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Evaluation of prestress losses in prestressed concretespecimens subjected to freezethaw cyclesDa-fu Caoa, Xiao-Chuan Qinb, Shao-Ping Mengb, Yong-Ming Tubc, Lennart Elfgrenc, NataliaSabourovac, Niklas Gripc, Ulf Ohlssonc & Thomas Blanksvrdca School of Civil Science and Engineering, Yangzhou University, No.198 HuaYang XiLu,HanJiang District, Yangzhou 225127, P.R. Chinab School of Civil Engineering, Southeast University, No.2 SiPaiLou, XuanWu District, Nanjing210096, P.R. Chinac Division of Structural Engineering, Lule University of Technology, SE-971 87, Lule,SwedenPublished online: 13 Feb 2015.

To cite this article: Da-fu Cao, Xiao-Chuan Qin, Shao-Ping Meng, Yong-Ming Tu, Lennart Elfgren, Natalia Sabourova,Niklas Grip, Ulf Ohlsson & Thomas Blanksvrd (2015): Evaluation of prestress losses in prestressed concrete specimenssubjected to freezethaw cycles, Structure and Infrastructure Engineering: Maintenance, Management, Life-Cycle Design andPerformance, DOI: 10.1080/15732479.2014.998241

To link to this article: http://dx.doi.org/10.1080/15732479.2014.998241

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Evaluation of prestress losses in prestressed concrete specimens subjected to freezethaw cycles

Da-fu Caoa1, Xiao-Chuan Qinb*, Shao-Ping Mengb2, Yong-Ming Tub,c3, Lennart Elfgrenc4, Natalia Sabourovac5,

Niklas Gripc6, Ulf Ohlssonc7 and Thomas Blanksvardc8

aSchool of Civil Science and Engineering, Yangzhou University, No.198 HuaYang XiLu, HanJiang District, Yangzhou 225127,P.R. China; bSchool of Civil Engineering, Southeast University, No.2 SiPaiLou, XuanWu District, Nanjing 210096, P.R. China; cDivision

of Structural Engineering, Lulea University of Technology, SE-971 87, Lulea, Sweden

(Received 9 January 2014; final version received 5 September 2014; accepted 4 October 2014)

Prestressed concrete structures are considered to be reliable and durable. However, their long-term performance whensubjected to frost attack is still unclear. In this work, experiments were carried out to evaluate the prestress losses in post-tensioned prestressed concrete specimens subjected to freezethaw cycles (FTCs). Two cases were considered: in one case,a series of specimens were prepared and tested in a freezethaw chamber; in the second case, the same series of specimenswere tested in an indoor environment (outside the chamber). The difference between the prestress losses of the specimensinside the freezethaw chamber and those outside the chamber equalled the prestress losses due to FTCs. When usingmathematical models to predict the prestress losses due to the FTCs, it was found that they were relatively small when theconcrete was slightly damaged. However, they increased rapidly when the FTCs were repeated. The eccentricity of theprestress wires led to larger prestress losses when subjected to FTCs. Moreover, the same cross section and eccentricityresulted in similar prestress losses due to the FTCs, and the relatively high-strength concrete could withstand more FTCs.

Keywords: concrete; post-tensioned; prestress loss; freezethaw cycles; experiments; mathematical model

Notations list

Es: Youngs modulus of longitudinal

reinforcement

Ep: Youngs modulus of prestressing

reinforcement

Ec: Youngs modulus of concrete before

freeze-thaw starts

As: cross-sectional area of longitudinal

reinforcement

Ap: cross-sectional area of prestressing

reinforcement

Ac: cross-sectional area of concrete

A: cross-sectional area of beam

I: inertia moment of cross-section

e: eccentricity

n: number of FTCs

f n: damage function after n FTCsDsl: total prestress lossDslO: prestress loss caused by other factorsDslF: prestress loss due to FTCsscon: tension control stressPn: pressure applied by prestressing

reinforcement after n FTCs

1cn: strain in the concrete at the layer of theprestressing wire after n FTCs

D1cn2 1; n: strain increment from the nth2 1 cycleto the nth cycle

DslFn: prestress loss after n FTCs

1. Introduction

In cold regions, the effect of freezethaw cycles (FTCs) is

one of the major factors that leads to a deterioration in the

durability of existing reinforced concrete structures

(Fagerlund, 1999; Pigeon & Pleau, 1995). As FTCs are

repeated, concrete material gradually loses its strength and

stiffness with the growth of internal cracks (Cho, 2007;

Ueda, Hasan, Nagai, Sato, &Wang, 2009). For prestressed

concrete structures, the deterioration of concrete material

can cause prestress loss as well as the degradation of load-

bearing capacity, which can eventually make the whole

structure incapable of service.

