasing vertical load, and the rebound deflection was 0.235 mm, which is less than the calculated acceptable rebound deflection of 0.345 mm, meeting the design strength requirements for the road-bridge link slab. (2) Through the sensitivity parameter numerical analysis, the effects of the slab thickness and equivalent elasticity modulus of the foundation on the mechanical performance of the R-ECC road-bridge link slab were studied. The internal force and tensile damage of the R-ECC road-bridge link slab decrease with increasing slab thickness and equivalent elasticity modulus of the foundation. Based on the calculation results of the evaluation evaluation parameter " C t " and " C e ", this paper suggests that the design thickness and equivalent elasticity modulus of the foundation for an R-ECC road-bridge link slab should be 180 mm and 800 MPa, respectively. (3)Due to space limitations, this paper only studied the mechanical properties of micro-cracked R-ECC road-bridge link slabs under vehicle loads. To verify the applicability of R-ECC mixtures in the construction of road-bridge link slabs for FJBs, the following research areas need to be studied: the dynamic simulation analysis of the R-ECC road-bridge link slab and R-ECC road-bridge link slabs suffering uneven settlement of abutments/piers or with different anchoring quality situtation of anchor beam as well. Declarations Author Contribution Xuefang Zhan wrote the main manuscript text，Tian-pu Zhao prepared figures 1-5，Fang Wang prepared figures 6-9，Yi-bin Zhao check all the tables and Hao-lei Wang element simulation. All authors reviewed the manuscript. Acknowledgement This research was funded by the Scientific Research Foundation of Hunan Provincial Education Department (Grant No.23B0243), and the National Natural Science Foundation of China (Grant No. 52278235). Data Availability Data is provided within the manuscript. References Ala N M, Azizinamini A. 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Cite Share Download PDF Status: Published Journal Publication published 27 Apr, 2025 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Accepted 23 Apr, 2025 Reviews received at journal 19 Apr, 2025 Reviews received at journal 10 Apr, 2025 Reviewers agreed at journal 10 Apr, 2025 Reviewers agreed at journal 09 Apr, 2025 Reviewers invited by journal 09 Apr, 2025 Submission checks completed at journal 06 Apr, 2025 First submitted to journal 27 Mar, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6060988","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":440445657,"identity":"10c98a51-e5cc-4056-be25-c8d70156f05c","order_by":0,"name":"Xue-fang Zhan","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABBklEQVRIiWNgGAWjYDACCQjFD8SMD6AMmCB+LZINDAzMBiBGDyla2CSI0iI/u/nZY942Gwn+2e3XKn78OSxhz8B88DYPg10eLi2Mc46ZG85sS5OQuHOm7GZv22EJHga2ZGsehuRiXFqYJRLMJD62Ha5juJGTdpux4XAdDwOPmTQPw4HEBhxa2CTSv0kktv2XkAdqKWb4A7KF/xteLTwSOSBbDkgY3Eg/xszABtLCw4ZXi4RETpnkjHPJEoY3cpgle9vSJXgOsxlbzjFIxqlFfkb6NmmeMjsJuRvpDz/8+GMtwd7e/PDGmwo7nFqQ3WgADREQYUBYPRCwPyBK2SgYBaNgFIw8AAAqSE8LVxgiHQAAAABJRU5ErkJggg==","orcid":"","institution":"Central South University of Forestry and Technology","correspondingAuthor":true,"prefix":"","firstName":"Xue-fang","middleName":"","lastName":"Zhan","suffix":""},{"id":440445658,"identity":"3c450a4a-38b8-411e-9cc5-428b9991ad91","order_by":1,"name":"Tian-pu Zhao","email":"","orcid":"","institution":"Central South University of Forestry and Technology","correspondingAuthor":false,"prefix":"","firstName":"Tian-pu","middleName":"","lastName":"Zhao","suffix":""},{"id":440445659,"identity":"e888732d-d232-4958-81a9-24dcb1c7dac4","order_by":2,"name":"Fang Wang","email":"","orcid":"","institution":"Central South University of Forestry and Technology","correspondingAuthor":false,"prefix":"","firstName":"Fang","middleName":"","lastName":"Wang","suffix":""},{"id":440445660,"identity":"af484f40-5a10-4994-b1ee-4907fb9fb286","order_by":3,"name":"Yi-bin Zhao","email":"","orcid":"","institution":"Central South University of Forestry and Technology","correspondingAuthor":false,"prefix":"","firstName":"Yi-bin","middleName":"","lastName":"Zhao","suffix":""},{"id":440445661,"identity":"f5789c0f-cefc-493d-896b-f54dd7c48664","order_by":4,"name":"Hao-lei Wang","email":"","orcid":"","institution":"Central South University of Forestry and Technology","correspondingAuthor":false,"prefix":"","firstName":"Hao-lei","middleName":"","lastName":"Wang","suffix":""}],"badges":[],"createdAt":"2025-02-19 06:08:33","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6060988/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6060988/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-025-99947-0","type":"published","date":"2025-04-27T15:57:27+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":80306326,"identity":"71c1d7e9-948a-4fa5-a0b7-795f7d47b95e","added_by":"auto","created_at":"2025-04-10 10:23:07","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":28036,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eECC road-bridge link slab for FJBs [13]\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6060988/v1/41f0b7868f7fb0817e12e19c.jpg"},{"id":80306328,"identity":"0684e12d-4019-484f-ab03-f1e40901e2f4","added_by":"auto","created_at":"2025-04-10 10:23:07","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":245159,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eModel design and casting process of the R-ECC slab(Units:cm)(a)Model elevation,(b)Model plan,(c)Wooden box,(d)EAS layer,(e)Steel bars,(f)Model casting,(g)Model Maintenance,(h)Test model\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6060988/v1/a54ea2546015885e3f112a38.jpg"},{"id":80307374,"identity":"b6567646-81df-4a5b-a681-d42373c70899","added_by":"auto","created_at":"2025-04-10 10:31:07","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":64060,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eLoading location (Unit: cm) (a) Crack Distribution of the R-ECC slab,(b) Loading point diagram\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6060988/v1/0ba2521d83532ae549309bbd.jpg"},{"id":80305892,"identity":"12128b4b-9fa6-4311-aed9-e5f2943d5857","added_by":"auto","created_at":"2025-04-10 10:15:07","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":43744,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eArrangement of the measuring points (unit:mm)\u003c/strong\u003e(a)\u003cstrong\u003eSchematic diagram,\u003c/strong\u003e (b)\u003cstrong\u003ePicture of bearing plate \u003c/strong\u003e'\u003cstrong\u003eB\u003c/strong\u003e', (c)\u003cstrong\u003ePicture of bearing plate \u003c/strong\u003e'\u003cstrong\u003eD\u003c/strong\u003e'\u003c/p\u003e","description":"","filename":"4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6060988/v1/5f1f4a02ee9a6db0a2cecee7.jpg"},{"id":80305894,"identity":"cafeae98-4bb8-480c-932d-9927c8fa0026","added_by":"auto","created_at":"2025-04-10 10:15:07","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":43399,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eMaximum micro-cracking (unit:µm)(a)a picture of the maximum micro-cracking,(b)The relationship between the maximum crack width and the vertical load\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6060988/v1/8b96f196dc2578b569697446.jpg"},{"id":80305897,"identity":"ed2bfad7-9b85-4b30-bb85-8445b8d07204","added_by":"auto","created_at":"2025-04-10 10:15:07","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":43543,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eA finite element simulation of the R-ECC road-bridge link slab（a）Grid division and constraints, （b）Loading simulation, （c）Bilinear constitutive model\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"6.