Research ArticleUsing Externally Bonded CFRP to Repair a PCCP with BrokenWires under Combined Loads

Kejie Zhai,1 Hongyuan Fang ,2,3,4 Bing Fu ,5 Fuming Wang,1,2,3,4 and Benyue Hu2,3,4

1School of Civil Engineering, Sun Yat-sen University, Guangzhou 510275, China2College of Water Conservancy & Environmental Engineering, Zhengzhou University, Zhengzhou 450001, China3National Local Joint Engineering Laboratory of Major Infrastructure Testing and Rehabilitation Technology,Zhengzhou 450001, China4Collaborative Innovation Center of Water Conservancy and Transportation Infrastructure Safety, Henan Province,Zhengzhou 450001, China5School of Civil and Transportation Engineering, Guangdong University of Technology, Guangzhou 510006, China

Correspondence should be addressed to Hongyuan Fang; 18337192244@163.com

Received 29 March 2019; Revised 5 September 2019; Accepted 11 September 2019; Published 20 October 2019

Academic Editor: Gianluca Cicala

Copyright © 2019 Kejie Zhai et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Prestressed concrete cylinder pipe (PCCP) is widely used for long-distance water pipelines throughout the world. However,prestressing wire breakage is the most common form of PCCP damage. For some pipelines that cannot be shut down, a newtechnique for in-service PCCP repair by externally bonding the pipe with layers of carbon fiber reinforced polymer (CFRP) wasproposed. A set of three-dimensional finite element models of the repaired PCCP have been proposed and implemented in theABAQUS software, which took into account the soil pressure, the weight of the PCCP, the weight of the water, and thehydrostatic pressure. The stress–strain features of the PCCP repaired with CFRP of various thicknesses were analyzed. Thestress–strain features of different wire breakage rates for the repaired PCCP were also analyzed. The results showed that thestrains and stresses decreased at the springline if the PCCP was repaired with CFRP, which improved the operation of thePCCP. It has been found that the wire breakage rates had a significant effect on the strains and stresses of each PCCPcomponent, but CFRP failed to reach its potential tensile strength when other materials were broken.

1. Introduction

The first prestressed concrete cylinder pipe (PCCP) wasdesigned and manufactured in 1939. PCCP is widely used inwater transfer projects all over the world because it resists exter-nal pressures and internal forces and it is impermeable. PCCP isa composite structure consisting of a concrete pipe core encasedin a steel cylinder surrounded by prestressing wires and a mor-tar coating. Structurally, PCCP can be divided into embeddedcylinder (ECP) and lined cylinder (LCP) types [1, 2].

PCCP is subjected to different loads from externalpressures and internal forces during its service life. Many stud-ies have focused on PCCP loading. Ross [3] analyzed the strainresponses of various structural materials by crushing and bend-ing tests with the pipe under hydrostatic pressure. Kennison [4]

and McCall [5] examined the behaviour of PCCPs in responseto combined loads using internal and external load tests.Gomez andMunoz [6] used two- and three- dimensional finiteelement models to investigate the effects of gradual loss of ten-sion in the prestressing wires. Zhang et al. [7] used ANSYS toexamine the mechanical properties of the PCCP during manu-facture, construction, and operation, and they developedmodels for PCCP design, manufacture and operation. Douet al. [8, 9] tested the various PCCP layers during pressurizationusing Brillouin optical time-domain analysis (BOTDA) andfiber Bragg grating (FBG) sensing techniques. Zhang et al.[10] comprehensively tested a jacking prestressed concrete cyl-inder pipe (JPCCP) with external loads, internal hydrostaticpressure, and combined loads and described the failure of theJPCCP under combined loads.

HindawiInternational Journal of Polymer ScienceVolume 2019, Article ID 8053808, 11 pageshttps://doi.org/10.1155/2019/8053808

Zarghamee et al. [11, 12] studied the separation of mortarand concrete under different mortar–prestressing wire bond-ing conditions through tests and finite element analysis. Huet al. [13] conducted an external load prototype test andmodeled the PCCP used in the South-to-North Water Diver-sion Project to predict the effects of existing cracks in theconcrete core of the PCCP. Gong et al. [14] conducted full-scale experimental research and modeling to evaluate thedamage caused during pipe jacking by different jacking forcesand different geological conditions. Sun et al. [15] combinedtesting and numerical analysis to identify the key factors con-trolling the rotation of PCCP pipelines and to guide PCCPdesign and engineering on soft soil foundations. Zhanget al. [16] conducted a full-scale test on a new JPCCP todetermine changes in pipe–soil contact stress during jackingand to provide a better basis for the manufacture and con-struction of the JPCCP. Xu et al. [17] used BOTDA to evalu-ate mortar cracks and PCCP structural states.