The performance of concrete material under FTCs has

been studied for many years by a number of researchers. For

example, in a series of experiments, Shang et al. investigated

the strength and deformation of plain concrete under uniaxial,

biaxial and triaxial compression after FTCs (Shang & Song,

2006; Shang, Song, &Qin, 2005, 2008; Shang, Yin, Song, &

Qin, 2006). Duan, Jin, and Qian (2011) proposed the stress

strain curves of frozenthawed confined and unconfined

concrete specimens. Hasan, Ueda, and Sato (2008)

q 2015 Taylor & Francis

*Corresponding author. Email: [email protected]

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investigated the stressstrain relationship of frost-damaged

concrete subjected to fatigue loading; coupling frost-damage

with load factors. Sun, Zhang, Yan, and Mu (1999) studied

the deterioration of concrete material by applying the static

load and FTCs simultaneously, and Li, Sun, and Jiang (2011)

studied the damage experienced by concrete undergoing a

flexural fatigue load and FTCs simultaneously.

However, less attention has been paid to reinforced

concrete members and prestressed concrete members

(Cao, Qin, & Yuan, 2013; Diao, Sun, Cheng, & Ye, 2011;

Hanjari, Kettil, & Lundgren, 2013). Diao et al. (2011)

investigated the coupling effects of mixed NaCl and

Na2SO4 corrosion, FTCs and persistent bending loads on

the structural behaviour of reinforced concrete beams and

found that a persistent load enhanced the damage in the

reinforced concrete beams. Moreover, a larger persistent

load ratio could result in a more severe degradation of

concrete. Hanjari et al. (2013) predicted the bending

behaviour of frost-damaged reinforced concrete beams by

the finite element method. Their comparison between the

predictions and available experimental data indicated that

the changes in failure mode and, to a rather large extent,

the effect of failure load caused by internal frost damage

were well predicted. Although there are some reports

concerning frost-damaged reinforced concrete beams, the

ways in which structures subjected to FTCs behave are not

well understood. Further investigations are required,

especially on the prestressed concrete structures in bridges

and other infrastructural constructions. In our previous

study (Cao et al., 2013), our group reported on the flexural

behaviours of prestressed concrete beams subjected to

FTCs. The cracking moment and ultimate bending

moment decreased as FTCs were repeated.

It is known that prestress loss often occurs due to

elastic shortening, bending, creep and shrinkage of the

concrete; and to steel relaxation, anchorage take-up and

frictional loss between the prestressing reinforcement and

its surrounding materials. Moreover, prestress losses can

also occur due to environmental factors, such as chloride

penetration, FTCs and so on. A prestressed concrete

member should maintain the effective prestressing force at

a significant level, together with appropriate material

properties, during the entire life of the structure. It is,

therefore, very important to estimate any prestress losses

that might occur (Kim, Yun, Ryu, & Cho, 2004).

For prestressed concrete members in cold regions,

prestress losses due to FTCs are critical to the performance

and life evaluation of prestressed concrete members. Zhou

(2008) attempted to measure the prestress losses of

uniaxial prestressed concrete members due to FTCs by a

through-hole load cell, but failed because the prestress loss

due to anchorage take-up was unexpectedly large, which

resulted in a very low effective prestress force in the

tendons. The short length of the prestressed concrete

member (only 400mm long) and an inappropriate

anchorage type (wedge anchor) may have been the main

factors that led to the absence of prestress in the members.

The main objective of this experimental research work

is to analyse the changes in prestress losses in post-

tensioned concrete when subjected to FTCs. In this work,

an experimental programme comprised over 125 FTCs,

which were performed on a series of post-tensioned

concrete specimens. We investigated the influences of

concrete mix design, and the cross section and eccentricity

of prestress wires on prestress loss while subjected to

FTCs. In addition, a mathematical model was used to

predict prestress losses; the predicted results were then

compared with the experimental measurements.

2. Test technique

Normally, two methods are used to monitor the prestress

force in the prestressing reinforcement. One method

monitors the force with a gauge, such as foil strain gauge

or vibrational chord strain gauge, attached to the prestressing

reinforcement. The strain in the prestressing reinforcement

measured by the gauge is then transformed into force by

multiplying it by Youngs modulus of the reinforcement.

The secondmethod is to place a through-hole load cell at the

anchorage end to test the prestress force directly.

A strain gauge is unsuitable for measuring the prestress

force in a freezethaw chamber. Because of the rapid

change of temperature in the chamber, it is hard to ensure

that the compensating gauge is at the same temperature as

that inside the specimen. There is also insufficient space

inside the specimen for the installation of the vibrational

chord strain gauge due to the limited chamber size.

Learning from the experience of Zhou (2008), we

successfully measured prestress losses in the freezethaw

chamber by making the following improvements to the test

method: (i) the length of the specimen was increased, (ii)

the prestress tendon and wedge-type anchorage were

replaced by a prestress wire and button-head anchorage,

respectively, which reduced the prestress loss due to the

anchorage take-up. In this study, specimens were prepared

using a post-tensioning method, as shown in Figure 1.

A hydraulic actuator with an end-adjustable anchorage

device was placed at one end of the specimen to tension

the prestress wire and permanent anchorage. At the

opposite end of the specimen, the applied prestress force

was monitored by a waterproof CCG though-hole load cell

(Applied Measurements Limited, Berkshire, UK) capable

of measuring up to 160 kN with a sensitivity of 0.15%.