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6060988/v1/faea4956389080e4437cf5f2.jpg"},{"id":80307375,"identity":"f1fec6e4-c574-441c-95d4-67a3eca13cd2","added_by":"auto","created_at":"2025-04-10 10:31:07","extension":"jpg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":21817,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eLocation of loading point\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"7.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6060988/v1/e5590358d24d5e861e778795.jpg"},{"id":80306329,"identity":"4b0b1f2c-4f74-4bab-b64f-db091b34dbaa","added_by":"auto","created_at":"2025-04-10 10:23:07","extension":"jpg","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":33810,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eMechanical properties of R-ECC slab with different thicknesses:(a)Maximum stress,(b)tensile damage\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"8.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6060988/v1/04bd885b91435133c4007e55.jpg"},{"id":80306336,"identity":"2f34da78-c191-4c00-98c4-bc88ddc92615","added_by":"auto","created_at":"2025-04-10 10:23:08","extension":"jpg","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":33477,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eMechanical properties of R-ECC slabs with different equivalent elasticity modulus of foundation: (a)maximum stress,(b)tensile damage\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"9.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6060988/v1/26e77426635f6cb45bcf07a1.jpg"},{"id":81569630,"identity":"da2e4574-01db-4e7b-af09-b585f4ee5e15","added_by":"auto","created_at":"2025-04-28 16:08:20","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2309981,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6060988/v1/d8cf5758-52e6-4bbf-97ae-74fa459f2f4c.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Study on the bending deformation properties of microcracked R-ECC road–bridge link slabs","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003eA jointless bridge is defined by the International Association of Jointless Bridges (IAJBs) as a bridge structure with a continuous superstructure without installing any expansion equipment within the whole bridge structure. This definition emphasizes the absence of expansion joints throughout the entire superstructure of a bridge [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. One novel design of the fully jointless bridges (FJBs) utilizes a road-bridge link slab further to eliminate the gaps between the continuous bridge ends and the approach road[\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. Currently, FJBs are suitable for the construction of medium and small bridges to improve ride comfort at road-bridge connections [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eIn preview research, an innovative road-bridge link slab made from engineered cementitious composites (ECCs), referred to as ECC road-bridge link slabs, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, effectively utilizes the high-strain hardening characteristics of the ECC material, including its multiple cracking characteristics[\u003cspan additionalcitationids=\"CR7\" citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e] and strong crack width control capability[\u003cspan additionalcitationids=\"CR10\" citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e], thereby significantly enhancing the performance of FJBs[\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. Zhan XF, et al.[\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e] studied the tensile performance of the ECC road-bridge link slab, and the results demonstrated its substantial ability to absorb longitudinal deformations, which aligns with the requirements for FJBs to accommodate the deformations of bridge structures. However, ECC is quite expensive because of the use of silica sand. Zhang ZG, et al.[\u003cspan additionalcitationids=\"CR15\" citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e] and Zhan XF, et al.[\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e] developed a rubberized engineered cementitious composite (R-ECC) by using river fine sand and rubber crumb to completely substitute for silica sand and reduce its cost. The experimental results validated the suitability of the R-ECC material used in the road-bridge link slab to absorb longitudinal deformations caused by system temperature loads[\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eSeasonal temperature loads is a key factor influence the performance of FJBs. Under seasonal temperature loads, micro-cracks developed on the surface of the R-ECC road-bridge link slabs of FJBs. But previous research proved that the microcracked R-ECC slabs exhibit strong crack control capabilities and meet the strength criteria for FJBs[\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. Compared to ECCs, R-ECCs have improved bending ability but lower compressive strength. At this point, whether the road-bridge link slab with micro-cracks can bear the vehicle load is worth studying. In order to demonstrate the successful application R-ECC in road-bridge link slabs for FJBs and establish a design theory for R-ECC road-bridge link slabs, further research is needed. This research should focus on the rebound deflection test of the microcracked R-ECC road-bridge link slab under vehicle loads. The objective was to evaluate whether the crack development and the bending deformation capacity of the R-ECC road-bridge link slabs with microcracks under vehicle load meet the durability and strength criteria of FJBs.\u003c/p\u003e"},{"header":"2 Rebound deflection test","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Objective and Overview\u003c/h2\u003e \u003cp\u003eIn practical projects, the road-bridge link slabs often develop microcracks due to seasonal temperature variations, particularly in winter. These slabs are subjected to pressure, impact, shear, and wear from vehicle loads, creating complex stress conditions that make it challenging to ensure the durability of microcracked slabs under these conditions.