PCCP performance deteriorates as the pipe ages. The pipecorrodes easily in the complex underground environment,and the prestressing wires may break, which reduces the integ-rity of the pipeline. There have been studies of PCCPs withbroken wires. Diab and Bonierbale [18] created two-dimensional and three-dimensional finite element modelsand developed effective repair procedures. Zarghamee et al.[19–21] studied the characteristics of broken PCCPs with dif-ferent diameters under combined loads using nonlinear finiteelement models. They empirically tested the failure modes andultimate bearing capacity of a PCCP with broken prestressingwires to give probabilistic risk assessments for a PCCP withbroken wires. Hu and Shen [22] used finite nonlinear elementanalysis with empirical testing and found that when the num-ber of broken wires reaches a certain value, the concrete coreis more likely to crack, which affects the long-term operationof a PCCP. Ge and Sinha [23] developed a theoretical methodfor calculating the length of prestress loss. They suggested thatbroken wires do not have a significant impact on a PCCPwith good mortar adhesion. Hajali et al. [24–26] consideredthe pipe–soil interaction, the interaction between neighboringpipes, and internal and external loads in modeling the effectsof the position and number of broken wires on a PCCP usinga three-dimensional finite element model.

The breakage of prestressing wires can easily cause a pipeburst event, resulting in almost incalculable loss. Reinforce-ment and repair of the PCCP has received increased atten-tion. Carbon fiber reinforced polymer (CFRP) is widelyused as reinforcement because of its light weight, highstrength, corrosion resistance, and many other advantages[27–30]. CFRP liner installation has gradually become thefocus of scholarly research. Lee and Karbhari [31] studiedthe mechanical behavior of CFRP lining under external andinternal forces by testing PCCP cross-sections. Engindenizet al. [32, 33] developed quality assurance procedures andtesting standards to be followed before, during and after theuse of CFRP liner to repair a PCCP. Then, the effects onthe design, materials, installation and quality control regula-tions of the AWWA were identified through testing.Alkhrdaji [34] introduced a hybrid FRP liner repair technol-ogy and verified its reliability through testing. Lee and Lee

[35] used finite element analysis to examine the effects ofthe number of CFRP liners, the lining angle, and the numberof broken wires on a PCCP. Hu et al. [36] modeled the com-plex CFRP–concrete bond interface using ABAQUS softwarefor finite element analysis and analyzed the CFRP liner inrepairing a PCCP under combined loads.

The preceding results show that PCCP can be effectivelyrepaired. However, the use of CFRP liner in repairs requiresthe pipe flow to be interrupted over a long constructionperiod. It is also difficult to use CFRP liner to repair smalldiameter PCCP. A method of repairing a PCCP with exter-nally bonded CFRP was proposed. We used ABAQUS finiteelement software to create a three-dimensional model forthe repair of a PCCP with broken wires using externallybonded CFRP layers. The 3D FEM model takes account ofthe pressure of the soil, the weight of the PCCP, the weightof the water, and the hydrostatic pressure. We analyzed theeffect of using CFRP externally to repair a PCCP with brokenwires under combined loads and the effect of the number ofCFRP layers and the proportion of broken wires on therepair. The research undertaken in this study provides novelideas and methods for PCCP reinforcement, and the resultscan guide PCCP repair in practice.

2. 3D FEM Model Description

2.1. Model State Description. The type of PCCP used in the3D FEM model is ECP. The structure of ECP is shown inFigure 1. The geometry of PCCP is shown in Table 1.

Concrete and mortar were modeled using three-dimensional eight-node solid brick elements to representthem [37]. The concrete and mortar were meshed as 25200and 5459 elements. Two failure mechanisms were associatedwith them in the 3D FEM model: compressive crushing andtensile cracking. The ABAQUS concrete damaged plasticitymodel (CDP) was used to describe the mechanical behaviorof the concrete and mortar, which were both classified asbrittle materials. The concrete damaged plasticity model isshown in Figure 2.

In Figure 2, σc is the compressive stress of the concrete; σtis the tensile stress of the concrete; σc0 is the maximum elasticcompression stress; σt0 is the maximum elastic tensile stress;σcu is the maximum compression stress; dc is the damage fac-tor of compression; dt is the damage factor of tension; ωc isthe compressive recovery factor; ωt is the tensile recovery fac-tor; E0 is the initial elastic modulus.

The steel cylinder was represented by a four-node quad-rilateral element with reduced integration (S4R) because itis classified as a thin-walled structure. The steel cylinderwas meshed as 1380 elements.

The wrapping stress of the prestressing wires is 70% ofthe tensile strength of the wire. The stress–strain relation ofthe prestressing wire is shown in Equation (1).

f s =εsEs εs ≤ f sg/Es

f su 1 − 1 − 0:6133 εsEs/f suð Þ½ �2:25� �εs > f sg/Es

(

ð1Þ

2 International Journal of Polymer Science

where: fs is the stress of the prestressing wire; εs is the strain ofthe prestressing wire; Es is the elastic modulus of the prestres-sing wire; fsu is the tensile strength of the prestressing wire;and fsg=0.75× fsu.

A three-dimensional truss element (T3D2) was used torepresent the prestressing wires. The prestressing wires were

considered as many rings, and every ring was meshed as80 elements.

Three methods can be used for prestressing wires: equiv-alent load, cooling, and wrapping [38]. We used the coolingmethod. The cooling value is determined by:

Δt = FαEA

ð2Þ

where: Δt is the temperature decrease (°C); F is the stress ofthe prestressing wire (N); α is the coefficient of expansionof the prestressing wire (10−6/°C); E is the elastic modulusof the prestressing wire (Pa); and A is the cross-sectional areaof the prestressing wire (m2).