3. Experimental programme

3.1. Materials

Two concrete mix designs (named Type A and Type B)

were used (Tables 1 and 2). The measured compressive

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strengths for Types A and B at the age of 60 days were

69.0MPa and 80.3MPa, respectively (Table 2). Hot-rolled

ribbed steel bar of either 10 or 8mm diameter was used

as the longitudinal reinforcement. The transverse steel

reinforcement was a hot-rolled plain steel bar with a

diameter of 4mm. The prestressing reinforcement was a

5mm low-relaxation steel wire with a nominal ultimate

strength of 1570MPa. The physical and mechanical

parameters of the reinforcements are shown in Table 3.

3.2. Specimens

Specimens were 1000mm long with either of two different

types of cross section: (i) two specimens with a cross

section of 100 100mm2 (a) and with a concentricprestress cable (Figure 2(a)); (ii) four specimens with a

cross section of 100 150mm2 (b) and with an eccentric

cable of 30mm (Figure 2(b)). All specimens were subjected

to the same casting and curing conditions.

After curing for 60 days, the specimens were

prestressed by a hydraulic actuator to a nominal prestress

level in the wires of about 65% of the ultimate strength.

The tensioning procedure of the wire is listed below:

. Lining up the prestress wire in the duct with anchoragedevices at both ends.

. Tensioning the prestress wire by the hydraulic actuator(Figure 3(a)).

. Tensioning the prestress wire up to 1.03 times of thenominal prestress level to decrease the prestress

relaxation losses.. Screwing the outer ring of the end-adjustableanchorage to create a permanent anchorage (Figure 3

(b)).. Demounting the hydraulic actuator by unscrewing itfrom the specimen (Figure 3(c)).

3.3. Programme

The specimens in the freezethaw chamber were used to

test the total prestress loss (Dsl). The correspondingspecimens exposed to the indoor environment were only

used to measure the prestress loss caused by other factors

(DslO), such as shrinkage and creep and so on. Theprestress loss of the specimens in the freezethaw

chamber minus the prestress loss of those outside was

used to estimate the prestress loss due to the FTCs (DslF).Table 4 shows the various combinations of concrete

mix design and cross section of each specimen and the

environment in which they were tested. Concrete mix

Type A was combined with both types of cross sections, a

(100 100mm2) and b (100 150mm2), while concretemix Type B was only combined with cross section b (100

150 mm2). It was not possible to test all thecombinations because of the limited size of the freeze

thaw chamber.

Each specimen is designated: MCS, where M is the

concrete mix type (A or B), C is the cross section of the

specimen (a or b) and S is the storage condition (F or U).

F represents the condition of in the freezethaw chamber

Figure 1. Post-tensioning layout.

Table 1. Materials used for the concrete mix.

Components

Cement PO, 42.5RWater Tap waterFine aggregates River sand, fineness module 2.6Coarse aggregates Crushed stone, 531.5mmFly ash Class II fly ashAdditives JM-9 composite water reducing agent

Note: PO represents ordinary Portland cement; JM-9 is a designationof composite water reducing agent (Jiangsu Sobute New MaterialsLimited, Nanjing, China).

Table 2. Concrete mix designs.

Designation A B

Cement (kg/m3) 463 380Watercement ratio 0.38 0.46River sand (kg/m3) 599 712Crushed stone (kg/m3) 1139 1103Fly ash (kg/m3) 62 50Composite water reducing agent (kg/m3) 8.93 6.02Air content (%) 2.8 3.0Compressive strength at 60 days (MPa) 80.3 69.0

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and U represents the condition of under the indoor

environment.

After prestressing was applied to the specimens for

30 days, three specimens designated F, i.e. A-a-F, A-b-F

and B-b-F, were placed into the freezethaw chamber to

perform a rapid freezethaw in water test, while the other

three specimens, i.e. the corresponding U group, were

placed outside under the indoor environment. All F

specimens were immersed in water for 48 h prior to

testing, and the corresponding U group were covered

with straw mats and sprayed with water twice per day to

ensure that groups both inside and outside of the chamber

experienced the same relative humidity.

The freezethaw test followed the ASTM C666-03

ASTM C666 (2008) Procedure A (Figure 4). In this FTC

procedure, the temperature of the specimen was first

decreased from 5 to 2168C and then increased from216 to 58C over a period of 2.8 h during which timecooling took 2.0 h and heating took 0.8 h, i.e. 28.6% of the

time was used for thawing. Moreover, the time taken to

decrease the core temperature of a specimen from 3 to2168C was about 1.7 h, and the time taken to increase itfrom 216 to 38C was 0.75 h. The period of transitionbetween the freezing and thawing phases of the cycle was

5min. As described above, a through-hole load cell was

installed at the end of the anchor to measure the load

applied by the steel wires (Figure 5), which was connected

to an electric resistive indicator (Yangzhou Test Limited,

Yangzhou, China) (Figure 6). This set-up allows

the measurement results to be recorded every 25 cycles

when the temperature at the centre of a single specimen

reaches 58C.In addition, cubic specimens with a side length of

100mm were also placed in the chamber to measure the

mechanical properties of the concrete under FTCs. These

cubic specimens were tested at the same time that the

prestress forces were recorded. The mechanical properties

of concrete that had been damaged by the FTCs are listed

in Table 5, and the deterioration trends of concrete under

FTCs are shown in Figure 7. These tests were performed

mainly by Cao Da-fu and Qin Xiao-chuan in Yangzhou

University in 2011.