\u003c/p\u003e \u003cp\u003eThe rebound deflection is directly related to the design strength of the pavement. It serves as one of the standards to check whether the construction of the pavement meets the design strength requirements. To explore the applicability of R-ECC road-bridge link slabs for FJBs, a vehicle load that directly acts on the most unfavourable cracking position of the R-ECC slab is used to test its rebound deflection.\u003c/p\u003e \u003cp\u003eThe contact pressure, contact shape, and contact area between the vehicles and surface course are difficult to simulate in the laboratory. In accordance with the Specifications for the Design of Highway Asphalt Pavement in China, a dual wheel with one single-axle load of 100 kN is designed as the standard axle load, denoted as BZZ-100. The tire contact pressure is calculated to be 0.7 MPa, and the diameter of a single-wheel contact area equivalent circle is 21.3 cm[\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. Then, the diameter of the steel bearing plate used to simulate the wheel effect is determined to be 21.3 cm, with a thickness of 2 cm.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Model Design\u003c/h2\u003e \u003cdiv id=\"Sec5\" class=\"Section3\"\u003e \u003ch2\u003e2.2.1 General description\u003c/h2\u003e \u003cp\u003eThe test model consists of an R-ECC slab measuring 5 m in length, 0.5 m in width, and 0.15 m in thickness, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e (a,b)[\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e].There are three layers: a 15cm R-ECC road-bridge link slab layer, a 25cm 5% cement-stabilized gravel base layer, and a 20cm grade gravel base layer, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(a). To prevent overflow of the base materials under vertical loading, the base materials are contained within a wooden box, as illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(c). As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e (d), a 2 mm thick emulsified asphalt sealing (EAS) layer is poured as a sliding layer between the 5% cement-stabilized gravel base layer and the R-ECC slab layer. Additionally, the detailed model design, casting process and reinforcement arrangement of the R-ECC slab are illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(c to h).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section3\"\u003e \u003ch2\u003e2.2.2 Model parameters\u003c/h2\u003e \u003cp\u003eBased on previous research findings[\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e], the R-ECC mix ratio for the design of the R-ECC road-bridge link slab is shown in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eMaterial mix ratio of R-ECC\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePortland Cement\u003c/p\u003e \u003cp\u003e(kg/m\u0026sup3;)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFly Ash\u003c/p\u003e \u003cp\u003e(kg/m\u0026sup3;)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eFine Sand\u003c/p\u003e \u003cp\u003e(kg/m\u0026sup3;)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eWater\u003c/p\u003e \u003cp\u003e(kg/m\u0026sup3;)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eRubber crumb replace ratio\u003c/p\u003e \u003cp\u003e(Vol%)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003ePVA fibers\u003c/p\u003e \u003cp\u003e(Vol%)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eHigh-range water reducing admixture\u003c/p\u003e \u003cp\u003e(Vol%)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e390\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e780\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e448\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e363\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe detailed material parameters for the R-ECC slab test specimen are shown in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eDetailed material parameters for the R-ECC slab\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNumbers of longitudinal steel bars\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eThe diameter of the longitudinal steel bars\u003c/p\u003e \u003cp\u003e(mm)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eLongitudinal reinforcement ratio of R-ECC slab (%)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eTensile strength of steel bars (MPa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eTensile strength of R-ECC\u003c/p\u003e \u003cp\u003e(MPa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eCompressive strength of R-ECC\u003c/p\u003e \u003cp\u003e(MPa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eElasticity modulus of R-ECC\u003c/p\u003e \u003cp\u003e(GPa)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.804%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e335\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e26.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e17.3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e2.3 Loading location\u003c/h2\u003e \u003cp\u003eBefore conducting the rebound deflection test, a low-cycle tensile/compression test of the R-ECC slab must be performed to simulate the cracking that occurs in the slab due to seasonal temperature fluctuations[\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. In this case, a low two-and-a-half cycle tensile/compression test was simulated[\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. At the end of the two-and-a-half tensile test, lots of microcracks appeared on the surface of the R-ECC slab and the larger cracks are primarily concentrated near the tension end. The crack distribution within the slab are shown in Fig.\u0026nbsp;3(a). To prevent a significant change in slab stiffness and to facilitate the placement of the bearing plate for vehicle load simulation, a position 50 cm away from the tension end is selected as the loading location, as shown in Fig.\u0026nbsp;3(b).\u003c/p\u003e\u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e2.4Layout of Measuring Instrument\u003c/h2\u003e \u003cp\u003eTwo bearing plates are used for vehicle load application, One is marked as 'B', located 0.5 meters away from the tension end, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e4\u003c/span\u003e(a,b). Four dial gauges are arranged along the bearing plate 'B' and labeled as 'B1' to 'B4'. The other bearing plate is labeled as 'D' and is positioned approximately 319.5 mm away from bearing plate 'B', at a distance of 1.5 times the radius (r) of the bearing plate. Additionally, four dial gauges are arranged along the bearing plate 'D' and labeled as 'D1' to 'D4', as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e4\u003c/span\u003e(a,c). These gauges are used to measure the vertical displacement of the bearing plates under vertical load. In addition, a dial gauge labeled as 'A' is positioned at the centre of the two bearing plates to measure the rebound deflection.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e2.5Loading process\u003c/h2\u003e \u003cp\u003eThe vertical load applied to the center of the bearing plate is divided into two levels, with each level carrying a load of 50 kN. After loading, the model rests for 5 minutes and the data is recorded. When unloading vertical loads, the process is completed all at once.