Relaxation behavior of prestressing basalt fiber-reinforced polymer tendons considering anchorage slippage

Abstract

Relaxation is a key factor that controls the application of prestressing fiber-reinforced polymer tendons. This paper focuses on the evaluation of the relaxation behavior of newly developed basalt fiber-reinforced polymer tendons through an approach considering anchorage slippage. A series of relaxation tests on basalt fiber-reinforced polymer tendons subjected to three levels of initial stresses (0.4f_u, 0.5f_u, and 0.6f_u, where f_u = ultimate strength) were conducted using a specially designed test setup that eliminates the impact of slippage at the anchor zone. An additional group of tests was conducted to validate the enhancement effect of pretension on the relaxation behavior. The relaxation rates at one million hours were predicted based on experimental fitting. Finally, the relaxation rates at 1000 h were predicted using the correlation between the relaxation and creep and were validated with the experimental relaxation rates. The results demonstrate the effectiveness of the proposed setup in measuring the relaxation loss of specimens and reveal that the relaxation rates of untreated basalt fiber-reinforced polymer tendons at 1000 h are 4.2%, 5.3%, and 6.4% at 0.4f_u, 0.5f_u, and 0.6f_u, respectively. Pretension treatment performs effective in relaxation loss controlling. BFRP tendons are recommended to be applied at an initial stress of 0.5f_u after pretension treatment, with one-million-hour relaxation rate equal to 6.7%. Furthermore, the relaxation rate at 1000 h can be predicted accurately based on the creep behavior. The conclusions of this study can provide guidance for the prestressing applications of basalt fiber-reinforced polymer tendons.

Keywords

Basalt fiber-reinforced polymer tendon relaxation prestressing prediction

Introduction

Fiber-reinforced polymer (FRP) is characterized by its advantages over steel, such as light weight, high strength, and corrosion resistance. Thus, it is considered a competitive type of structural material used in strengthening, retrofitting, and new construction.^1,2 Although FRPs have wide applications in infrastructure, tension-only prestressing tendons, developing the high strength in the axial direction of fiber, are treated as the most efficient form.^3,4 In addition to traditional carbon, aramid, and glass fibers, novel basalt fiber has also been developed recently. As an inorganic fiber drawn from a single raw material (molten volcanic rock), basalt fiber performs environmental friendly in its production and disposal process.⁵ In recent years, the potential advantages of basalt FRP (BFRP) in structural engineering have been gradually recognized along with the progressive development of related researches.^6,7 BFRP, with a fiber volume fraction of 60%, has been validated to have approximately 30% higher strength and modulus than E-glass FRP (GFRP) with a fiber volume fraction of 54%.^8,9 Compared to carbon FRP (CFRP), BFRP possesses a much lower cost and better ductility.¹⁰ BFRP provides satisfactory long-term fatigue behavior and is capable of surviving two million cycles of fatigue loading at a maximum stress of 0.55f_u to 0.6f_u (f_u = ultimate strength).^11,12 BFRP also has a relatively high creep rupture limit of 0.52f_u.⁹ These advantageous properties facilitate BFRP’s application as prestressing members competitive to CFRP and aramid FRP (AFRP), which are both recommended as prestressing members by ACI 440.4R.¹³ The low creep rupture stress of GFRP (0.29f_u) makes it unsuitable for prestressing applications.¹⁴ In addition to the fatigue and creep rupture behaviors, relaxation is an important factor that controls the applications of prestressing tendons. Excessive relaxation loss can seriously weaken the prestressing effect of tendons on prestressed structures. However, due to the deficiency of the existing test setups, the relaxation behavior of BFRP tendons has not been accurately clarified yet, so their applications as a prestressing component are limited. Thus, a correct and comprehensive understanding of the relaxation behavior of BFRP is critical for the application of BFRPs as prestressing members.