Figure 2. Cross sections of the specimens, (a) 100 100mm2 cross section, (b) 100 150mm2 cross section. Length unit: mm.

Figure 3. Tensioning procedure of prestress wire, (a) tensioningthe prestress wire by the hydraulic actuator, (b) screwing the outerring of the end-adjustable anchorage to create a permanentanchorage, (c) demounting the hydraulic actuator by unscrewingit from the specimen.

Table 3. Physical and mechanical properties of the reinforcements.

Characteristics Longitudinal reinforcementTransverse

reinforcementPrestressingreinforcement

Diameter (mm) 10 8 4 5Yield strength (MPa) 373 360 462 1550Ultimate strength (MPa) 526 517 569 1624Youngs modulus (GPa) 186 176 187 198

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4. Numerical simulation of freezethaw prestress loss

4.1. General considerations

To the best of our knowledge, the issue of prestress loss

due to FTCs is not mentioned in the available standards,

and no equations have been developed for predicting such

freezethaw prestress losses. Youngs modulus of the

concrete material gradually decreases as the FTCs are

repeated (Duan et al., 2011). The damage function of

Youngs modulus is described by Equation (1):

Ecn Ecf n; 1

where Ec is Youngs modulus of the concrete before

freezethaw starts and f n is the function that affects thevalue of Youngs modulus following damage to the

specimen subjected to n FTCs.

The respective functions affecting Youngs modulus of

FTC-damaged specimens made from the two different

concrete mix designs were obtained by fitting equation (1)

to the experimental data presented in Table 5. The fitted

results are shown in Equations (1.1) and (1.2).

For the concrete mix design Type A: Ec EcA 36:8GPa;

f n fAn 1:01745 20:01681 e0:01686n: 1:1For the concrete mix design Type B: Ec EcB

35:5GPa;

f n f Bn 1:00611 20:00605 e0:02999n: 1:2In prestressed concrete members, the decrease of

Youngs modulus of the concrete causes an additional

deformation of the member. According to the deformation

compatibility condition, this deformation also occurs in

prestressing reinforcements which will cause further

prestress loss.

This modelling analysis incorporates the following

assumptions: (1) Youngs modulus of prestress wires does

not change under FTCs, (2) the concrete and prestress

wires deform compatibly.

4.2. Case of uniaxial prestressed concrete members

The bottom chord of a prestressed concrete truss is usually

a direct tension member with prestressed reinforcements at

the centroid of the section, so it can be simplified into a

uniaxial prestressed concrete member. We assume the

pressure applied to the test specimen by prestressing wires

to be P0 before the FTCs start. The strain 1c0 in theconcrete at the layer of the prestressing wire is

1c0 P0AsEs AcEcf 0 ; 2

where Es is Youngs modulus of the longitudinal

reinforcement, As is the cross-sectional area of the

longitudinal reinforcement and Ac is the net cross-

sectional area of the concrete specimen.

Figure 4. Freezethaw procedure (ASTM C666-03 (2008Procedure A)).

Table 4. Test programme.

SpecimensConcretemix

Crosssections

Prestressforce (kN)

Initial compressivestress in the

concrete at thelayer of theprestressingwires (MPa)

A-a-F A a 60.07 5.63A-a-U A a 60.07 5.63A-b-F A b 60.07 5.93A-b-U A b 60.07 5.93B-b-F B b 60.07 6.14B-b-U B b 60.07 6.14

Figure 5. Load cell at the passive end.

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Hence, the strain increment D1cn2 1; n from thenth2 1 cycle to the nth cycle is described according toEquation (3).

D1cn2 1; n PnAsEs AcEcf n

2Pn2 1

AsEs AcEcf n2 1 : 3

The pressure applied by the prestressing reinforcement

after n FTCs is then calculated according to Equation (4).

Pn Pn2 12 EpApD1cn: 4

Equation (5) is then obtained from Equations (3)

and (4)

PnPn2 1

1 EpAp=AsEs AcEcf n2 11 EpAp=AsEs AcEcf n ; 5

where Ap represents the cross-sectional area of the

prestress wires.

Let An 1 EpAp=AsEs AcEcf n, Equation (5)can be simplified as:

Pn P0A0An : 6

The prestress loss of the concrete specimen after n

FTCs is then expressed as

DslFn P012 A0=AnAp

: 7

Figure 6. Test apparatus.

Table 5. Mechanical properties of concrete damaged by FTCs.