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e2.6 Results and discussion\u003c/h2\u003e \u003cdiv id=\"Sec11\" class=\"Section3\"\u003e \u003ch2\u003e2.6.1Crack development\u003c/h2\u003e \u003cp\u003eThe largest crack width of the microcracks near the tension end is 65 \u0026micro;m, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e5\u003c/span\u003e(a). As the load increases, the crack width grows slightly, but remains constant beyond 100 \u0026micro;m, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e5\u003c/span\u003e(b). When the vertical loads reaches 100kN, the maximum crack width(\u003cem\u003ew\u003c/em\u003e\u003csub\u003e\u003cem\u003emax\u003c/em\u003e\u003c/sub\u003e)reaches 90 \u0026micro;m and after unloading, the crack width decreases to 85 \u0026micro;m. It indicates that the microcracked R-ECC slab possesses strong crack control capabilities and durability resistance under vehicle loads.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section3\"\u003e \u003ch2\u003e2.6.2 Rebound deflection\u003c/h2\u003e \u003cp\u003eThe recorded vertical deflections are shown in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. The vertical deflection results of bearing plate 'B' and 'D' are obtained by averaging the deflection measured from 'B1' to 'B4' and 'D1' to 'D4', respectively. The maximum vertical deflection at 'B' and 'D' is 0.279 mm and 0.282 mm, respectively, and the vertical residual deflection is 0.011 mm and 0.012 mm after unloading, respectively. Then the rebound deflection at 'B' and 'D' are 0.268mm and 0.270mm, respectively. While the rebound deflection at 'A' is 0.235 mm.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eThe recorded vertical deflections(mm)\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"12\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c12\" colnum=\"12\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eF/kN\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eB1\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eB2\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eB3\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eB4\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eB\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eD1\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003eD2\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c10\"\u003e \u003cp\u003eD3\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c11\"\u003e \u003cp\u003eD4\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c12\"\u003e \u003cp\u003eD\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c12\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.139\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.137\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.136\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.138\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.137\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.110\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.138\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.140\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.141\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e \u003cp\u003e0.140\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c12\"\u003e \u003cp\u003e0.140\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.280\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.279\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.278\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.279\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.279\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.243\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.281\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.280\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.283\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e \u003cp\u003e0.282\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c12\"\u003e \u003cp\u003e0.282\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e0(unload)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.012\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.011\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.011\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.009\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.011\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.008\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.013\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.012\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.014\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e \u003cp\u003e0.009\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c12\"\u003e \u003cp\u003e0.012\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRebound deflection\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.268\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.235\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c12\"\u003e \u003cp\u003e0.270\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003cp\u003eThe standard value for the rebound deflection of a 5% cement-stabilized gravel base is given in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, and the acceptance rebound deflection can be calculated via the following equation [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]:\u003c/p\u003e\u003cp\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"488\" height=\"74\"\u003e\u003c/p\u003e\u003c/div\u003e \u003cp\u003ewhere \u003cem\u003eP\u003c/em\u003e is the tire contact pressure under the standard axle load, which is 0.7 MPa; \u003cspan class=\"InlineEquation\"\u003e\u003c/span\u003e is the equivalent circular radius of the dual wheels, which is 16 cm; \u003cspan class=\"InlineEquation\"\u003e\u003c/span\u003e is the theoretical deflection; and \u003cspan class=\"InlineEquation\"\u003e\u003c/span\u003e is the rebound modulus of the base course.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u003cb\u003eStandard values for the rebound deflection\u003c/b\u003e\u003csup\u003e[19]\u003c/sup\u003e\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTheoretical rebound deflection /mm\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eAcceptance rebound deflection /mm\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eCalculated acceptable rebound deflection /mm\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5% cement-stabilized gravel base\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.170\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.371\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.345\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTherefore, the rebound deflection of the microcracked R-ECC road\u0026ndash;bridge link slab is 0.235 mm, less than the acceptable rebound deflection of 0.345 mm. This indicates that the microcracked R-ECC road-bridge link slab meets the strength requirements under vehicle loads.