Review of previous work

Previous researches on the relaxation behavior of FRPs mainly focused on CFRPs and AFRPs. Those researches have predicted the relaxation rates at 50 years to be 5.87% and 7.43% for CFRP tendons at initial stresses of 0.4f_u and 0.6f_u, respectively, and 10.9% and 12.7% for AFRP tendons at 0.4f_u and 0.6f_u, respectively.^15,16 However, those results do not reflect the real material conditions because the predictions were based on the data collected between 1 h and 3000 h. The slippage at the anchorages was mainly concentrated in the first hour, and this impact should be eliminated. To improve this test method, Zou¹⁷ proposed a relaxation test setup that used a dial gage to monitor the slippage of the tendon at the anchorages, but the details of the setup were not provided. The predicted relaxation rates of CFRP and AFRP tendons at one million hours based on experiments using the proposed setup were approximately 3.0% and 12.5%, respectively, with an initial stress of 0.5f_u. Zou’s results are similar to those of another study,¹⁸ which showed that the 50-year relaxation rates were 2.0% and 18.4% for CFRP and AFRP tendons, respectively, at 0.7f_u.

Few studies of the relaxation behavior of BFRP can be found in the existing literature. Gunnarsson¹⁹ conducted relaxation tests on BFRP tendons with durations of more than 2000 h at an initial stress of 0.5f_u (f_u = 1000 MPa) and predicted that the 50-year relaxation rate of the BFRP tendon would be 11%. The relatively large relaxation might be caused by failure to consider the slippage at anchorage and by the low fiber content of the adopted BFRPs since the tensile strength was only 1000 MPa. Another study²⁰ reported that the relaxation of BFRP tendons in prestressed concrete beams was equal to 20%, which was significantly greater than the relaxation of the tendon itself and demonstrated that the relaxation of FRP tendons in concrete beams was a combined effect of the creep and shrinkage of the concrete and the interface slip between the tendon and concrete. In the authors’ previous studies, the creep rates of BFRP tendons were demonstrated to be 3.6% for 0.5f_u (628 MPa) at 1000 h and can be decreased to less than 3% by pretension treatment.²¹ Those results indicate potentially less prestressing losses when using BFRPs as prestressed structural elements.

Due to the deficiency of the previous experimental results, eliminating the impacts of the anchorage slippage is a key issue in evaluating relaxation behavior. Also, a comprehensive study of BFRP tendons at different initial stresses is necessary. In this paper, relaxation tests were conducted at three levels of stress. An additional test group was designed to validate the effect of pretension on the relaxation behavior of BFRP tendons. The relaxation rate at one million hours was predicted based on experimental fitting. Furthermore, the predicted relaxation rates at 1000 h were calculated based on the correlation between the creep and relaxation. The results of this study can serve as guidance for prestressing applications of BFRP tendons.

Experimental program

Specimen preparation

BFRP tendons adopted in this study were manufactured with 2400 tex unidirectional basalt fiber roving and vinyl ester resin through pultrusion. The fiber volume fraction of the BFRP tendons was approximately 65%. The nominal diameter and total length of each specimen were 6 mm and 1260 mm, respectively. Bond anchorage with seamless steel sleeves and resin was adopted. The surface of two anchor ends was treated by sand blasting. The outer diameter and thickness of the steel sleeves were 16 mm and 3 mm, respectively (Figure 1). Rust on the inner surface of the steel sleeves was removed by sandpaper and cleaned with alcohol. Then, the gap between steel sleeve and tendon was filled with epoxy resin. The resin was allowed to cure for 7 days to ensure sufficient strength. In the relaxation test, the cross sections of the steel sleeves at the loading ends were processed to be flat to guarantee their smooth contact with the steel plates in the relaxation loading setup. For the short-term tensile test, the anchorages were 300 mm long, while for the relaxation test, the anchorages were 250 mm long based on the length of the relaxation testing equipment.

Loading setup

The short-term tensile tests were conducted on a RD-200 electronic tension tester with load capacity of 200 kN. The deformations of specimens were measured by two extensometers synchronously with gage length of 120 mm.