In the model, all broken wires were removed and theposition of the broken wires is the midpoint of the PCCP.

The soil was represented as three-dimensional eight-node brick elements described by the Mohr–Coulombmodel. The depth of soil covering the PCCP was 5m, andthere was soil cushion under the pipe.

The CFRP was represented as a four-node quadrilateralelement with reduced integration (S4R), like the steel cylin-der, and it was classified as elastic-brittle material. The direc-tion of the material is shown in Figure 3(c). Each layer ofCFRP is 0.167mm thick and 500mm wide.

2.2. Material Properties and the Model of Contact. Themechanical properties of the materials used in the modelare shown in Table 2.

Pipe–soil and CFRP–soil contact was simulated using thesurface-to-surface contact technique. This is described as“hard contact” with a penalty condition to allow the stresstransmission between the surfaces. The concrete and mortarwere combined, as were the CFRP and the mortar. The pre-stressing wires and the steel cylinder were embedded in theconcrete core. The bottom surface of the soil was fully con-strained, the normal directions were assigned to the shell,and the top surface was not constrained [39, 40].

2.3. Model Verification of PCCP. The size and materialparameters of the PCCP model used in this paper are thesame as those in [41]. Also, the calculation results of the soil-less PCCP model were compared with that in reference [41],as shown in Figure 4. The initial strain was calculated fromthe beginning of internal pressure. Figure 4 shows that thePCCP model agrees well with the results of reference, whichverifies the reliability of the PCCP structural model.

3. Effects of Different CFRP Thicknesses onthe Repair

Externally bonded CFRPs with different thicknesses weremodeled to study the effects of repair when there were com-bined loads. The proportion of broken wires on the PCCPwas 10%. The five models had identical conditions exceptfor the thickness of the CFRP. The five different models areshown in Table 3.

Using a hydrostatic pressure of 1.12MPa, which is thedesigned value, the effects of the repair on the whole pipe

Mortar coating

Prestressing wire

Outer concrete core

Steel cylinder

Inner cocrete core

Spigot end

Figure 1: Structure of ECP.

Table 1: Geometry of PCCP.

Dimension Size (mm)

Length of PCCP (h) 6000

Inner diameter of PCCP (Di) 2800

Total concrete thickness including cylinder (hc) 200

Thickness of the steel cylinder (ty) 1.5

Diameter of steel cylinder (Dy) 2923

Diameter of wires (d) 7

Spacing of wires 14.1

Thickness of mortar (tm) 32

𝜔t = 1

𝜔c = 1

𝜀c𝜀t

𝜔c = 0

𝜔t = 0

(1–dc) E0(1–dt) E0

𝜎c𝜎cu

𝜎t0

𝜎t

𝜎c0

E0

Figure 2: ABAQUS concrete damaged plasticity model.

3International Journal of Polymer Science

during the period of operation were analyzed. The stressesand strains of the concrete core, steel cylinder, prestressingwires, and CFRP at different positions were compared.

3.1. Effect of CFRP Repair on the Concrete Core. Figures 5 and6 show the circumferential strain of the outer and inner con-crete cores during the period of operation. In the Figures, theabscissa shows the distance along the length of the PCCP andthe ordinate shows the circumferential strain.

The Figures show that the concrete core had maximumstrain at the springline of the PCCP and that the springlinewas the weakest position. Using externally bonded CFRP torepair a PCCP with broken wires significantly reduces thecircumferential strain of the concrete core at the springline.Reduced strain on the outer concrete core can be clearly seen,and the concrete strain at the springline showed the greatestreduction when CFRP thickness was 0.334mm. As the CFRPthickness increased, the effect of the repair increased linearly.However, the strain of the concrete at the crown and theinvert changed very little.

In summary, using externally bonded CFRP to repair aPCCP with broken wires significantly increases the stress ofthe concrete core at the springline, especially for the outerconcrete core and less so for the inner concrete core, andthere was almost no effect at the crown and the invert. Alongthe length of the PCCP, the affected area of the concrete wasabout 3.3 times that of the broken-wire area.

Figure 7 shows the strain maps of the outer concrete coreat the springline under the combined loads. It shows the

effects of the repair using the externally bonded CFRP. Itcan be seen that the concrete strain decreased as CFRP thick-ness increased. The strain in the middle section of the PCCPwas larger and gradually decreased towards the ends, which isconsistent with Figure 5.

3.2. Effect of CFRP Repair on the Steel Cylinder. Figure 8shows the circumferential strain of the steel cylinder duringthe period of operation. The abscissa shows the length ofthe pipe and the ordinate shows the circumferential strain.

The Figure shows that the strain of the steel cylinder wassimilar to that of the concrete core. Using externally bondedCFRP to repair a PCCP with broken wires significantlyreduces the circumferential strain of the steel cylinder at thespringline. The steel cylinder strain at the springline showedthe greatest reduction when CFRP thickness was 0.334mm;as the CFRP thickness further increased, the steel cylinderstrain at the springline still decreased. However, the CFRPrepair had little effect on the circumferential strain of the steelcylinder at the crown or the invert. The affected area of thesteel cylinder along the PCCP was about 3.3 times that ofthe broken-wire area, which is consistent with the effects onthe concrete core.