Designation FTCs

Compressive strength Youngs modulus

Abs.(MPa)

Rel.(%)

Abs.(GPa)

Rel.(%)

A 0 80.3 100 36.8 10025 76.4 95 36.5 9950 72.0 90 35.9 9875 67.3 84 35.3 96100 58.4 73 34.0 92125 48.7 61 32.4 88

B 0 69.0 100 35.5 10025 65.3 95 35.3 9950 61.3 89 34.8 9875 55.6 81 33.6 95100 45.2 66 31.5 89125 30.8 45 26.6 75

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4.3. Case of prestressed concrete beams

The prestressed concrete beam is the most common type

of member in a prestressed concrete structure. Under

FTCs, the prestress loss in a beam is similar to that in a

uniaxial member. As described in Section 4.2, if we

assume the pressure applied by the prestress wires to

be P0 before the FTCs start, then the strain 1c0 inthe concrete at the layer of the prestressing wire is given

by

1c0 P01=A e2=I

Ecf 0 ; 8

where A is the cross-sectional area of the beam, I is the

inertia moment of the cross section and e is the

eccentricity.

Following the deduction process of the uniaxial

prestressed concrete member, and letting Bn 11=A e2=IEpAp=Ecf n, then Pn and DslFn aredescribed as follows:

Pn P0B0Bn ; 9

DslFn P012 B0=BnAp

: 10

5. Results and discussions

5.1. Test results

The test results under 0, 25, 50, 75, 100 and 125 FTCs are

summarised in Table 6, including the prestress losses of A-

a-F, A-b-F and B-b-F (Dsl) and those of A-a-U, A-b-U andB-b-U (DslO) of the corresponding specimens placed inthe indoor environment.

In order to show the process of separating the prestress

loss due to the FTCs from other sources, the prestress losses

Table 6. Prestress losses.

Concretemix

Crosssection

Testresults

FTCs

Specimens Exposure 0 25 50 75 100 125

A-a-F A a F sAaF (MPa) 1019.94 1018.94 1016.94 1013.93 1012.43 1006.42DsAal (MPa) 0 1 3 6.01 7.51 13.52

A-a-U A a U sAaU (MPa) 1003.75 1002.87 1001.73 998.92 998.6 993.49DsAalO (MPa) 0 0.88 2.02 4.83 5.15 10.26

A-b-F A b F sAbF (MPa) 1013.17 1012.89 1011.88 1010.21 1007.09 1003.93DsAbl (MPa) 0 0.28 1.29 2.96 6.07 9.23

A-b-U A b U sAbU (MPa) 1014.68 1014.68 1013.96 1012.5 1010.33 1008.88DsAblO (MPa) 0 0 0.73 2.18 4.35 5.8

B-b-F B b F sBbF (MPa) 1020.17 1018.67 1016.67 1015.68 1012.68 1006.69DsBbl (MPa) 0 1.5 3.5 4.49 7.49 13.48

B-b-U B b U sBbU (MPa) 1015.68 1014.99 1014.3 1013.61 1012.92 1011.54DsBblO (MPa) 0 0.69 1.38 2.07 2.76 4.14

Note: A represents concrete mix A; B represents concrete mix B. a represents 100 100mm2 cross section with a concentrically located hole; brepresents 100 150mm2 cross section with an eccentricity of 30mm. F represents In the freezethaw chamber, and U represents Under the indoorenvironment.

Figure 7. Deteriorations of concrete under FTCs, (a) relativecompressive strength under FTCs, (b) relative Youngs modulusunder FTCs.

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of specimen A-a are depicted as an example in Figure 8 in

which Curve 1, which was obtained from the prestress loss

of the specimen in the freezethaw chamber at each of 25

FTCs, represents the total prestress loss (Dsl). Curve 2 wasobtained from the prestress loss in the corresponding

specimen under the indoor environment to determine the

prestress loss caused by other factors (DslO). By subtractingthe prestress loss of the specimen under the indoor

environment from that under the FTCs in the freezethaw

chamber, i.e. Dsl DslO, the prestress losses due to FTCs(DslF) at each of 25 FTCs were obtained.

Figure 9 shows the prestress losses caused by the FTCs

and by other factors for all specimens tested. For those

specimens formulated with the same concrete mix, i.e. A-a

and A-b, the total prestress losses of the specimen with the

smaller cross section and non-eccentricity (A-a) are larger

than those for the specimen with the larger cross section (A-

b). On the other hand, the proportional prestress loss of A-b

under theFTCs in the freezethawchamber is larger than that

of A-a. For those specimens with the same cross section and

eccentricity (B-b and A-b), the freezethaw prestress losses

of the specimens formed with the Type Bmix are larger than

those of concrete Type A. In these specimens, the greatest

prestress loss due to the FTCs was 9.34MPa, which occurred

in B-b after 125 FTCs. However, compared with the tension

control stressscon (65%of the nominal ultimate strength), theprestress losses due to the FTCs (DslF) are very small, beingless than 1%ofscon. This indicates that the damage due to theFTC has only a small effect on the prestress loss of the

specimens at the early stage.

5.2. Comparison of test results and predictedprestress losses

The prestress losses of the specimens were predicted

according to Equations (7) and (10). The test results and

the predicted prestress losses for specimens A-a, A-b and

B-b are shown in Figure 10. Figure 10(a) shows that

Equation (7) fits the results of specimen A-a quite well.

