Evaluation and prediction of carbon fiber–reinforced polymer cable anchorage for large capacity

Abstract

Aiming to address the problems of stress concentration on conical wedge anchorage, a fiber-reinforced polymer cable anchorage with segmental variable stiffness of the load transfer medium was proposed. The key parameters that affect the anchorage behavior were investigated. The mechanical properties of the carbon fiber–reinforced polymer tendon and load transfer medium were tested. The failure mode, anchoring efficiency, stress, and displacement in the anchor zone were studied. The parameter optimization was performed using an experimentally verified finite element simulation. The parameters of the anchorage system with large capacity were evaluated. The results demonstrate that the compressive strength of the load transfer medium is the designed stress limit for the anchorage system. The cable does not slip or become damaged in the anchor zone, and the anchoring efficiency reaches 91%. The distribution of the shear and radial stress on the cable surface is smooth, and the stress concentration is greatly relieved. The result of the finite element simulation is consistent with the experimental values when the friction coefficient is 0.15, and the material and geometric parameters of the anchorage system with cable forces of 5000, 10,000, 15,000, and 20,000 kN are suggested. The geometric parameters of the anchor system with diverse cable capacity can be preliminarily designed based on the fitting equations.

Keywords

anchorage system anchoring behavior carbon fiber–reinforced polymer cable evaluation and prediction larger capacity

Introduction

Cables are generally used as the main tension members in long-span structures such as cable-stayed bridges and suspension bridges (Xiong et al., 2011). At present, steel cables are widely applied in cable structures (Wang and Wu, 2010b). However, because of environmental factors and the increasing span, many problems have arisen in the bridges. The notable problems are the lower load-carrying efficiency, easy corrosion, and fatigue damage (Li et al., 2012; Takena et al., 1992). Carbon fiber–reinforced polymer (CFRP) has certain advantages compared to steel, such as higher tensile strength, lightweight, anti-corrosion, excellent fatigue, and creep resistance, which make it an attractive option to replace steel as the cable material and solve the problems of steel cable (Wang and Wu, 2010a). Since the transverse compressive strength of fiber-reinforced polymer (FRP) tendons is much lower than the longitudinal tensile strength, the traditional anchorage for steel cables is not suitable to anchor FRP cables (Al-Mayah et al., 2007). It may cause extrusion damage of the cable in the anchor zone, particularly for large-diameter or multiple tendons. Therefore, it is imperative to develop a reliable anchorage system, which will greatly promote the development of FRP cable structures in the future (Liu et al., 2015).

Up until now, different types of FRP cable anchorage systems have been designed and studied and can be divided into two main types based on the anchoring mechanism: mechanical anchorage (friction only) and bonding anchorage (adhesive and friction; Wang et al., 2018). For mechanical anchorage, the load transfer medium uses metal clamps with a high elastic modulus (180–200 GPa), which produces high compression stress in the anchor zone and causes premature failure of the FRP tendons (Schmidt et al., 2011). In addition, the diameter of the mechanical anchorage for numerous FRP tendons may be too large, and they are inconvenient to install (Noisternig, 2000). For the bonding anchorage, however, the load transfer medium generally uses a resin and cementitious matrix with a relatively low elastic modulus (2–35 GPa), which can obviously reduce the degree of stress concentration (Wang et al., 2015b). In addition, the spacing between the tendons is small, and the diameter of the anchorage is not large. Therefore, the bonding anchorage is more suitable for anchoring multiple FRP tendons with larger cable force than the mechanical anchorage is (Wu et al., 2018). Numerous experimental and numerical studies have been performed on this type of anchorage. Wang et al. (2015a) proposed a new anchorage and its manufacturing technology for multiple basalt fiber–reinforced polymer (BFRP) tendons. The key factors that affect the anchoring behaviors are optimized by finite element (FE) model; the anchoring effectiveness is verified by experiment. However, the manufacturing process is notably complex, and the change in stiffness of the load transfer material is difficult to accurately control. Fang et al. (2013) presented a bond-type anchorage system with a high-capacity bonding medium using reactive power concrete (RPC) to anchor CFRP cables. Although the anchorage system is applied as ground anchorage in the Aizhai Bridge in China, the nonuniform distribution of the axial stress among the tendons results in a low-capacity reduction factor. Mei et al. (2016) tested a CFRP cable anchorage with bonding medium using a mixture of resin and quartz sand. The anchorage is applied to the first CFRP cable–stayed bridge in China. The anchoring efficiency is excellent, but the dimension of the anchorage must be further optimized. Carvelli et al. (2009) developed an anchorage system to test the tension of a large-diameter glass fiber–reinforced polymer (GFRP) bar, whose ends were embedded in a conical polymeric head. The test outcomes strengthen the confidence in the proposed anchorage system. However, the established numerical model was not compared and verified with experimental data, so it may not accurately predict subsequent experiments. Meier (1996) and Meier and Farshad (2012) studied an anchorage system with advanced gradient materials based on ceramics and polymers; 241 CFRP wires with a diameter of 5 mm were applied to the Stork Bridge in Switzerland. Unfortunately, there is no relevant critical anchorage information such as the dimensions and stiffness of the load transfer medium. Although the anchorage system of large-capacity FRP cable has been extensively studied in experimental and numerical analyses, some problems remain to be solved and further improved.