JSCE-534 (1995) includes a strict limitation for the strain variation (less than 25 μɛ) during long-term relaxation tests. Because long-term slippage at the anchorages is inevitable, a set of reaction equipment was designed to eliminate the impact of slippage (Figure 2). The load was applied to the tendon through a special loading screw. A load cell with a minimum resolution of 10 N was set to monitor the load in the tendon during the loading procedure and the relaxation stage. Two 3-mm-thick aluminum sheets were fixed on the surface of the tendon with epoxy adhesive to monitor the relative slippage between the tendon and the anchorage during the relaxation test. Slippage at the loading end of the anchorage was monitored because previous research²² showed that the maximum slippage occurred at that location (Figure 3). Two linear variable differential transformers (LVDTs) were installed in contact with the aluminum sheets to measure the displacement due to slippage at the anchorages. The minimum resolution of the LVDTs was 0.001 mm.

Considering the slippage of the specimens at the two anchorages, the axial load on the specimen was modified through

F = F_{0} + EA (d_{1} + d_{2}) / l

(1)

where F is the modified load; F₀ is the measured load; E is the actual value of elastic modulus; A is the actual value of tendon’s cross-sectional area; d₁ and d₂ are the values of slippage measured by the two LVDTs, and l is the original distance between the two monitoring points (Figure 4).

Loading procedure

According to JSCE-531,²³ the loading rate for the short-term tensile tests was determined to be 500 MPa/min. The data of load and deformation were recorded by a computer once every second. The tensile properties of the BFRP tendon were determined by the test on five effective specimens. The measured strength was used as a reference for the different initial loads that were applied in the relaxation tests.

For the relaxation tests, the loads were applied to the tendons manually by two wrenches. One was kept still on the loading screw, and the other was used to twist the nut during the loading procedure. The loading procedure lasted approximately 3 min. Initial stresses of 0.4f_u, 0.5f_u, and 0.6f_u were determined to investigate the relaxation behavior of the BFRP tendons at different stress levels according to JSCE-534.²⁴ To validate the effect of the pretension, another group of tests was conducted on the specimens with an initial stress of 0.5f_u after a pretension of 0.6f_u for 3 h, which was shown to be the optimum pretension treatment for BFRP tendons.²¹ The specimens in that test group were unloaded to 0.5f_u after the pretension stage. Three specimens were prepared for each test group according to JSCE-534.²⁴

According to JSCE-534,²⁴ the load and displacement data were recorded at the following times: 1, 3, 6, 9, 15, 30, and 45 min and 1, 1.5, 2, 4, 10, 24, 48, 72, 96, and 120 h. Subsequent measurements were conducted once every 120 h. The total duration of each relaxation test was 1000 h.

Results and discussions

Short-term tensile properties

In the short-term tensile test, BFRP specimens showed a typical dispersed failure of fibers (Figure 5). The anchorage performed reliable to test the ultimate tensile strength of BFRP tendons. The measured short-term tensile properties are shown in Table 1. The average tensile strength up to 1571 MPa is comparable to that of prestressed steel strand, and the coefficient of variation (CV) less than 3% guarantees the stability of BFRP tendon’s tensile strength. These properties demonstrate the effectiveness of BFRP tendon as prestressing member. The 95% guaranteed strength is calculated to be 1500 MPa by the following equation based on GB 50608.²⁵

f_{k} = μ_{f} - 1.645 σ_{f}

(2)

where f_k is the standard value, μ_f is the average value, σ_f is the standard deviation. f_u equals to f_k hereinafter.

Table 1.

Tensile properties of the BFRP tendon specimens.

	Tensile capacity, F_u (kN)	Tensile strength, f_u (MPa)	Elastic modulus, E (GPa)	Fracture strain, ɛ_u (%)
BV-1	44.0	1556	54	2.88
BV-2	42.4	1500	55	2.72
BV-3	44.9	1588	54	2.94
BV-4	46.1	1630	55	2.96
BV-5	44.7	1581	56	2.82
Mean value	44.4	1571	55	2.87
Standard deviation (SD)	1.22	42.99	0.75	0.09
Coefficient of variation (CV)	2.74%	2.74%	1.36%	3.14%
95% guaranteed strength	42.4	1500

BV denotes BFRP composed of basalt fibers and vinyl ester resin.