Equation (10) fits the results of specimens A-b and B-b

well with only small errors which might have been caused

by the test system, as shown in Figure 10(b),(c). It is clear

that Equations (7) and (10) are capable of predicting the

freezethaw prestress loss of the uniaxial prestressed

concrete member and of the prestressed concrete beam,

respectively.

From both Equations (7) and (10), it can be seen that

the prestress loss of a concrete specimen depends on the

damage function affecting Youngs modulus f n.Figure 11 shows the relationships between Equations (7)

and (10) and f n. Each open circle on the dashed linerepresents the predicted results based on Equation (7) or

Equation (10) with f n being 1, 0.9 and 0.8, etc.Moreover, since the effectiveness of Equations (7) and

(10) has already been proven, as shown in Figure 10, and

the trends of prestress loss due to the FTCs calculated by

the models are in good accordance with the deterioration

law of the concrete under the FTCs, the extrapolation of

the models might shed light on the discussion about the

freezethaw prestress loss over 125 FTCs.

As shown in Figure 11, during the early stage of the

FTC test, for example when there have been less than 100

FTCs, the variation of f n and DslF is quite small, whichindicates that the prestress loss due to the FTCs is small

during this period even if some damage has already

occurred in the concrete material. However, with an

increase of the FTCs, both f n and DslF decrease rapidly,and DslF falls at a faster rate than f n. For specimen A-a(Figure 11(a)), if f n is larger than 0.3, the prestress lossdue to the FTCs is less than 50MPa (5% scon), while iff n equals 0.1, DslF is more than 100MPa (10% scon).For specimens A-b and B-b (Figure 11(b),(c)), DslF is

Figure 8. Prestress losses for specimen A-a.

Figure 9. Measured prestress losses.

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more than 200MPa (20% scon) if f n equals 0.1. Thisclearly shows that the prestress loss is highly dependent on

the damage suffered by the concrete, which can be

correlated with the significant decrease of Youngs

modulus of elasticity.

Comparing the ultimate state of Figure 11(a) with that

of Figure 11(b), the predicted freezethaw prestress loss

of specimen A-a is 114MPa, which is about 100MPa less

than that of specimen A-b. It is probably the eccentricity

factor that causes this difference. The comparison of the

ultimate states in Figure 11(b),(c) shows that the

specimens with the same cross section and eccentricity

result in a similar prestress loss due to the FTCs, and that

the relatively high strength concrete could withstand more

FTCs. The effects of these two factors, i.e. the eccentricity

and the concrete strength, on the prestress loss due to the

FTCs according to Equations (7) and (10) are shown in

Figures 12 and 13.

As shown in Figure 12, specimen A-b was assumed to

have different eccentricities, i.e. 10, 20 and 30mm.

It should be noted that results for specimens with

eccentricities of 10 and 20mm, and specimens subjected

to more than 125 FTCs were not physically tested, but

were predicted by Equation (10) and have been included in

Figure (12) to better show the relationship between the

prestress losses due to the FTCs and eccentricity.

Moreover, all the results shown in Figure 12 were

calculated according to Equation (10). As shown in

Figure 12, the larger the eccentricity, the more the

prestress loss will be obtained. However, the prestress loss

does not increase at as fast a rate as that shown in

Figure 13. Comparing the case of e 10mm with that ofe 30mm after 200 FTCs, although the eccentricity hasincreased by 200%, the prestress loss only increased from

19.51 to 26.97MPa, which is equivalent to about 38%.

The compressive stress in the concrete at the layer of

the prestressing wires in the specimen with the eccentricity

of 10mm is 4.22MPa, which is smaller than that in the

specimen with the eccentricity of 30mm (5.93MPa).

If other conditions are the same, a larger eccentricity will

Figure 10. Test results and predicted prestress loss, (a) comparison of the test results with the predicted results by Equation (7) for theconcrete specimen A, (b) comparison of the test results with the predicted results by Equation (10) for the concrete specimen A-b,(c) comparison of the test results with the predicted results by Equation (10) for the concrete specimen B-b.

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produce larger compressive stress in concrete in the

longitudinal direction as well as larger splitting stress in

the transverse direction. Furthermore, the tensile stress in

the longitudinal direction might occur at the concrete layer

that is farthest from the prestress wires due to the larger

eccentricity. These stresses in the concrete may result in

more internal cracks prior to the FTCs. Thus, the concrete

specimen with the eccentricity of e 30mm will havemore internal cracks, which allow water to penetrate into

it. Furthermore, more expansion in the concrete can be

caused when frozen. When the expansion tensile stress

exceeds the tensile strength of the concrete, new internal

cracks will occur and the old cracks will propagate. In that

Figure 12. Effects of eccentricity on prestress loss due to FTCs.Figure 13. Effects of concrete strength on prestress loss due toFTCs.

Figure 11. Comparison of the concrete freezethaw damage and the prestress loss due to the FTCs, (a) comparison of the concretefreezethaw damage fA(n) with the predicted results by Equation (7) for the concrete specimen A-a, (b) comparison of the concretefreezethaw damage fA(n) with the predicted results by Equation (10) for the concrete specimen A-b, (c) comparison of the concretefreezethaw damage fB(n) with the predicted results by Equation (10) for the concrete specimen B-b.