At present, the cable force of the cable-stayed bridge in practical engineering is generally within the range of 1500–6500 kN (Lozano-Galant et al., 2012). When the safety factor of CFRP cables is 3, the ultimate bearing capacity of the anchorage system can be 4500–19,500 kN. Therefore, it is necessary to design and evaluate an anchorage system that satisfies the bearing capacity in this range. Because of the limitation of test equipment, experiments were rarely performed with a cable force of more than 5000 kN. In order to have an accurate evaluation, a method that combines the experimental study of the anchoring performance of 37 CFRP tendons with the numerically simulated parameter is used. Three aspects of research have been performed: first, the mechanical properties of the materials including CFRP cables and load transfer medium were tested, and the design stress limit of the anchorage system was determined. Then, the anchoring properties of the specimen were studied, including the stress and displacement distribution of the cable in the anchor zone, which verify the result of the FE model. The synchronous mechanical behavior of the cables and anchoring efficiency was also evaluated. The influence of the load transfer medium, the friction coefficient (FC), and the geometric parameters on the stress and displacement distribution of the CFRP cable were investigated. Finally, the performance and parameters of the anchorage system with diversity cable capacity were evaluated by the refined FE model.

Materials and methods

Specimen

CFRP tendons

The CFRP tendon is composed of carbon fibers (T300-12 K, Japan) and vinyl ester resins (by Reichhold group, Inc., USA). The CFRP tendon with a nominal diameter of 4 mm is fabricated by a pultrusion technique, and its fiber volume fraction is 67%. The tendons have a helical surface to enhance the friction force and bond strength. The mechanical properties of the CFRP tendon are obtained from the manufacturer and testing based on American Concrete Institute (ACI) 440.3R-04 (2004), which are listed in Table 1.

Table 1.

The basic mechanical properties of CFRP tendon.

Properties	Carbon fibers	Ester resin	CFRP tendon
Density (kg/m³)	1760	1150–1350	1700
Tensile strength (MPa)	3530	80–90	2230
Elastic modulus (GPa)	230	2.5–3	164
Elongation (%)	1.5	–	1.4

CFRP: carbon fiber–reinforced polymer.

Both carbon fibers and ester resin are from manufacturer and only CFRP tendon is from test results.