3.3. Effect of CFRP Repair on the Prestressing Wires. Figure 9is the strain diagram of the prestressing wires during theperiod of operation. The abscissa shows the distance alongthe length of the PCCP, and the ordinate shows the circum-ferential strain.

The Figure shows that the strain of the prestressing wiresat the springline was slightly greater than those at the crownand the invert, similar to the strain of the concrete and thesteel cylinder. When the CFRP thickness was 0.334mm, thestrain of the prestressing wires at the springline decreasedsignificantly. However, as the CFRP thickness increased, thestrain of the prestressing wires hardly changed. The strainof the prestressing wires at the crown and the invert changedvery little as the CFRP thickness changed. The affected areaof the prestressing wires was about 3.3 times that of thebroken-wire area along the length of the PCCP, which is con-sistent with the previous analysis.

3.4. Analysis of CFRP Stress. Figure 10 is the circumferentialstrain diagram of CFRP during the period of operation. The

(a) (b)

12

(c)

Figure 3: Three-dimensional mesh: (a) soil; (b) PCCP; (c) CFRP.

Table 2: Material parameters.

MaterialDensity(kg/m3)

Elasticmodulus(MPa)

Poissonratio

Tensilestrength(MPa)

Concrete 2500 34500 0.2 2.64

Steel cylinder 7850 206000 0.3 215

Prestressing wire 7850 205000 0.3 1570

Mortar 2400 24165 0.2 3.49

CFRP 1796 240000 0.307 3400

PCCPfoundation

1890 80 0.29

Soil cushion 2200 40 0.35

Backfilling soil 1890 30 0.35

4 International Journal of Polymer Science

abscissa shows the CFRP thickness and the ordinate showsthe corresponding strain.

The Figure shows that the CFRP strain at the springlinewas significantly greater than that at the crown or the invertand that CFRP strain at the springline decreased as the thick-

ness increased. When CFRP thickness reached 0.668mm, thedecreasing trend lessened. The CFRP strains at the crownand the invert were almost unaffected by CFRP thickness,which agrees with the analysis of the results for the concretecore, steel cylinder, and prestressing wires.

Internal pressure (MPa)

Stra

in (𝜇

𝜀)

120

100

80

60

40

20

00.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Concrete of referenceWires of referenceMortar of reference

Concrete of simulationWires of simulationMortar of simulation

Figure 4: Strain comparisons between PCCP model and reference results.

Table 3: The five models.

Model name1 P-t-0 P-t-2 P-t-4 P-t-6 P-t-8

The thickness of CFRP(mm) Unrepaired 0.334 0.668 1.002 1.3361P is pipe, t is thickness, and the number indicates the number of layers of CFRP at 0.167mm per layer.

Stra

in (𝜇

𝜀)

440

400

360

320

280

240

200

0 1 2 3 4 5 6Springline (m)

Wire-broken area

P-t-0P-t-2P-t-4

P-t-6P-t-8

(a)

Stra

in (𝜇

𝜀)

150

148

146

144

142

140

138

0 1 2 3 4 5 6Crown (m)

P-t-0P-t-2P-t-4

P-t-6P-t-8

(b)

150

148

146

144

142

140

138

Stra

in (𝜇

𝜀)

0 1 2 3 4 5 6Invert (m)

P-t-0P-t-2P-t-4

P-t-6P-t-8

(c)

Figure 5: Circumferential strain of the outer concrete core: (a) springline; (b) crown; (c) invert.

5International Journal of Polymer Science

Figure 11 shows the stress maps of CFRP under com-bined internal and external loads. The maps show that whenthe thickness of CFRP was 0.334mm, CFRP stress was about

136MPa, which was much less than the ultimate tensilestrength. As CFRP thickness increased, the stress graduallydecreased.

0

170

Stra

in (𝜇

𝜀)

180

190

200

210

220

230

1 2 3 4 5 6Springline (m)

P-t-0P-t-2P-t-4

P-t-6P-t-8

Wire-broken area

(a)

184186188190192194196198200

Stra

in (𝜇

𝜀)

0 1 2 3 4 5 6Crown (m)

P-t-0P-t-2P-t-4

P-t-6P-t-8

(b)

184186188190192194196198200

Stra

in (𝜇

𝜀)

0 1 2 3 4 5 6Invert (m)

P-t-0P-t-2P-t-4

P-t-6P-t-8

(c)

Figure 6: Circumferential strain of the inner concrete core under combined loads: (a) springline; (b) crown; (c) invert.

LE, LE22 (assembly)(Avg: 75%)

+3.878e-04+3.279e-04+2.681e-04+2.082e-04+1.484e-04+8.852e-05+2.867e-05−3.118e-05−9.103e-05−1.509e-04−2.107e-04−2.706e-04−3.304e-04

(a) (b) (c) (d) (e)

Figure 7: Strain maps of outer concrete core at the springline under combined loads: (a) P-t-0; (b) P-t-2; (c) P-t-4; (d) P-t-6; (e) P-t-8.