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case, the concrete specimen will absorb more water during

the next thawing period. When subjected to such FTCs, the

concrete will become crispy and Youngs modulus will

decrease. Therefore, the larger the eccentricity, the quicker

Youngs modulus drops, and the larger the freezethaw

prestress loss will be.

As observed in Figure 13, the damage function of the

concrete, in which Youngs modulus equals 36.2GPa

(compressive strength at 60 days is equal to 74.7MPa),

was obtained through an interpolation between fAn andf Bn. Similar to the case shown in Figure 12, the concretewith the interpolated damage function was not a tested

concrete; instead, its prestress loss results that were

predicted by Equations (7) and (10) are included in

Figure 13 to better show the relationship between the

freezethaw prestress loss and the concrete strength.

Furthermore, the predicted results for the concrete

specimen with cross section a (concentrically prestressed)

were calculated by Equation (7), and those for the concrete

specimen with cross section b (e 30mm) werecalculated by Equation (10). It is obvious that the prestress

losses of the concrete specimen due to the FTCs increase

sharply while the concrete strength decreases, especially

under high FTCs. Taking b (150 FTCs) as an example,

the prestress loss of the concrete Type B (Ec 35.5 GPa)is 35.93MPa, which is nearly five times higher than that of

the concrete Type A (Ec 36.8GPa), 7.38MPa.The different concretes exhibit different resistance to

the FTCs after the same number of FTCs. This is because

the formation and growth of the internal cracks of the

different concretes during the FTCs are not the same.

These cracks exist mainly in the paste and paste

aggregate interfaces when the concrete hardens, even if

there is no load or environmental effect. During the

concrete hardening process, the concrete (e.g. Type B

concrete in this test) with a higher watercement ratio,

i.e. with a relatively lower strength, tends to contain more

internal cracks. When the concrete specimen is immersed

in water, it will absorb more water into the concretes

pore system. As the temperature drops below the freezing

point of water, the water will turn into ice accompanied

by a 9% volume increase, which causes tensile stress

inside the concrete. If the tensile stress in concrete is

higher than the tensile strength of concrete material, new

internal cracks will form and the old cracks will grow

larger. As the FTCs are repeated, more and more water

will be absorbed into the concrete during thawing, which

causes larger expansion and more internal cracks during

freezing. The load carrying area will decrease with the

formation and growth of the internal cracks, which leads

to a decrease in the compressive strength. Because there

are fewer micro-units to carry the load with the FTCs

being repeated, each unit will reach its elastic limit more

quickly. Hence, the value of Youngs modulus of the

relatively low-strength concrete after being subjected to

FTCs decreases more quickly than does that of the

relatively high-strength concrete. The quicker the value

of Youngs modulus falls, the larger the freezethaw

prestress loss will be.

For the two factors mentioned above, i.e. the

eccentricity and the concrete strength, which were

considered in the test programme, less prestress losses

were recorded for those cases with smaller values of

eccentricity and greater concrete compressive strength.

Concrete strength is the most dominant factor influencing

prestress losses due to FTCs.

6. Conclusions

The prestress losses due to the FTCs in the post-tensioned

prestressed concrete specimens have been studied by

experiments and theoretical analysis. The present exper-

imental study and numerical simulation have shown that

FTCs accelerate the degradation process of concrete

material: the concrete is slightly affected when the number

of FTCs is small, but the internal cracks will grow as the

FTCs are repeated, thus making the macroscopic

mechanical properties of the concrete deteriorate quicker

and quicker. This leads to the fact that the freezethaw

prestress loss is relatively small when the concrete is not

severely damaged, but becomes greater at an ever-

increasing rate as the FTCs are repeated.

When the concrete mix design, the cross section of the

concrete specimen and the tension control stress in the

prestress wires are the same, greater eccentricity produces

larger compressive stress in the concrete in the

longitudinal direction as well as larger splitting stress in

the transverse direction. Furthermore, the tensile stress

might occur at the concrete layer that is farthest from

the prestress wires due to the larger eccentricity.

These stresses in the concrete result in more internal

cracks, forming before the FTCs start, which is the reason

why the freezethaw damage is more severe in members

with larger eccentricity. Thus, under the same conditions,

the larger the eccentricity, the more the freezethaw

prestress loss will be. When the concrete material has been

severely damaged by a number of FTCs, the frame of the

reinforcing steel bars will be the main structure to carry the

prestress. That is to say, the same cross section and

eccentricity will result in a similar ultimate prestress loss

due to the severe effects of the FTCs even when the mix

designs are different. However, due to there being fewer

internal cracks in the relatively high-strength concrete, the

concrete will absorb less water into the concrete pore

systems when it is immersed in water, which will result in

less freezethaw damage inside the concrete. The load

carrying area decreases more slowly with the formation

and growth of the internal cracks compared to the freeze

thaw damage process in the relatively low-strength

concrete. Because there are more micro-units to carry

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the load as the FTCs are repeated, each unit reaches its

plastic stage more slowly. Hence, Youngs modulus of

relatively high-strength concrete after it has been

subjected to FTCs decreases at a slower rate than does

that of relatively low-strength concrete. The slower the

rate at which Youngs modulus falls, the smaller the

freezethaw prestress loss. In other words, the relatively

high-strength concrete structure can withstand more FTCs.