One of the key factors in anchorage design is the transversal mechanical property of the cable. Therefore, the transversal compressive strength of CFRP tendons was tested. Transversal compression test for CFRP tendon was conducted on the LFV-1000 servo-hydraulic dynamic fatigue tester through a specially designed setup closed to real conditions as shown in Figure 1(a). Five specimens were prepared for each experimental group. The length of specimens is 120 mm, and the length of the compression zone is 50 mm. Loading rate is determined to be 1 mm/min with a preload of 500 N based on TIA/EIA-455-41A (1993). The failure mode of the compressive test is shown in Figure 1(b). Transversal compressive strength is calculated by dividing the load by the area of the compression zone. The transversal compressive strength is positively correlated with the deformation as shown in Figure 1(c). When the CFRP tendon with a diameter of 4 mm was loaded to transversal displacement of 1 mm, the load still shows no decreasing trend. At this status, longitudinal cracks of CFRP tendon had been observed. However, the CFRP bar was crushed when the transversal loading displacement was 1.2 mm based on the literature (Sayed-Ahmed and Shrive, 1998). Since no significant damage was observed from the failure mode at the loading displacement of 0.5 mm comparing with the damage mode of loading displacement of 1 and 1.5 mm, it can be inferred that the transversal compressive stress at this condition does not cause a reduction in the longitudinal mechanical properties of the tendon. Therefore, the transversal compressive strength of 119 MPa is taken as the transversal strength limit of the CFRP cable in the anchor zone, as shown in Table 2.

Figure 1.

The transversal compressive test of CFRP tendon: (a) transversal compressive test, (b) the failure mode, and (c) load–displacement curves.

Table 2.

Transversal compressive strength of CFRP tendon.

Property	Deformation (mm)	Specimens					Average
Property	Deformation (mm)	S1	S2	S3	S4	S5	Average
Transversal compressive strength (MPa)	0.5	150	100	135	122	90	119
Transversal compressive strength (MPa)	1	435	385	415	390	353	396

CFRP: carbon fiber–reinforced polymer.

Deformation means transversal deformation of the tendon.

Load transfer medium

The filling material, which consists of epoxy resin, silicon sand, polymer mortar, and cement mortar, was used as the load transfer medium as shown in Figure 2. The type of epoxy resin produced by Nantong Xingchen Synthetic Material Co., Ltd. in China is E51. The mesh of quartz sand with powder form is 200. Polymer materials and cement mortar are manufactured by Good Bond Technology Development Co., Ltd. in China. The bonding materials near the loading end adopt a mixture of quartz sand and epoxy resin with lower stiffness, and the mass fractions (quartz sand:epoxy resin) are 0.4:1 and 1:1, respectively. The load transfer materials near the free end are polymer mortar and cement mortar with higher stiffness; the mass fraction is 100:15 (mortar: polymer) and 1:1:0.3:0.02 (cement:sand:water:polyphosphate water reducer), respectively. The mechanical properties of the load transfer medium for each section are listed in Table 3.

Figure 2.

Load transfer medium.

Table 3.

The properties of load transfer medium for each section.

Property	Mixture A	Mixture B	Polymer mortar	Cement mortar
Compressive strength (MPa)	98	105	75	70
Modulus of elasticity (GPa)	4	8	26	32

Anchorage system

The bonding anchorage system is composed of four parts: CFRP cable, protective layer, load transfer medium, and steel sleeve with internal tap. The protective layer consists of two ring tendons with different lengths, which can increase the area in the anchor zone and prevent the cable from being directly squeezed. The stiffness gradient change for the load transfer medium aims to reduce the stress concentration of the cable in the anchor zone, as shown in Figure 3(a). The steel sleeve with the internal taper of 3.8 degree is 400 mm long and 190 mm in diameter, as shown in Figure 3(b). The length ratio of each section for the load transfer medium is 3:3:2:2. Compared with the compressive strength of the load transfer medium and circumferential compressive strength of the cables, the cement mortar due to the lowest compressive strength in the load transfer medium is selected as the control objective of design stress for the following optimization design.

Figure 3.

Constitution and dimension of cable anchorage: (a) constitution and (b) dimension.

Test setups and procedure

Specimen fabrication

The CFRP cable consists of 37 tendons arranged in parallel. The transverse spacing of the tendons is 2 mm, and the longitudinal length is 4000 mm. The cross-sectional shape of the cable is a regular hexagon, the transverse position of the tendons is fixed by the positioning plate, and the longitudinal position is fixed to both ends of the anchorage by a clamping device (see Figure 4(a)). The function of the steel framework between the anchorages is to fix the anchorage position and protect the cable as shown in Figure 4(b). It is also convenient for the integral lifting. The stiffness of the load transfer medium is changed by the vertical layered casting as shown in Figure 4(c). Basalt chopped fiber yarn is added between the layers to enhance the overall mechanical properties of the load transfer material. Each section of the load transfer material can be poured before the preliminary solidification of the previous one. The mechanical properties of the cable anchorage system can be tested only after the peak strength has been attained.