230

220

210

200

190

180

170

240

Stra

in (𝜇

𝜀)

Wire-broken area

P-t-0P-t-2P-t-4

P-t-6P-t-8

0 1 2 3 4 5 6Springline (m)

(a)

172

174

176

178

180

182

184

186

Stra

in (𝜇

𝜀)

0 1 2 3 4 5 6Crown (m)

P-t-0P-t-2P-t-4

P-t-6P-t-8

(b)

172

174

176

178

180

182

184

186

Stra

in (𝜇

𝜀)

0 1 2 3 4 5 6Invert (m)

P-t-0P-t-2P-t-4

P-t-6P-t-8

(c)

Figure 8: Circumferential strain of the steel cylinder under combined loads: (a) springline; (b) crown; (c) invert.

6 International Journal of Polymer Science

4. Effects of Repairs for Different WireBreakage Rates

In practice, the number of broken wires may vary for differ-ent PCCPs. Therefore, we examined the effects of a repairfor different wire breakage rates. The CFRP was 500mmwideand 1.002mm thick in the models used for this analysis. Thewire breakage rates were 5%, 10%, 15% and 20%. The modelsare shown in Figure 12.

We examined the effects of the repair on the whole pipeduring the period of operation at a hydrostatic pressure of1.12MPa, which is the designed value. We compared thestress and strain of the concrete core, steel cylinder, pre-stressing wires and CFRP when the wire breakage rateswere different.

4.1. Effect of Wire Breakage Rates on the Concrete Core. Thedamage maps of the concrete core under the combined inter-nal pressure and external loads are shown in Figure 13. The

Figure shows that when the wire breakage rate was 5%, therewas no damage to the concrete core. As the wire breakagerate increased, damage to the concrete core graduallyincreased. When the wire breakage rate was 10%, a little ten-sile damage occurred at the middle of the springline. How-ever, the damage was not serious, and there was no damageto the concrete core at the crown or the invert, and the PCCPoperates normally. When the wire breakage rate reached15%, the concrete damage was serious at the springline, andthe damage extended to the crown and the invert. At a 20%wire breakage rate, serious damage occurred around theentire circumference at the center of the pipe, but the twoends of the pipe were almost unaffected.

The concrete damage levels suggest that CFRP 500mmwide and 1.002mm thick can repair a PCCP having a wirebreakage rate of <10%, but when the rate is greater, themethod of repair must be reconsidered.

4.2. Effect of Wire Breakage Rates on the Steel Cylinder.Figure 14 shows the circumferential strain of the steel cylin-der during the period of operation. The abscissa shows thedistance along the length of the PCCP, and the ordinateshows the circumferential strain. The Figure shows that thestrain at the springline was greater than at the crown or theinvert. When the wire breakage rate was 5%, there was almostno effect on the steel cylinder. As the wire breakage rateincreased, the strain of the steel cylinder increased at thecenter of the pipe. When the wire breakage rate was 20%,the circumferential strain of the steel cylinder was 1025 με,and the steel cylinder yielded. The wire breakage rate had asignificant effect on the steel cylinder.

4.3. Effect of Wire Breakage Rates on the Prestressing Wires.Figure 15 shows the strain of the prestressing wires duringthe operation period. The abscissa shows the length of thePCCP, and the ordinate shows the strain. The Figure showsthat the strain of the prestressing wires at the springlinewas greater than at the crown or the invert. The strains ofthe crown and the invert did not change much when the wire

Stra

in (𝜇

𝜀)

0 1 2 3 4 5 6Springline (m)

Wire-broken area

200

220

240

260

280

P-t-0P-t-2P-t-4

P-t-6P-t-8

(a)

Stra

in (𝜇

𝜀)

138

137

136

135

134

2.0 2.5 3.0 3.5 4.0Crown (m)

P-t-0P-t-2P-t-4

P-t-6P-t-8

(b)

Stra

in (𝜇

𝜀)

138

137

136

135

134

2.0 2.5 3.0 3.5 4.0Invert (m)

P-t-0P-t-2P-t-4

P-t-6P-t-8

(c)

Figure 9: Strain of prestressing wires under combined loads: (a) springline; (b) crown; (c) invert.

Stra

in (𝜇

𝜀)

The thickness of CFRP (× 0.167 mm)

SpringlineCrownInvert

10 2 3 4 65 7 8 9

500

450

400

350

300

130128

Figure 10: Strain of CFRP under combined loads.

7International Journal of Polymer Science

breakage rate increased from 5% to 10%. In general, thewire breakage rate had a large influence on prestressingwire strain.

4.4. Effect of Wire Breakage Rates on CFRP. Figure 16 showsthe circumferential strain of the CFRP during the period ofoperation. The abscissa shows the wire breakage rates and

S, S22 (assembly-SNEG, (fraction = -(Avg: 75%)

+1.364e+08

+1.250e+08

+1.137e+08

+1.023e+08

+9.093e+07

+7.957e+07

+6.820e+07

+5.683e+07

+4.547e+07

+3.410e+07

+2.273e+07

+1.137e+07

+0.000e+00

−1.432e+05

(a) (b) (c) (d)

Figure 11: Stress maps of CFRP under combined loads: (a) P-t-2; (b) P-t-4; (c) P-t-6; (d) P-t-8.

5%

(a)

10%

(b)

15%

(c)

20%

(d)

Figure 12: The different models: (a) P-r-5; (b) P-r-10; (c) P-r-15; (d) P-r-20. (P is pipe, r is rate, and the number is the value of the wirebreakage rate).