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"3 Sensitivity parameter analysis","content":"\u003cp\u003eAn investigation of the sensitive influencing parameters (such as the slab thickness and the equivalent elasticity modulus of foundation) on the performance of the R-ECC road-bridge link slab was performed to obtain the design parameters for the R-ECC road-bridge link slab. In this paper, a finite element analysis model of R-ECC road-bridge link slab is established based on the experimental results[\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e].The mechanical properties of the R-ECC road-bridge link slabs were simulated via the concrete damaged plasticity (CDP) plasticity damage failure criterion.\u003c/p\u003e \u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Model specifications\u003c/h2\u003e \u003cp\u003eA finite element model of the R-ECC slab was established via the discrete simulation method. In this model, the R-ECC slab, tension end, anchor end, and base course were simulated with C3D8R solid elements, whereas the steel bars were simulated with T3D2 truss elements. To ensure computational accuracy, different parts of the model were divided into different grids. Therefore, the R-ECC slab and steel bars used a finer mesh, whereas the base course used a coarser mesh, as shown in Fig.\u0026nbsp;6(a). The effect of slipping between the steel bars and the R-ECC slab was not considered. The anchor end and the base course of the R-ECC slab were fully constrained, as shown in Fig.\u0026nbsp;6(b). The interaction between the R-ECC slab and the 5% cement-stabilized gravel base was simulated through surface-to-surface contact, allowing for separation after contact. The tangential interaction was modeled via Coulomb friction, with a friction coefficient of 1.15[\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. The base course at a depth of 20 m was treated as an isotropic elastic material with a Poisson's ratio of 0.3, and variations in the Young's modulus were used to simulate changes in the ERM of the base course. The PVA fibers were modeled by inputting their three-dimensional parameters with a fixed volume fraction of 2%. The steel bars were modeled via an ideal elastic-plastic material model.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec15\" class=\"Section2\"\u003e \u003ch2\u003e3.2 traffic loads simulation\u003c/h2\u003e \u003cp\u003eAs we mentioned before, the most unfavorable position (0.5 m away from the tensile end) was selected as the control point to apply the vertical vehicle load, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e7\u003c/span\u003e and the vehicle load for each bearing plate is 100kN.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec16\" class=\"Section2\"\u003e \u003ch2\u003e3.3 Results and discussion\u003c/h2\u003e \u003cdiv id=\"Sec17\" class=\"Section3\"\u003e \u003ch2\u003e3.3.1Influence of the slab thickness\u003c/h2\u003e \u003cp\u003eThe mechanical performance of R-ECC road\u0026ndash;bridge link slabs with five different thicknesses (\u003cem\u003et\u003c/em\u003e\u0026thinsp;=\u0026thinsp;100 mm, 120 mm, 150 mm, 180 mm, and 200 mm) was investigated. The influence of slab thickness on the maximum stress and tensile damage of R-ECC slabs was evaluated and the results are shown in Fig.\u0026nbsp;8.\u003c/p\u003e \u003cp\u003eFrom Fig.\u0026nbsp;8(a), it can be seen that the maximum stress decreased with the increase in the thickness of the R-ECC slab. But when the thickness of the R-ECC slab increased from 120 mm to 150 mm, the maximum internal force decreased rapidly, it decreased by 18.9%. From Fig.\u0026nbsp;8(b), it can be seen that the tensile damage also decreased with the increase in the thickness of the R-ECC slab. But when the thickness of the R-ECC slab increased from 150 mm to 180 mm, the tensile damage decreased rapidly, it decreased by 91.2%.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec18\" class=\"Section3\"\u003e \u003ch2\u003e3.3.2 Influence of the equivalent elasticity modulus of the foundation\u003c/h2\u003e \u003cp\u003eThe effects of six different equivalent elasticity modulus of the foundation (\u003cem\u003eE\u003c/em\u003e\u0026thinsp;=\u0026thinsp;200 MPa, 400 MPa, 600 MPa, 800 MPa, 1000 MPa, and 1200 MPa) on the maximum stress and tensile damage of the R-ECC slab were investigated and the results are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e9\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eAs seen in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e9\u003c/span\u003e(a), as the equivalent elasticity modulus of the foundation increases, the maximum decreases consistently. Meantime, the tensile damage in the R-ECC slab diminishes as the equivalent elasticity modulus of the foundation rises. Once the equivalent elasticity modulus of the foundation exceeds 800 MPa, there are minimal changes observed in the results.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec19\" class=\"Section3\"\u003e \u003ch2\u003e3.3.3 discussion\u003c/h2\u003e \u003cp\u003eBased on the results of sensitive parameter calculations, a relationship between the slab thickness and the maximum stress and tensile damage of the R-ECC slab were established. It was found that the thicker the slab thickness, the better the performance. However, increasing the slab thickness also raises construction costs. We introduce the evaluation parameter \"\u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e\" to quantify the relationship between the decrement of maximum stress/tensile damage and the increment of the constrution cost. Here, the construction cost is calculated in units of 1,000 USD. A larger value of \"\u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e\" indicates a greater stress/tensile damage reduction for the same increment of the construction cost, suggesting that this structural type is a more cost-effective option. The calculation for this parameter is as follows:\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:{C}_{t}=\\frac{\\text{D}\\text{e}\\text{c}\\text{r}\\text{e}\\text{m}\\text{e}\\text{n}\\text{t}\\:\\text{o}\\text{f}\\:\\text{m}\\text{a}\\text{x}\\text{i}\\text{m}\\text{u}\\text{m}\\:\\text{s}\\text{t}\\text{r}\\text{e}\\text{s}\\text{s}（\\text{M}\\text{P}\\text{a}）/\\text{t}\\text{e}\\text{n}\\text{s}\\text{i}\\text{l}\\text{e}\\:\\text{d}\\text{a}\\text{m}\\text{a}\\text{g}\\text{e}\\:}{\\text{I}\\text{n}\\text{c}\\text{r}\\text{e}\\text{m}\\text{e}\\text{n}\\text{t}\\:\\text{o}\\text{f}\\:\\text{c}\\text{o}\\text{n}\\text{s}\\text{t}\\text{r}\\text{u}\\text{c}\\text{t}\\text{i}\\text{o}\\text{n}\\:\\text{c}\\text{o}\\text{s}\\text{t}\\:（\\text{\\$}1000）}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe value of \"\u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e\" can be determined using Eq.