Figure 4.

Manufacture technique of cable anchorage system: (a) straightening, (b) assembly, and (c) infusion.

Experimental methods

The anchoring performance of the cables is tested on a reaction device and tensioned by a hydraulic jack as shown in Figure 5. The loading capacity of the hydraulic jack can reach 1200 kN with a maximum stroke of 400 mm. One end of the cable anchorage assembly is connected with a spoke load sensor by a transferred steel plate. The range of the spoke load sensor is 1600 kN with the accuracy of 0.1%. The loading speed is 500 MPa/min based on ACI440.3R-04 (2004). Strain gauges were attached to the surface of the CFRP tendons in the middle portion and anchor zone to evaluate the tensile stress and shear stress. A displacement sensor was fixed at both ends of the anchorage to measure the relative displacement between the load transfer medium and the steel sleeve, which reflect the degree of compression on the cable. Data acquisition system TDS-530 was used to record the strain and displacement with intervals of 1 s.

Figure 5.

The equipment and monitoring location for tensile test: (a) loading equipment, (b) displacement sensor, and (c) strain sensor.

FE simulation

The FE model

A three-dimensional FE model of the anchorage performance of the CFRP cable was established using the ANSYS software as shown in Figure 6(a). The symmetry boundary conditions are applied on the transversal surfaces. The displacement of the nodes in the cross section of the steel sleeve at the loading end is constrained based on the actual restriction of the anchorage at the counterforce device. The uniform load is applied to the cross section of the cable to simulate the complex stress state in the anchor zone. The effects of the interface between the steel sleeve and the load transfer medium on the stress and displacement distributions of the CFRP cable in the anchor zone are discussed.

Figure 6.

FE model and optimized parameters of anchorage system with variable stiffness: (a) FE model and (b) optimized parameters.

Two types of element are included in the FE model: solid and contact. In the solid element, SOLID185 was used to simulate a steel sleeve, load transfer medium, and CFRP cable. CONTA174 and TARGE170 were used to simulate the follow-up and extrusion action between the load transfer medium and the steel sleeve. The FC at the interface between steel and resin is usually taken as 0.1–0.3 (Cai et al., 2016; Feng et al., 2014). Because the load transfer medium has varying stiffness, it is necessary to determine the appropriate FC to accurately evaluate the design parameters of the anchorage system with different cable capacities. The key factor can be determined by comparison with experimental data. According to the following experimental phenomena, the anchorage system can provide sufficient anchoring force (adhesion and friction), so the method of coupling nodes between the CFRP cable and the load transfer medium is used. The material properties of each component are given in Table 4.

Table 4.

Material properties in FE model.^12,22

Properties	CFRP tendon		Load transfer medium	Steel sleeve
Properties	Fiber direction	Radial direction	Load transfer medium	Steel sleeve
Elastic modulus (GPa)	165	11	4-35	200
Shear modulus (GPa)	7	9	–	77
Poisson ratio	0.3	0.03	0.2–0.3	0.3

CFRP: carbon fiber–reinforced polymer; FE: finite element.

The method of optimization design

The structural dimensions and material properties were optimized using FE simulation methods.

Optimization purpose: reducing the stress concentration to improve the structural stress characteristics and extend the structural life.

Optimization target: using the ultimate compressive stress of cement mortar $(σ_{radial} < 70 MPa)$ as the control target in the anchorage design because it has the lowest compressive strength for anchorage components.

Optimization content: the geometry and internal shape of the anchorage system are investigated, such as the length, the wall thickness, and the internal taper for the steel sleeve and the stiffness and the radius at the loading end for the load transfer medium (see Figure 6(b)). The effect of the stiffness variation of the load transfer medium on the mechanical behavior of the cable in the anchor zone is analyzed. The parameters of anchorage systems with diverse capacity are evaluated and predicted.