Damage(Avg: 100%)

(a) (b) (c) (d)

+9.888e-01+9.064e-01+8.240e-01+7.416e-01+6.592e-01+5.768e-01+4.944e-01+4.120e-01+3.296e-01+2.472e-01+1.648e-01+8.240e-02+0.000e+00

Figure 13: Concrete damage under combined loads: (a) P-r-5; (b) P-r-10; (c) P-r-15; (d) P-r-20.

8 International Journal of Polymer Science

the ordinate shows the circumferential strain. The Figureshows that CFRP strain at the springline was greater thanat the crown or the invert. CFRP strains at the crown andat the invert did not change much when the wire breakagerate increased from 5% to 10%. This phenomenon was con-sistent with the results for the strain of prestressing wires.The wire breakage rates had a significant effect on CFRP.Figure 17 shows the stress maps of CFRP under combinedloads. The maximum CFRP stress was 290.6MPa when thewire breakage rate was 20%, which was much less than theultimate tensile strength.

5. Conclusion

In this study, externally bonded CFRP of different thick-nesses was used to repair a PCCP with broken wires. We con-structed a three-dimensional finite element model of therepaired PCCP, using ABAQUS software, that took intoaccount the pressure of the soil, the weight of the water, theweight of the PCCP, and the hydrostatic pressure. The effectsof the repairs on each PCCP component material for

Stra

in (𝜇

𝜀)

0 1 2 3 4 5 6Springline (m)

450

400

350

300

250

200

150

11001000900800700600500400300200100

P-r-20P-r-15P-r-5

P-r-10

(a)

Stra

in (𝜇

𝜀)

1000900800700600500400300200100

0 1 2 3 4 5 6Crown (m)

250240230220210200190180170160

P-r-20P-r-15P-r-5

P-r-10

(b)

Stra

in (𝜇

𝜀)

250240230220210200190180170160

0 1 2 3 4 5 6

1000900800700600500400300200100

Invert (m)

P-r-5P-r-20P-r-15

P-r-10

(c)

Figure 14: Strain of steel cylinder under combined loads: (a) spring; (b) crown; (c) invert.

Stra

in (𝜇

𝜀)

0 1 2 3 4 5 6Springline (m)

340320300280260240220200180160

P-r-5P-r-10 P-r-20

P-r-15

(a)

260

240

220

200

180

160

140

120

1000 1 2 3 4 5 6

Crown (m)

Stra

in (𝜇

𝜀)

P-r-5P-r-10 P-r-20

P-r-15

(b)

Stra

in (𝜇

𝜀)

260

240

220

200

180

160

140

120

1000 1 2 3 4 5 6

Invert (m)P-r-5P-r-10 P-r-20

P-r-15

(c)

Figure 15: Strain of prestressing wires under combined loads: (a) springline; (b) crown; (c) invert.

1000

800

600

400

200

400

350

300

250

200

150

100

Wire breakage rates (%)5 10 15 20

Stra

in (𝜇

𝜀)

SpringlineInvertCrown

Figure 16: Strain of CFRP under combined loads.

9International Journal of Polymer Science

different CFRP thicknesses and different wire breakage rateswere analyzed. The main conclusions are as follows.

(1) Under the combined loads, the stresses of the con-crete core and the prestressing wires were greater atthe springline than at the crown or the invert. Thestrain at the springline can be reduced by repairingthe PCCP with the CFRP.

(2) When the rate of wire breakage was 10%, the strainedarea of each material was about 3.3 times the broken-wire area along the length of the PCCP; when the rateof wire breakage was <10%, CFRP that is 1.002mmthick and 500mm wide can be used for repair.

(3) The rate of wire breakage had a large influence on thestrain of each material. However, the stress of CFRPis much less than its tensile strength.

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

This work was supported by the National Key Research andDevelopment Program of China (No. 2016YFC0802400),the National Natural Science Foundation of China (No.51978630, 51678536), the Program for Science and Technol-ogy Innovation Talents in Universities of Henan Province(Grant No. 19HASTIT043), the Outstanding Young TalentResearch Fund of Zhengzhou University (1621323001)and the Program for Innovative Research Team (inScience and Technology) in University of Henan Province(18IRTSTHN007). The authors would like to thank forthese financial supports.

References

[1] ANSI/AWWA C304-2014, Design of Prestressed Concrete Cyl-inder Pipe, American National Standards Institute, AmericanWater Works Association, 2014.

[2] SL702-2015, Technical Specifications of Prestressed ConcreteCylinder Pipe, Beijing: China Water & Power Press, 2015.

[3] C. W. Ross, “Tests of prestressed concrete pipes containinga steel cylinder,” ACI Journal Proceedings, vol. 42, no. 9,pp. 37–48, 1945.

[4] H. F. Kennison, “Tests on prestressed concrete embedded cyl-inder pipe,” Journal of the Hydraulics Division, vol. 86, no. 9,pp. 77–98, 1960.

[5] J. T. Mccall and F. P. Valenziano, “Combined load tests on 108inch prestressed concrete embedded cylinder pipe,” in Pro-ceedings of Symposia on Prestressed Concrete, pp. 1–16, Sidney,Australia, 1961.