\u0026nbsp;(\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e1\u003c/span\u003e), and the results are presented in Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e with different slab thicknesses(\u003cem\u003et\u003c/em\u003e)\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003et\u003c/em\u003e\u003c/p\u003e \u003cp\u003e(mm)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMaximum stress(MPa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTensile damage\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eIncrement of construction cost(\u003cspan\u003e$\u003c/span\u003e1000)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003eti\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003ett\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4.198\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.538\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e120\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e3.746\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.494\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.020\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.262\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.220\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e150\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e3.037\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.424\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.030\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.362\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.231\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e180\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2.918\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.037\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.030\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.400\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.290\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e200\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2.868\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.005\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.020\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.249\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.162\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003epl\u003c/b\u003e:\u003cb\u003eC\u003c/b\u003e\u003csub\u003e\u003cb\u003eti\u003c/b\u003e\u003c/sub\u003e \u003cb\u003erepresents the relationship between the decrement of maximum stress and the increment of construction cost.\u003c/b\u003e \u003cb\u003eC\u003c/b\u003e\u003csub\u003e\u003cb\u003ett\u003c/b\u003e\u003c/sub\u003e \u003cb\u003erepresents the relationship between the decrement of tensile damage and the increment of construction cost.\u003c/b\u003e\u003c/p\u003e \u003cp\u003eIt can be seen from Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e that the value of \u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003eti\u003c/em\u003e\u003c/sub\u003e decreases with the increase of slab thickness. Especially when the thickness of the slab increases from 150 mm to 180 mm, the value of \u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003eti\u003c/em\u003e\u003c/sub\u003e reduction decreases. This shows that when the slab thickness is greater than 150 mm, increasing the slab thickness can only slightly reduce the reduction of the maximum stress. And when the slab thickness reaches 180 mm, the value of \u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003ett\u003c/em\u003e\u003c/sub\u003e is the largest. Therefore, this paper recommends a slab thickness of 180 mm to minimize the slab's performance and construction cost.\u003c/p\u003e \u003cp\u003eMeantime, the relationship between the equivalent elasticity modulus of the foundation and the performance of the R-ECC slab also has been examined. It was found that a higher equivalent elasticity modulus of the foundation corresponds to improved mechanical properties of the slab. However, increasing the equivalent elasticity modulus of the foundation will also lead to higher construction costs. However, no research results have been found on the relationship between cost and the equivalent elastic modulus of the foundations. In this paper, we propose an evaluation parameter \"\u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003ee\u003c/em\u003e\u003c/sub\u003e\" to assess the relationship between the mechanical properties and the equivalent elasticity modulus of the foundation of R-ECC slabs. A larger value of \"\u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003ee\u003c/em\u003e\u003c/sub\u003e\" indicates a greater stress/tensile damage reduction for the same increment of the equivalent elasticity modulus of the foundation, suggesting that this structural type is a more cost-effective option.The calculation for this parameter is as follows:\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:{C}_{e}=\\frac{\\text{D}\\text{e}\\text{c}\\text{r}\\text{e}\\text{m}\\text{e}\\text{n}\\text{t}\\:\\text{o}\\text{f}\\:\\text{m}\\text{a}\\text{x}\\text{i}\\text{m}\\text{u}\\text{m}\\:\\text{s}\\text{t}\\text{r}\\text{e}\\text{s}\\text{s}（\\text{M}\\text{P}\\text{a}）/\\text{t}\\text{e}\\text{n}\\text{s}\\text{i}\\text{l}\\text{e}\\:\\text{d}\\text{a}\\text{m}\\text{a}\\text{g}\\text{e}\\:}{\\begin{array}{c}Increment\\:of\\:equivalent\\:elasicity\\:modulus\\:of\\:the\\:foundation\\:（GPa\\end{array}）}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe value of \"\u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003ee\u003c/em\u003e\u003c/sub\u003e\" can be determined using Eq.\u0026nbsp;(\u003cspan refid=\"Equ3\" class=\"InternalRef\"\u003e2\u003c/span\u003e), and the results are presented in Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003ee\u003c/em\u003e\u003c/sub\u003e with the different equivalent elasticity modulus of the foundation\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEquivalent elasticity modulus of the foundation(MPa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMaximum stress(MPa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTensile damage\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eIncrement of equivalent elasticity modulus of the