Results and discussion

Failure modes and anchoring efficiency

Figure 7 shows the failure mode of the anchorage system of the CFRP cable. Fracture occurred in the CFRP cable between two anchorages. Tendon Nos 1, 4, 7, 18, 19, 20, 31, 34, and 37 in the middle portion were selected to observe the synchronous tensile performance of the cable as shown in Figure 8. In addition, eight strain gauges were attached to tendon No. 20 in the anchor zone to analyze the stress distribution of the cable. In the experiment, three tendons consecutively broke before the cable reached the ultimate load; then, almost all fractures occurred in a notably short time (2 s), when the load rapidly decreased from the peak value to zero. The anchoring efficiency was 91% based on the Post-Tensioning Institute (1997) as shown in equation (1), where $η_{a}$ is the experimental static tension capacity $(F_{apu})$ divided by the standard value of tension capacity $(F_{pm})$ ; $F_{pm}$ is obtained by multiplying the standard strength value $(f_{s})$ , cross-sectional area of the tendon $(A_{f})$ and the number of FRP tendons $(N_{f})$ ; $f_{s}$ is calculated by multiplying the average tensile strength of the tendons $(f_{avg})$ and strength reduction coefficient $(1 - 1.645 CV)$ as shown in equation (2) to ensure 95% strength reliability

η_{a} = \frac{F_{apu}}{F_{pm}} = \frac{F_{apu}}{f_{s} A_{f} N_{f}}

(1)

f_{s} = f_{avg} (1 - 1.645 CV)

(2)

Figure 7.

The damage mode of cable anchorage system. (a) The cable between the anchorages and (b) The cable near the anchorage.

Figure 8.

The tensile strain of the cables.

Stress analysis on the CFRP cable in the anchor zone

Influence of the FC on the stress and displacement

The interface roughness has little influence on the distribution of shear stress and axial stress of the cable as shown in Figure 9(a) and (b). Although the experimental values are not completely consistent with the FE analysis results, the error is not large. One of the reasons for the shear stress error is the insufficient amount of strain gauges on the surface of the cable, which cannot continuously characterize the shear stress distribution on the cable surface. The error of the axial stress distribution on both ends of the anchorage may result from the stiffness setting in the FE model, which slightly deviates from the actual stiffness of the load transfer medium. The interface roughness has a great influence on the radial stress and axial displacement of the cable as shown in Figure 9(c) and (d). When the FC decreases, the radial stress and axial displacement proportionally increase. The test data at both ends of the anchorage were compared with the FE analysis results. When the FC was 0.15, the data are consistent with the experimental values for both radial stress and axial displacement. Based on the above analysis, it is appropriate and accurate to characterize the complicated stress and displacement distributions in the anchor zone using a FC of 0.15 between the load transfer medium and the steel sleeve in the FE model for the proposed anchorage.

Figure 9.

The stress and displacement of the cable in anchor zone with different friction coefficients: (a) shear stress, (b) axial stress, (c) compressive stress, and (d) axial displacement.

Influence of variable stiffness on stress and displacement

In this section, the influence of the stiffness of the load transfer medium on the mechanical properties of the cable in the anchor zone is analyzed based on the interfacial roughness (0.15) determined in section “Influence of the FC on the stress and displacement.” The gradient change of the stiffness can obviously reduce the radial and shear stress concentration on the cable surface and make the stress distribution in the anchor zone more uniform than the constant stiffness (32 GPa only for cement mortar) as shown in Figure 10(a) and (c). For the load transfer medium with variable stiffness, the axial stress of the cable is gently transferred from the loading end to the free end as shown in Figure 10(b), which also indicates that the gradient change in stiffness is beneficial to the uniform stress transmission. Therefore, this method can reduce the stress concentration and hopefully improve the short-term and long-term anchoring capacity. Figure 10(d) shows that the axial displacement distribution of the cable with variable stiffness of the load transfer medium is larger than the constant stiffness. This is due to the low stiffness of the load transfer medium near the loading end causing the overall larger follow-up. The following analysis is also based on the anchorage system with the stiffness gradient change (32, 26, 8, and 4 GPa) for load transfer medium.