The models developed in this paper are capable of

predicting the prestress loss in the uniaxial prestressed

concrete member and in the prestressed concrete beam

when subjected to FTCs if the mechanical properties of the

concrete material at the corresponding ages and environ-

mental conditions are available. In engineering practice,

real-time monitoring of the prestress loss due to the FTCs

could be performed by measuring the mechanical proper-

ties of concrete material under the same environmental

conditions. Moreover, if these properties can be predicted

in future investigations, it will be possible to apply the

models proposed here.

Disclosure statement

No potential conflict of interest was reported by the authors.

Funding

Funding for this experimental research work was provided bythe National Natural Science Foundation of China [grantnumber 50978224], [grant number 51378104] and the PriorityAcademic Program Development of Jiangsu Higher EducationInstitutions. Tests were conducted at the School of CivilScience and Engineering of the Yangzhou University, China.

Notes

1. Email: [email protected]. Email: [email protected]. Email: [email protected]. Email: [email protected]. Email: [email protected]. Email: [email protected]. Email: [email protected]. Email: [email protected].

References

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Cao, D.-F., Qin, X.-C., & Yuan, S.-F. (2013). Experimental studyon mechanical behaviors of prestressed concrete beamssubjected to freeze-thaw cycles. Tumu Gongcheng Xuebao/China Civil Engineering Journal, 46, 3844.

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Diao, B., Sun, Y., Cheng, S.-H., & Ye, Y.-H. (2011). Effects ofmixed corrosion, freeze-thaw cycles, and persistent loads onbehavior of reinforced concrete beams. Journal of ColdRegions Engineering, 25, 3752. doi:10.1061/(ASCE)CR.1943-5495.0000019

Duan, A., Jin, W.-L., & Qian, J.-R. (2011). Effect of freeze-thawcycles on the stress-strain curves of unconfined and confinedconcrete. Materials and structures, 44, 13091324. doi:10.1617/s11527-010-9702-9

Fagerlund, G. (1999). Modeling the service life of concreteexposed to frost. Paper presented at the internationalconference on ion and mass transport in cement-basedmaterials. Westerville, OH: American Ceramic Society.

Hanjari, K.Z., Kettil, P., & Lundgren, K. (2013). Modelling thestructural behaviour of frost-damaged reinforced concretestructures. Structure and Infrastructure Engineering, 9,416431. doi:10.1080/15732479.2011.552916

Hasan, M., Ueda, T., & Sato, Y. (2008). Stressstrainrelationship of frost-damaged concrete subjected to fatigueloading. Journal of Materials in Civil Engineering, 20,3745. doi:10.1061/(ASCE)0899-1561(2008)20:1(37)

Kim, J.-T., Yun, C.-B., Ryu, Y.-S., & Cho, H.-M. (2004).Identification of prestress-loss in PSC beams using modalinformation. Structural Engineering and Mechanics, 17,467482. doi:10.12989/sem.2004.17.3_4.467

Li, W.-T., Sun, W., & Jiang, J.-Y. (2011). Damage of concreteexperiencing flexural fatigue load and closed freeze/thawcycles simultaneously. Construction and Building Materials,25, 26042610. doi:10.1016/j.conbuildmat.2010.12.007

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Shang, H.-S., & Song, Y.-P. (2006). Experimental study ofstrength and deformation of plain concrete under biaxialcompression after freezing and thawing cycles. Cement andConcrete Research, 36, 18571864. doi:10.1016/j.cem-conres.2006.05.018

Shang, H.-S., Song, Y.-P., & Qin, L.-K. (2005). Experimentalstudy on the property of concrete after freezethaw cycles.China Concrete and Cement Products, 32, 911.

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Shang, H.-S., Yin, Q.-X., Song, Y.-P., & Qin, L.-K. (2006).Experimental study on the influence of freezing and thawingcycles on deformation features of common concrete. YangtzeRiver, 39, 6063.

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Ueda, T., Hasan, M., Nagai, K., Sato, Y., & Wang, L.-C. (2009).Mesoscale simulation of influence of frost damage onmechanical properties of concrete. Journal of Materials inCivil Engineering, 21, 244252. doi:10.1061/(ASCE)0899-1561(2009)21:6(244)

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AbstractNotations list1. Introduction2. Test technique3. Experimental programme3.1. Materials3.2. Specimens3.3. Programme

4. Numerical simulation of freeze-thaw prestress loss4.1. General considerations4.2. Case of uniaxial prestressed concrete members4.3. Case of prestressed concrete beams

5. Results and discussions5.1. Test results5.2. Comparison of test results and predicted prestress losses

6. ConclusionsDisclosure statementFundingNotesReferences