foundation(GPa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003eei\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003eet\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e200\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2.747\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.175\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e400\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2.424\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.122\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.614\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.264\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e600\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2.214\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.081\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.054\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.203\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e800\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2.073\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.040\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.703\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.162\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.966\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.043\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.535\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.032\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1200\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.879\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.045\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.435\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-0.010\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003epl\u003c/b\u003e:\u003cb\u003eC\u003c/b\u003e\u003csub\u003e\u003cb\u003eei\u003c/b\u003e\u003c/sub\u003e \u003cb\u003erepresents the relationship between the decrement of maximum stress and the increment of equivalent elasticity modulus of the foundation.\u003c/b\u003e \u003cb\u003eC\u003c/b\u003e\u003csub\u003e\u003cb\u003eet\u003c/b\u003e\u003c/sub\u003e \u003cb\u003erepresents the relationship between the decrement of tensile damage and the increment of equivalent elasticity modulus of the foundation.\u003c/b\u003e\u003c/p\u003e \u003cp\u003eIt can be seen from Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e that the value of \u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003eei\u003c/em\u003e\u003c/sub\u003e decreases with the increase of equivalent elasticity modulus of the foundation. Especially when the equivalent elasticity modulus of the foundation is greater than 800 MPa, the value of \u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003eei\u003c/em\u003e\u003c/sub\u003e reduction decreases. This shows that when the equivalent elasticity modulus of the foundation is greater than 800 MPa, the increase of equivalent elasticity modulus of the foundation can only slightly reduce the reduction of the maximum stress. And when the equivalent elasticity modulus of the foundation reaches 1000 MPa, the value of \u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003ett\u003c/em\u003e\u003c/sub\u003e is drops the most. Therefore, in order to minimize the performance and construction cost of the slab, this paper recommends an equivalent elasticity modulus of the foundation of 800 MPa.\u003c/p\u003e \u003cp\u003eIn conclusion, in light of the mechanical properties and cost constraints of the R-ECC road-bridge link slab, this paper proposes that the design specifications for the R-ECC road-bridge link slab should be as follows: a thickness of 180 mm and an equivalent elasticity modulus of the foundation of 800 MPa.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"4 Conclusions","content":"\u003cp\u003eBased on the results of this study, the following conclusions can be drawn:\u003c/p\u003e \u003cp\u003e(1) Through the vertical bearing plate test, it is found that microcracked R-ECC road-bridge link slab has strong crack control capabilities and durability resistance. The vertical deformation of the microcracked R-ECC road-bridge link slab increased with increasing vertical load, and the rebound deflection was 0.235 mm, which is less than the calculated acceptable rebound deflection of 0.345 mm, meeting the design strength requirements for the road-bridge link slab.\u003c/p\u003e \u003cp\u003e(2) Through the sensitivity parameter numerical analysis, the effects of the slab thickness and equivalent elasticity modulus of the foundation on the mechanical performance of the R-ECC road-bridge link slab were studied. The internal force and tensile damage of the R-ECC road-bridge link slab decrease with increasing slab thickness and equivalent elasticity modulus of the foundation. Based on the calculation results of the evaluation evaluation parameter \"\u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e\" and \"\u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003ee\u003c/em\u003e\u003c/sub\u003e\", this paper suggests that the design thickness and equivalent elasticity modulus of the foundation for an R-ECC road-bridge link slab should be 180 mm and 800 MPa, respectively.\u003c/p\u003e \u003cp\u003e(3)Due to space limitations, this paper only studied the mechanical properties of micro-cracked R-ECC road-bridge link slabs under vehicle loads. To verify the applicability of R-ECC mixtures in the construction of road-bridge link slabs for FJBs, the following research areas need to be studied: the dynamic simulation analysis of the R-ECC road-bridge link slab and R-ECC road-bridge link slabs suffering uneven settlement of abutments/piers or with different anchoring quality situtation of anchor beam as well.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eXuefang Zhan wrote the main manuscript text，Tian-pu Zhao prepared figures 1-5，Fang Wang prepared figures 6-9，Yi-bin Zhao check all the tables and Hao-lei Wang element simulation. All authors reviewed the manuscript.\u003c/p\u003e\u003ch2\u003eAcknowledgement\u003c/h2\u003e\u003cp\u003eThis research was funded by the Scientific Research Foundation of Hunan Provincial Education Department (Grant No.23B0243), and the National Natural Science Foundation of China (Grant No. 52278235).\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eData is provided within the manuscript.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eAla N M, Azizinamini A. Proposed design provisions for a seamless bridge system: cases of flexible and jointed pavements[J]. Journal of Bridge Engineering, 2016, 21(2): 04015045. \u003c/li\u003e\n\u003cli\u003eEichwalder B, Kollegger J. Durable transition structure for long integral abutment bridges[J]. Structural Concrete, 2018, 19(4): 1092-1100.\u003c/li\u003e\n\u003cli\u003eZhan XF, Shao XD.Temperature effect of reinforced approach pavement of semi-integral abutment jointless bridge with pre-cutting cracks for temperature drop.China Civil Engineering Journal,2011,44(11):74-78.(in Chinese)\u003c/li\u003e\n\u003cli\u003eZhan XF, Wang X, Liu KL,et al. Experimental Research on the Tensile Performance of Road-Bridge Link Slab of Jointless Bridges.\u003cstrong\u003eJournal of Chang\u0026rsquo;an University(Natural Science Edition),\u003c/strong\u003e 2022,42(2):68-78.(in Chinese)\u003c/li\u003e\n\u003cli\u003eZhan XF, Liu KL, Zhao YB, etal.Tensile Performance of SHCC Road-Bridge Link Slabs in Fully Jointless Bridges.Advances in Civil Engineering,2021,https://doi.org/10.1155/2021/6643643\u003c/li\u003e\n\u003cli\u003eLi VC. Engineered cementitious composite (ECC):Material,structural,and durability performance// NAWY E. Concrete Construction Engineering Handbook. Los Angeles:CRC Press,2008:1023-1070.