Figure 10.

The stress and displacement of the cable in anchor zone with variable stiffness: (a) shear stress, (b) axial stress, (c) compressive stress, and (d) axial displacement.

Parameter evaluation of the anchorage system for diverse cable capacity

The anchorage system with a cable force of 5000 kN

In the above analysis, the key mechanical parameters that affect the anchorage properties were obtained, such as the load transfer material (stiffness) and interface properties (FC). Based on the determined mechanical parameters, the geometric parameters of the anchorage system were optimized for the CFRP cable with the ultimate cable force of 5000 kN. The main parameters and optimization method are based on section “The method of optimization design.”

The effect of the internal taper on the radial stress in the anchor zone was analyzed in Figure 11(a) by fixing the length of the anchor (600 mm) and the radius (30 mm) of the load transfer medium at the loading end. The range of the internal taper is 3°–7°, which is the design of internal taper for most anchorages. Compared with the effect on stress at the free end and the central part, the change in the internal taper has great influence on the radial stress near the loading end. Unlike traditional anchorages, the new anchorage system with the larger internal taper has a smaller stress peak because the load transfer medium near the loading end has much less stiffness than that it is near the free end. Thus, a higher stiffness of the load transfer medium has greater effect corresponding to the internal taper variation on the radial stress. In general, when the internal taper decreases, the radial stress gradually increases. When the internal taper is 5°, the stress in the anchor zone can be guaranteed to be less than the target design stress, and the stress distribution can be more uniform.

Figure 11.

The influence of parameters on radial stress: (a) radial stress with different angles, (b) radial stress with different lengths, and (c) radial stress with different radii.

The influence of the change in anchor length on the radial stress in the anchor zone was analyzed based on the internal taper (5°) and the radius (30 mm) of the load transfer medium at the loading end, as shown in Figure 11(b). The change in anchor length has little effect on the radial stress near the loading end but has an obvious effect on the stress in the middle and near the free end. In general, the increase in anchor length helps to reduce the peak value of radial stress. However, anchor length that is too long increases the economic cost and leads to the stress peak at the loading end, which is a situation that is carefully avoided in the design. Therefore, the anchor length of 600 mm is suitable.

Based on the optimized internal taper (5°) and anchor length (600 mm), the impact of the radius of the load transfer medium at the loading end on the radial stress in the anchor zone is analyzed in Figure 11(c). Contrary to the above two variations’ (internal taper and anchorage length) effect on the stress distribution, the change in radius has a greater effect on the radial stress near the loading end but a smaller influence on the radial stress in the central zone and near the free end. In general, a larger radius can produce a smaller peak value of radial stress, which can be interpreted as an increase in the volume of the anchoring zone and results in a decrease in stress. The radius can be taken to 30 mm, which can satisfy the strength requirement of anchorages.

Then, the stress distribution of the steel sleeve with different wall thicknesses is analyzed as shown in Figure 12. The cloud diagram of von Mises stress shows that the stress is maximal at the position of the inner wall of the steel sleeve near the free end. An increase in wall thickness contributes to a reduction in peak stress. The wall thickness of 30 mm is selected when its maximum stress (277 MPa) is lower than the yield strength (320 MPa) of the steel sleeve adopted.

Figure 12.

Von Mises stress of the barrel with different wall thickness: (a) wall thickness of 20 mm, (b) wall thickness of 30 mm, and (c) wall thickness of 40 mm.

Based on the above analysis, various parameters that affect the anchorage performance are optimized and determined for a cable force of 5000 kN as shown in Figure 13.

Figure 13.

Optimized parameters of the anchorage with the cable force 5000 kN.