[6] R. Gomez, D. Muñoz, R. Vera, and J. A. Escobar, “Structuralmodel for stress evaluation of Prestressed concrete pipesof the Cutzamala system,” Pipeline Engineering, vol. 21,pp. 831–856, 2004.

[7] S. R. Zhang and C. X. Zhang, “Numerical simulation analysisof prestressed concrete cylinder pipe,” Journal of Harbin Insti-tute of Technology, vol. 41, no. 8, pp. 118–122, 2009.

[8] T. S. Dou, B. Q. Cheng, H. Hu, S. F. Xia, J. X. Yang, andQ. Zhang, “The prototype test study of prestressed concretecylinder pipe structure deformation law I. the internal pres-sure,” Journal of Hydraulic Engineering, vol. 48, no. 12,pp. 1438–1446, 2017.

[9] T. S. Dou, B. Q. Cheng, H. Hu, S. F. Xia, J. X. Yang, andQ. Zhang, “The prototype test study of prestressed concretecylinder pipe structure deformation law II. The external pres-sure,” Journal of Hydraulic Engineering, vol. 49, no. 2, pp. 207–215, 2018.

[10] Y. Zhang, Z. G. Yan, H. H. Zhu, and J. W. Ju, “Experimentalstudy on the structural behaviors of jacking prestressedconcrete cylinder pipe,” Tunnelling and Underground SpaceTechnology, vol. 73, pp. 60–70, 2018.

[11] M. S. Zarghamee, R. P. Ojdrovic, and W. R. Dana, “Coatingdelamination by radial tension in Prestressed concrete pipe.I: experiments,” Journal of Structural Engineering, vol. 119,no. 9, pp. 2701–2719, 1993.

[12] M. S. Zarghamee, R. P. Ojdrovic, and W. R. Dana, “Coatingdelamination by radial tension in Prestressed concrete pipe.

S, S22 (assembly_SNEG, (fraction = -(Avg: 75%)

+2.906e+08+2.663e+08+2.421e+08+2.179e+08+1.937e+08+1.695e+08+1.453e+08+1.211e+08+9.685e+07+7.264e+07+4.843e+07+2.421e+07+0.000e+00

(d)(c)(b)(a)

Crown

Springline

Invert

Figure 17: Stress maps of CFRP under combined loads: (a) P-r-5; (b) P-r-10; (c) P-r-15; (d) P-r-20.

10 International Journal of Polymer Science

II: analysis,” Journal of Structural Engineering, vol. 119, no. 9,pp. 2720–2732, 1993.

[13] S. W. Hu, J. Shen, D. L. Wang, and X. Cai, “Experiment andnumerical analysis on super caliber prestressed concrete cylin-der pipes with cracks,” Journal of Hydraulic Engineering,vol. 41, no. 7, pp. 876–882, 2010.

[14] Q. Gong, H. Zhu, Z. Yan, B. Huang, Y. Zhang, and Z. Dong,“Fracture and delamination assessment of prestressed com-posite concrete for use with pipe jacking method,”Mathemat-ical Problems in Engineering, vol. 2015, Article ID 579869, 11pages, 2015.

[15] L. Q. Sun, J. J. Zhang, H. Li, S. W. Yan, and Z. L. Huo,“Research on key factors influencing relative angle of pre-stressed concrete cylinder pipe in soft soil foundation,” Rockand Soil Mechanics, vol. 36, no. S1, pp. 293–298, 2015.

[16] Y. Zhang, Z. G. Yan, and H. H. Zhu, “Site-based researches onmechanical behavior of new large-diameter pipes during pipejacking,” Chinese Journal of Geotechnical Engineering, vol. 39,no. 10, pp. 1842–1850, 2017.

[17] Z. Xu, X. Feng, S. Zhong, and W. Wu, “Surface crack detectionin Prestressed concrete cylinder pipes using BOTDA strainsensors,” Mathematical Problems in Engineering, vol. 2017,Article ID 9259062, 12 pages, 2017.

[18] Y. G. Diab and T. Bonierbale, “A numerical modeling and aproposal for rehabilitation of PCCPs,” in Pipeline Division Spe-cialty Conference 2001, pp. 1–8, San Diego, California, UnitedStates, 2001.

[19] M. S. Zarghamee, D. W. Eggers, and R. P. Ojdrovic, “Finite-element modeling of failure of PCCP with broken wiressubjected to combined loads,” in Pipeline Division SpecialtyConference 2002, pp. 1–17, Cleveland, Ohio, United States,2002.

[20] M. S. Zarghamee, “Hydrostatic pressure testing of prestressedconcrete cylinder pipe with broken wires,” in Pipeline Engi-neering and Construction International Conference 2003,pp. 294–303, Baltimore, Maryland, United States, 2003.

[21] M. S. Zarghamee, D. W. Eggers, R. P. Ojdrovic, and B. Rose,“Risk analysis of Prestressed cylinder pipe with broken wires,”Pipelines, vol. 83, pp. 599–609, 2003.

[22] S. W. Hu and J. Shen, “Study on impact from wire-breakinginside of super-large diameter PCCP on its bearing capacity,”Water Resources and Hydropower Engineering, vol. 42, no. 4,pp. 41–44, 2011.