\u003c/li\u003e\n\u003cli\u003eM\u0026uuml;ller S, Mechtcherine V. Use of strain-hardening cement-based composites (SHCC) in real scale applications//MECHTCHERINE V,SLOWIK V,KABELE P.Strain-Hardening Cement-Based Composites,RILEM Book series. Dordrecht: Springer,2017:690-700.\u003c/li\u003e\n\u003cli\u003eLi V C, Yang EH,Li M.Field demonstration of durable link slabs for jointless bridge decks based on strain-hardening cementitious composites-phase 3:shrinkage control.Ann Arbor:Michigan Department of Transportation,2005.\u003c/li\u003e\n\u003cli\u003eDong ZF,Tan HL,Yu JT , Jiang FM.Using special coarse aggregate to enhance the tensile strain capacity of engineered cementitious composites .Cement and Concrete Composites ,2024,145:105347.\u003c/li\u003e\n\u003cli\u003eLeng Z, Xue X.A review on design theory and mechanical performance of strain hardening cementitious composites (SHCC).Composites Science and Engineering,2023(3):120-132.\u003c/li\u003e\n\u003cli\u003eWang S, Li VC.Engineered cementitious composites with high-volume fly ash.ACI Mater J 2007,104(3)：233-41.\u003c/li\u003e\n\u003cli\u003eZhan XF, Wang X, Yan HL, et al.Tensile performance and application of LEM-SHCC road-bridge Link slab mixed with rubber powder for fully jointless bridge.Journal of Traffic and Transportation Engineering,2022,22(5):104-118(in Chinese)\u003c/li\u003e\n\u003cli\u003eZhan XF, Chen JY, Wang X, Yan HL. Experimental and numerical study of road-bridge link slabs in fully jointless bridges using rubberized engineered cementitious composites (R-ECC).Case Studies in Construction Materials,2024,20: e02768.\u003c/li\u003e\n\u003cli\u003eZhang ZG, Ma H, Qian SZ.Investigation on properties of ECC incorporating crumb rubber of different sizes.Journal of Advance Concrete Technology,2015,13(5):241-251.\u003c/li\u003e\n\u003cli\u003eHuang XY, Rande R, Ni W, et al.On the use of recycled tire rubber to develop low E-modulus ECC for durable concrete repairs.Construction and Building Materials,2013,46:134-141.\u003c/li\u003e\n\u003cli\u003eAi-fakih A, Mohammed BS, Liew M S.On rubberized engineered cementitious composites(R-ECC)：a review of the constituent material.Case Studies in Construction Materials,2021,14:.10.1016/j.cscm.2021.e00536.\u003c/li\u003e\n\u003cli\u003eBo Chen,Pengbo Ding,Guojie Wei,Chunlong Xiong,etal. A Study on the Contact Characteristics of Tires\u0026ndash;Roads Based on Pressure-Sensitive Film Technology,Materials,2023,16(18):6323.\u003c/li\u003e\n\u003cli\u003eTsinidis G, Papantou M, Mitoulis S. Response of integral abutment bridges under a sequence of thermal loading and seismic shaking[J]. Earthquakes and Structures, 2019, 16(1): 11-28.\u003c/li\u003e\n\u003cli\u003eMaalej M, Li VC. Flexural/tensile-strength ratio in engineered cementitious composites[J].Journal of Materials in Civil Engineering,ASCE,1994,6(4):513-528.\u003c/li\u003e\n\u003cli\u003eLi VC,Wu HC. Pseudo strain-hardening design in cementitious composites[J]. Proceedings of High performance fiber reinforced cement composites, edited by Reinhardt H W and Naaman A E, 1992,371-387.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Fully jointless bridges, Microcracked R-ECC road-bridge link slabs, Seasonal temperature variation, Traffic loads, Crack development, Rebound deflection, Sensitive parameter finite element analysis","lastPublishedDoi":"10.21203/rs.3.rs-6060988/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6060988/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eA novel road-bridge link slab utilizing rubberized engineered cementitious composites(R-ECC) has been proposed for fully jointless bridges (FJBs). Preliminary research has shown that R-ECC road-bridge link slabs possess superior deformation absorption capacity, tensile strength, and crack control capabilities. However, micro-cracks developed on the surface of these slabs due to seasonal temperature fluctuations. While R-ECCs demonstrate improved bending ability compared to conventional ECCs, they exhibit lower compressive strength. Further research is necessary to investigate the crack development and bending deflection of microcracked R-ECC road-bridge link slabs under vehicle loads, which will help determine the suitability of R-ECCs for this application.The microcracked R-ECC slab has a great crack control capacity, and the rebound deflection measured in the experiment is less than the allowable value, indicating that the microcracked R-ECC slab meets the durability and strength standard. A sensitivity parameter finite element analysis was conducted considering the effects of slab thickness and equivalent elasticity modulus of the foundation on the R-ECC road-bridge link slab. Two evaluation indexes \u0026lsquo;\u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e\u0026rsquo; and \u0026lsquo;\u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003ee\u003c/em\u003e\u003c/sub\u003e\u0026rsquo; are proposed to evaluate the performance and construction cost of the R-ECC slab. To improve performance and minimize construction costs, a design thickness of 180 mm and an equivalent elasticity modulus of the foundation of 800 MPa were recommended for the R-ECC road-bridge link slab.\u003c/p\u003e","manuscriptTitle":"Study on the bending deformation properties of microcracked R-ECC road–bridge link slabs","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-04-10 10:15:02","doi":"10.21203/rs.3.rs-6060988/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Accepted","date":"2025-04-23T14:48:49+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-04-19T11:33:32+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-04-10T15:52:19+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"297264434981289764216239681153546113096","date":"2025-04-10T10:13:04+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"331612182327345609532398706201461486595","date":"2025-04-09T06:43:52+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-04-09T06:23:44+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-04-06T14:57:50+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2025-03-28T01:27:08+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"0a0cc9a5-e185-43f0-9cf5-ad178bc2f313","owner":[],"postedDate":"April 10th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":46889822,"name":"Physical sciences/Engineering"},{"id":46889823,"name":"Physical sciences/Materials science"}],"tags":[],"updatedAt":"2025-04-28T16:01:31+00:00","versionOfRecord":{"articleIdentity":"rs-6060988","link":"https://doi.org/10.1038/s41598-025-99947-0","journal":{"identity":"scientific-reports","isVorOnly":false,"title":"Scientific Reports"},"publishedOn":"2025-04-27 15:57:27","publishedOnDateReadable":"April 27th, 2025"},"versionCreatedAt":"2025-04-10 10:15:02","video":"","vorDoi":"10.1038/s41598-025-99947-0","vorDoiUrl":"https://doi.org/10.1038/s41598-025-99947-0","workflowStages":[]},"version":"v1","identity":"rs-6060988","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6060988","identity":"rs-6060988","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}