The predicted parameters for an anchorage system with different cable capacities

Based on the above optimization method, the parameters of the anchorage system with bearing capacities of 10,000, 15,000, and 20,000 kN were designed and evaluated, where the equivalent diameter of the CFRP cable was 76.1, 93.2, and 107.6 mm, respectively. The stiffness of the segments of the load transfer medium, with a length ratio of 3:3:2:2, is 32, 26, 8, and 4 GPa, as shown in Figure 14. For each 5000 kN increase in cable force, the length of the anchor increases by 300 mm, the radius of the load transfer medium at the loading end increases by 10 mm, and the thickness of the steel sleeve increases by 10 mm, but the internal taper of steel sleeve decreases by 0.5°, which indicates that a larger cable force requires a smaller internal taper to increase the anchoring force and make its stress distribution uniform. The radius of the load transfer medium at the loading end and anchor length is linearly and positively correlated with the cable force, whereas the wall thicknesses of the steel sleeve and internal taper are nonlinearly and positively correlated with the cable force. Through the fitting equation, the geometric parameters of the anchor system with diverse cable capacity can be preliminarily designed as shown in Figure 15.

Figure 14.

Optimized parameters of the novel anchorage with different cable capacity: (a) cable force 10,000 kN, (b) cable force 15,000 kN, and (c) cable force 20,000 kN.

Figure 15.

The relationship between geometric parameters and cable capacity.

Conclusion

In this study, a new anchorage was proposed to investigate the anchoring properties of CFRP cables. The mechanical properties of the cable and load transfer medium were tested, and the design strength limits of the anchorage were determined. The fabrication technique and test and optimization methods were introduced. The FE analysis of the load transfer medium and interface roughness that affect the anchorage performance was performed and compared with the experimental results. Based on the optimization analysis of the cable force of 5000 kN, the design parameters of the anchorage system with diverse cable forces were evaluated. The following conclusions can be drawn:

The key factor in the design of the new anchorage system with variable stiffness is the mechanical properties of the load transfer medium instead of the radial compressive strength of the FRP cable for the traditional anchorage system. The variable stiffness is realized through the construction technology with vertical layered pouring, which can greatly reduce the stress concentration and fully exert the longitudinal mechanical properties of the cable; the creep resistance will also improve because of the larger stiffness near the loading end.

The anchoring efficiency reaches 91% with preferable synchronous tensile behavior, and the failure mode is the central fracture. The FC between the load transfer medium and the steel sleeve in the FE simulation model is 0.15 to better match the experimental results. The FC greatly influences the radial stress and the axial displacement of the cable in the anchor zone, and it is negatively correlated with the radial stress and the axial displacement.

The geometric parameters of the anchorage system with the cable force of 5000 kN are optimized as follows: the steel sleeve has a length of 600 mm, a diameter of 356 mm, an internal taper of 5°, and a wall thickness of 30 mm. The load transfer medium has a radius of 30 mm, a length ratio of 3:3:2:2, and stiffness values of 32, 26, 8, and 4 GPa. The increases in anchor length and radius contribute to an increase in anchoring area to reduce the radial stress, whereas a decrease in internal taper results in an increase in radial stress.

The radius of the load transfer medium at the loading end and the anchor length is linearly and positively correlated with the cable force, whereas the wall thickness values of the steel sleeve and internal taper are nonlinearly and positively correlated with the cable force. The geometric parameters of the anchor system with diverse cable capacity can be a preliminary design based on the fitting equations.

Footnotes

Declaration of Conflicting Interests

The author(s) declared the following potential conflicts of interest with respect to the research, authorship, and/or publication of this article: All authors have seen and approved the final version of the manuscript being submitted. They warrant that the article is the authors’ original work, has not received prior publication, and is not under consideration for publication elsewhere. There are no potential conflicts and financial or personal interest that could affect their objectivity.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors gratefully acknowledge the financial support provided by the National Key Research and Development Program of China (2017YFC0702000) and the National Natural Science Foundation of China (No 51678139). The authors also acknowledge Jiangsu GMV Co., Ltd. for providing CFRP tendons.

ORCID iD

Bo Feng

References

Al-Mayah

Soudki

Plumtree

(2007) Novel anchor system for CFRP rod: finite-element and mathematical models. Journal of Composites for Construction 11(5): 469–476.