Relaxation curves

Figure 6 shows the curves of the load retention (ratio of the modified load to the initial load expressed as a percentage) with time (i.e. the relaxation curves). The curves for different initial stresses perform similarly and can be divided into two stages. A rapid decrease of stress occurs during the first stage, and the rate of relaxation loss then gradually decreases with time. That tendency of relaxation loss is caused by the gradual straightening of the originally uneven fibers with the viscoelastic deformation of the resin. The specimen experiences a stable and slow rate of relaxation loss during the second stage. During this stage, the fibers are straightened, and the relaxation loss can be controlled. Several slight fluctuations can be observed in the relaxation curves, which are caused by the differences in the thermal expansion rates of the steel frame and the BFRP tendon when the ambient temperature varies. A similar phenomenon was found in other studies of the relaxation of FRPs.¹⁵

Pretension has been demonstrated to be effective in controlling creep strain.²¹ Figure 6(d) shows the relaxation curves of the pretension treated specimens, which perform significantly less relaxation loss than those without pretension treatment. The mean relaxation rate is 2.6%, comparable to the low relaxation rate of prestressed steel strands of 2.5% at 0.7f_u.²⁶ Figure 7 shows the mechanism of relaxation behavior enhancement through pretension treatment. Pretension facilitates the straightening of uneven fibers through the viscoelastic deformation of the resin, which allows better cooperation between the fibers and controls the creep deformation. These results indicate a good potential of using BFRP tendons as prestressing components.

Effects of the initial stress

The relaxation rate was defined as the percentage of load (or stress) reduction, and the experimental values are shown in Table 2. The total relaxation rates increase linearly with increasing stress. At 1000 h, the relaxation rates are 4.2%, 5.3%, and 6.4% for stresses of 0.4f_u, 0.5f_u, and 0.6f_u, respectively. Higher stresses lead to greater viscoelastic deformation in the BFRP tendon, which results in greater relaxation loss. Furthermore, Table 2 shows that during the first 10 h, the relaxation rates for different initial stresses have no significant differences. During the stage from 10 h to 480 h, the relaxation rates for the initial stress of 0.6f_u are significantly greater than those for 0.4f_u and 0.5f_u. All of the relaxation rates are relatively small in the final stage (480–1000 h).

Table 2.

Relaxation rates of BFRP tendons at 1000 h.

Initial stress	0.4f_u (600 MPa)			0.5f_u (750 MPa)			0.6f_u (900 MPa)
Number of specimen	1	2	3	1	2	3	1	2	3
Relaxation rate (0–1 h, %)	1.6	1.71	1.57	2.53	1.61	1.00	1.27	1.19	0.89
Relaxation rate (1–10 h, %)	0.79	0.32	1.38	0.86	1.95	1.06	0.76	0.82	0.87
Relaxation rate (10–480 h, %)	1.14	1.98	1.45	2.09	1.55	2.30	4.01	4.16	3.94
Relaxation rate (480–1000 h, %)	0.37	0.27	0.06	0.28	0.37	0.14	0.40	0.53	0.28
Total relaxation rate (%)	3.9	4.3	4.5	5.8	5.5	4.5	6.4	6.7	6.0
Mean value (%)		4.2			5.3			6.4

Figure 8 compares the relaxation rate and the creep rate with similar stress levels (approximately 750 MPa and 900 MPa, respectively) at 1000 h. The values of the creep rate were measured in the authors’ previous research.⁹ The relaxation rates are slightly lower than the creep rates because the stress reduction leads to smaller viscoelastic strains during the relaxation process. However, in some previous experiments without consideration of the slippage at anchorage, relaxation rate behaved much larger than creep rate.¹⁵ The comparison in Figure 8 further demonstrates the effectiveness of the proposed relaxation setup and the validity of the results in this study.

Prediction of the relaxation rate at one million hours

According to JSCE-534,²⁴ the relaxation curve can be fitted with a logarithmic curve in the form of the following

R_{r} = a - b \ln t

(3)

where R_r is the load retention (%); a and b are empirical constants, and t is the test time (h).