[23] S. Ge and S. Sinha, “Effect of mortar Coating’s bond quality onthe structural integrity of Prestressed concrete cylinder pipewith broken wires,” Journal of Materials Science Research,vol. 4, no. 3, pp. 59–75, 2015.

[24] M. Hajali, A. Alavinasab, and C. A. Shdid, “Effect of the loca-tion of broken wire wraps on the failure pressure of prestressedconcrete cylinder pipes,” Structural Concrete, vol. 16, no. 2,pp. 297–303, 2015.

[25] M. Hajali, A. Alavinasab, and C. A. Shdid, “Effect of the num-ber of broken wire wraps on the structural performance ofPCCP with full interaction at the gasket joint,” Journal of Pipe-line Systems Engineering and Practice, vol. 7, no. 2, article04015026, 2016.

[26] M. Hajali, A. Alavinasab, and C. Abi Shdid, “Structural per-formance of buried prestressed concrete cylinder pipes withharnessed joints interaction using numerical modeling,”Tunnelling and Underground Space Technology, vol. 51,pp. 11–19, 2016.

[27] J.-Y. Lee, H.-O. Shin, K.-H. Min, and Y.-S. Yoon, “Flexuralassessment of blast-damaged rc beams retrofitted with cfrpsheet and steel fiber,” International Journal of Polymer Science,vol. 2018, Article ID 2036436, 9 pages, 2018.

[28] G. Cicala, G. Cristaldi, G. Recca, G. Ziegmann, A. Elsabbagh,and M. Dickert, An Hybrid Glass/Hemp Fibers Solution FRPPipes: Technical and Economic Advantages of Hand Lay upVs Light RTM, American Institute of Physics, 2008.

[29] G. Cicala, G. Cristaldi, G. Recca, G. Ziegmann, A. el-Sabbagh,and M. Dickert, “Properties and performances of varioushybrid glass/natural fibre composites for curved pipes,”Materials & Design, vol. 30, no. 7, pp. 2538–2542, 2009.

[30] G. Cicala, I. Blanco, A. Latteri, G. Ognibene, F. AgatinoBottino, and M. Fragalà, “PES/POSS soluble veils as advancedmodifiers for multifunctional Fiber reinforced composites,”Polymers, vol. 9, no. 12, p. 281, 2017.

[31] D. C. Lee and V.M. Karbhari, “Rehabilitation of large diameterPrestressed cylinder concrete pipe (PCCP) with FRP compos-ites–experimental investigation,” Advances in Structural Engi-neering, vol. 8, no. 1, pp. 31–44, 2005.

[32] M. Engindeniz, R. P. Ojdrovic, and M. S. Zarghamee, “Qualityassurance procedures for repair of concrete pressure pipeswith CFRP composites,” in Pipelines Conference 2011,pp. 616–627, Seattle, Washington, United States, 2011.

[33] M. Engindeniz and M. S. Zarghamee, “Experimental basis ofCFRP renewal of PCCP,” in Pipelines 2014, pp. 920–931,Portland, Oregon, 2014.

[34] T. Alkhrdaji, S. Rocca, and N. Galati, “PCCP rehabilitationusing advanced hybrid FRP composite liner,” in Pipelines2013, pp. 672–681, Fort Worth, Texas, United States, 2013.

[35] Y. Lee and E. T. Lee, “Analysis of prestressed concrete cylinderpipes with fiber reinforced polymer,” KSCE Journal of CivilEngineering, vol. 19, no. 3, pp. 682–688, 2015.

[36] H. Hu, F. Niu, T. Dou, and H. Zhang, “Rehabilitation effectevaluation of CFRP-lined Prestressed concrete cylinder pipeunder combined loads using numerical simulation,” Mathe-matical Problems in Engineering, vol. 2018, Article ID3268962, 16 pages, 2018.

[37] B. Li, H. Y. Fang, H. He, K. J. Yang, C. Chen, and F. M. Wang,“Numerical simulation and full-scale test on dynamic responseof corroded concrete pipelines under multi-field coupling,”Construction and Building Materials, vol. 200, pp. 368–386,2019.

[38] H. Xiong, P. Li, and Q. Li, “FE model for simulating wire-wrapping during prestressing of an embedded prestressedconcrete cylinder pipe,” Simulation Modelling Practice andTheory, vol. 18, no. 5, pp. 624–636, 2010.

[39] H. Fang, B. Li, F. Wang, Y. Wang, and C. Cui, “Themechanical behaviour of drainage pipeline under traffic loadbefore and after polymer grouting trenchless repairing,”Tunnelling and Underground Space Technology, vol. 74,pp. 185–194, 2018.

[40] F. M. Wang, H. Y. Fang, B. Li, and C. Chen, “Dynamicresponse analysis of drainage pipe with gasketed bell-and-spigot joints subjected to traffic load,” Chinese Journal of Geo-technical Engineering, vol. 40, no. 12, pp. 2274–2280, 2018.

[41] B. Hu, H. Fang, F. Wang, and K. Zhai, “Full-scale test andnumerical simulation study on load-carrying capacity of pre-stressed concrete cylinder pipe (PCCP) with broken wiresunder internal water pressure,” Engineering Failure Analysis,vol. 104, pp. 513–530, 2019.

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