American Concrete Institute (ACI). (2004) Guide test methods for fiber reinforced polymers (FRPs) for reinforcing or strengthening concrete structures. ACI 440.3R-04. Farmington Hills, MI. Available at: http://www.radyab.co/content/media/article/4403R_04_0.pdf

Cai

D-s

Z-h

Yin

et al . (2016) A numerical investigation on the performance of composite anchors for CFRP tendons. Construction and Building Materials 112: 848–855.

Carvelli

Fava

Pisani

(2009) Anchor system for tension testing of large diameter GFRP bars. Journal of Composites for Construction 13(5): 344–349.

Fang

Zhang

(2013) Experimental investigation of a bond-type anchorage system for multiple FRP tendons. Engineering Structures 57(0): 364–373.

Feng

Zhang

Meng

et al . (2014) Mechanical analysis of stress distribution in a carbon fiber-reinforced polymer rod bonding anchor. Polymers 6(4): 1129–1143.

Lan

et al . (2012) Experimental and numerical study of the fatigue properties of corroded parallel wire cables. Journal of Bridge Engineering 17(2): 211–220.

Liu

Zwingmann

Schlaich

(2015) Carbon fiber reinforced polymer for cable structures-a review. Polymers 7(10): 2078–2099.

Lozano-Galant

Payá-Zaforteza

et al . (2012) Analysis of the construction process of cable-stayed bridges built on temporary supports. Engineering Structures 40: 95–106.

10.

Mei

Seracino

(2016) An experimental study on bond-type anchorages for carbon fiber-reinforced polymer cables. Construction and Building Materials 106: 584–591.

11.

Meier

(2012) Carbon fiber reinforced polymer cables: why? Why Not? What If? Arabian Journal for Science and Engineering 37(2): 399–411.

12.

Meier

Farshad

(1996) Connecting high-performance carbon-fiber-reinforced polymer cables of suspension and cable-stayed bridges through the use of gradient materials. Journal of Computer-Aided Materials Design 3(1–3): 379–384.

13.

Noisternig

(2000) Carbon fibre composites as stay cables for bridges. Applied Composite Materials 7(2–3): 139–150.

14.

Post-Tensioning Institute (1997) Post-Tensioning Manual. 5th ed. Phoenix, AZ: Post-Tensioning Institute.

15.

Sayed-Ahmed

Shrive

(1998) A new steel anchorage system for post-tensioning applications using carbon fibre reinforced plastic tendons. Canadian Journal of Civil Engineering 25(1): 113–127.

16.

Schmidt

Smith

Täljsten

et al . (2011) Numerical simulation and experimental validation of an integrated sleeve-wedge anchorage for CFRP rods. Journal of Composites for Construction 15(3): 284–292.

17.

Takena

Miki

Shimokawa

et al . (1992) Fatigue resistance of large-diameter cable for cable-stayed bridges. Journal of Structural Engineering 118(3): 701–715.

18.

TIA/EIA-455-41A (1993) FOTP-41 Compressive loading resistance of fiber optic cables. TIA/EIA-455-41A. Available at: http://tia.ihs.com/tia-eia-455-41a.htm

19.

Wang

Zhang

et al . (2018) Anchorage systems of CFRP cables in cable structures—a review. Construction and Building Materials 160: 82–99.

20.

Wang

(2010a) Evaluation of FRP and hybrid FRP cables for super long-span cable-stayed bridges. Composite Structures 92(10): 2582–2590.

21.

Wang

(2010b) Integrated high-performance thousand-metre scale cable-stayed bridge with hybrid FRP cables. Composites Part B: Engineering 41(2): 166–175.

22.

Wang

et al . (2015a) A novel anchor method for multi-tendon FRP cable: concept and FE study. Composite Structures 120: 552–564.

23.

Wang

(2015b) A novel anchor method for multi-tendon FRP cable: manufacturing and experimental study. Journal of Composites for Construction 19: 04015010.

24.

Xian

(2018) A novel anchorage system for CFRP cable: experimental and numerical investigation. Composite Structures 194: 555–563.

25.

Xiong

Cai

Zhang

et al . (2011) Study of super long span cable-stayed bridges with CFRP components. Engineering Structures 33(2): 330–343.