The predicted values of the load retention and relaxation rate at one million hours (114 years) can be determined by fitting the relaxation curves as shown in Table 3. The load retention at one million hours peaks at the stress of 0.4f_u, but that stress level may be too low to develop the high strength of the BFRP tendon. On the other hand, stresses of up to 0.6f_u can incur excessive prestressing losses, so they are also irrational. A moderate stress level of 0.5f_u, with pretention treatment is recommended. The relaxation rate of BFRP tendons at 0.5f_u with pretension treatment is predicted to be 6.7% at one million hours, which is 18% lower than that of untreated BFRP tendons subject to the same initial stress.

Table 3.

Predicted values of the relaxation rate at one million hours.

Initial stress	Specimen no.	a	b	Regression coefficient	Predicted load retention (%)	Predicted relaxation rate (%)	Mean value of relaxation rate (%)
0.4f_u	1	0.9854	0.003	0.9108	94.4	5.6	6.2
	2	0.9845	0.003	0.9156	94.3	5.7
	3	0.9824	0.004	0.9908	92.7	7.3
0.5f_u	1	0.9776	0.005	0.9694	90.9	9.1	8.2
	2	0.9821	0.005	0.9781	91.3	8.7
	3	0.9882	0.004	0.9503	93.3	6.7
0.6f_u	1	0.9915	0.007	0.876	89.5	10.5	10.0
	2	0.9919	0.006	0.7702	90.9	9.1
	3	0.9921	0.007	0.9019	89.5	10.5
0.5f_u (with pretension)	1	1.0151	0.006	0.9606	93.3	6.7	6.7
	2	1.018	0.006	0.9657	93.5	6.5
	3	1.0150	0.006	0.9876	93.2	6.8

Correlation between relaxation and creep

Because the creep and relaxation of FRPs are both caused by viscoelastic strain, they are correlated. Compared to creep tests, relaxation tests are generally relatively complex to conduct because a constant strain is difficult to guarantee due to the slippage at the anchorage. In contrast, the requirement for a sustained load in creep tests is easy to achieve. Thus, a method is proposed to predict the relaxation rate using the creep data. The detailed method is described as follows.

The stress in the tendon over time can be expressed by

σ = E \cdot ɛ_{total} - E \cdot ɛ_{v} (σ, t)

(4)

where σ is the stress in the tendon; ɛ_total is the total strain, which is equal to the sum of the elastic and viscoelastic strains, and ɛ_v is the viscoelastic strain, which is associated with the stress (σ) and time (t). Assuming that the elastic modulus E is constant during the relaxation, the relaxation rate can be written as

r = (σ_{ini} - σ) / σ_{ini} = E \cdot ɛ_{v} (σ, t) / E \cdot ɛ_{total} = ɛ_{v} (σ, t) / ɛ_{total}

(5)

where r is the relaxation rate, and σ_ini is the initial stress in the tendon, which is equal to E·ɛ_total.

Table 2 shows that the relaxation rate is directly proportional to the first power of the initial stress. Because ɛ_total is associated with the first power of the initial stress, it can be speculated from equation (5) that ɛ_v is directly proportional to the square of the stress, which is a basic assumption in the following prediction of the relaxation rate.

Considering the influence of the stress variance on the increase of viscoelastic strain, the stress at 1000 h should be calculated through an iterative method as

σ_{n} = σ_{n - 1} - E \cdot Δ ɛ_{vn} (σ_{n - 1}, t_{n})

(6)

where σ_n and σ_n₋₁ are the stresses calculated in the nth and the (n−1)th iterative step, respectively, and Δɛ_vn is the variation of the viscoelastic strain from the (n−1)th iterative step to the nth iterative step, which is assumed to be associated with σ_n₋₁ and the time of the nth iterative step (t_n). In this study, the elastic modulus E is considered to be constant during relaxation (55 GPa). The relationship between the viscoelastic strain and time at a constant stress has been measured in previous creep research.⁹ In each iterative step, Δɛ_vn is assumed to be directly proportional to

σ_{n - 1}^{2}

as mentioned above. Thus, the values of Δɛ_vn in each iterative step are modified based on the viscoelastic strain measured in the creep research (Δɛ_vn′) (i.e. the creep strain)⁹ considering the influence of the stress variance as shown in equation (7), where σ_cr denotes the sustained stress in the previous creep test.⁹

Δ ɛ_{vn} = Δ ɛ'_{vn} \times (σ_{n - 1} / σ_{cr}) 2

(7)

Iterative calculations were conducted at 1, 5, 10, 20, 40, 60, 80, 100, 500, and 1000 h. Table 4 shows the results of each iteration step. Only relaxation rates at initial stresses of 0.5f_u (750 MPa) and 0.6f_u (900 MPa) are predicted because no creep data at 0.4f_u (600 MPa) were collected in the previous study.⁹ The relaxation rates are calculated to be 5.0% and 6.0% at 1000 h for 0.5f_u and 0.6f_u, with small relative errors of 5.7% and 6.7%, respectively, compared to the experimental values. This calculation associates the relaxation with the creep and provides a method to predict the relaxation rate using the creep strain, which is relatively easy to measure.

Table 4.

Calculated results of the iterations.

n	Time (h)	0.5 f_u (750 MPa)		0.6 f_u (900 MPa)
n	Time (h)	Δɛ_vn (μɛ)	σ_n (MPa)	Δɛ_vn (μɛ)	σ_n (MPa)
0	0	0	750.0	0	900.0
1	1	65	746.4	383	879.0
2	5	231	733.8	225	866.6
3	10	55	730.7	49	863.8
4	20	48	728.1	47	861.3
5	40	55	725.1	54	858.3
6	60	39	722.9	38	856.2
7	80	48	720.3	49	853.5
8	100	6	720.0	5	853.3
9	500	96	714.7	95	848.1
10	1000	35	712.7	41	845.8
Predicted relaxation rate		5.0%		6.0%
Experimental relaxation rate		5.3%		6.4%

Conclusions

This paper systematically investigated the relaxation behavior of BFRP tendons. Relaxation tests were conducted at initial stresses of 0.4f_u, 0.5f_u, and 0.6f_u. Effect of pretension on relaxation controlling was validated, and the relaxation rates at one million hours were predicted. Using the correlation between creep and relaxation, the relaxation rates at 1000 h were predicted and compared with experimental results. The main conclusions are as follows.

The proposed setup for the relaxation test can provide the real relaxation losses of FRP tendons by eliminating the impact of slippage at the anchor zone. The relaxation rate increases in proportion to the stress due to the greater viscoelastic strain at higher stresses. At 1000 h, the relaxation rates are 4.2%, 5.3%, and 6.4% at the initial stresses of 0.4f_u, 0.5f_u, and 0.6f_u. The relaxation rates are slightly lower than the corresponding creep rates, demonstrating the effectiveness of the proposed relaxation setup.

The pretension treatment is effective in relaxation loss controlling. The relaxation rate can be decreased to approximately 2.6% at 1000 h at 0.5f_u, which is comparable to the low relaxation of prestressed steel strands at 0.7f_u (2.5%). This result further demonstrates the effectiveness of BFRP tendons as prestressing components.

The relaxation rates of untreated BFRP tendons at one million hours are predicted to be 6.2%, 8.2%, and 10.0% at initial stresses of 0.4f_u, 0.5f_u, and 0.6f_u, respectively. A relaxation rate of 6.7% is predicted for BFRP tendons at 0.5f_u initial stress with pretension treatment. An initial stress of 0.5f_u with pretension treatment is recommended for prestressing applications of BFRP tendons.

Due to the correlation between relaxation and creep, the relaxation rate can be predicted based on the viscoelastic strain at a constant stress (obtained by creep tests) considering the influence of the stress variance. The theoretical method associates creep with relaxation, and the predicted relaxation rates at 1000 h are consistent with the experimental values.

Footnotes

Acknowledgment

The authors acknowledge Jiangsu GMV Co., Ltd. for providing the BFRP tendons.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This study was supported by the National Key Basic Research Program of China, 973 Program (No. 2012CB026200), National Science Foundation of China (NSFC, 51378109) and a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (No. CE02-2-43). The name of the funder is “National Twelfth Five-year Plan Science & Technology Support Development Program of China (No. 2014BAB15B01)”.

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