Prestressed concrete cylinder pipe (PCCP) has been widely used for water transfer and transit projects. However, prestressing wire breaks may result in the rupture of pipes and cause catastrophes. Carbon fiber reinforced polymer (CFRP) liners adhered to the inner concrete core can provide an effective method of internal repair and strengthening of PCCP. To evaluate the rehabilitation effect of CFRP-lined PCCP under combined loads, two contrasting three-dimensional finite element models that investigated the visual cracking of concrete and the yielding of steel cylinders were developed. A conceptual zone was introduced to analyze the different states of the pipe during the phase of wire break. In particular, the complex CFRP-concrete bonded interface was simulated by a cohesive element layer with a bilinear traction-separation response. The results show that CFRP has a good rehabilitation effect on the inner concrete core and steel cylinder but only a slight effect on the outer concrete core, prestressing wire, or mortar. A one-hoop CFRP layer diminishes the area of a yielding steel cylinder of 4.72 m2. In addition, CFRP works more effectively along with an increase in the number of broken wires. This research can provide a basis for strengthening distressed PCCP pipelines.
Prestressed concrete cylinder pipe (PCCP) has been widely used in many areas including municipal, industrial, and water diversion because of its structural advantages such as a large diameter, low water head loss, and strong earthquake resistance. PCCP generally consists of a concrete core, high-tensile steel wires that spirally wound around the concrete, a steel cylinder encased in concrete, and a mortar coating layer. The prestressing wires are typically designed to withstand all of the hydrostatic pressure. Owing to corrosion and hydrogen embrittlement, prestressing wire may break. If many wires broke, the rupture of pipe can lead to a catastrophe. Therefore, it is necessary for water supply engineers to understand the wire-break process of PCCP and determine a feasible repair plan.
Combined with former theories and technologies, some methods were proposed to rehabilitate PCCP. However, all these methods require excavation of the cover soil and processing of the complicated construction technologies by heavy machinery, which are costly and time-consuming [
Lee and Karbhari [
Lee et al. [
To study the nonlinear behavior and ultimate resisting capacity of a CFRP-repaired concrete structure, many numerical modeling methods have been adopted [
Installing CFRP liner, a completely new method for PCCP renewal, has a distinctive failure pattern [
The main function of PCCP is to divert water resources under internal loads plus external soil pressure. Therefore, maintaining a safe service state under combined loads is the essential level that the pipe must reach. For the finite element (FE) models, a three-dimensional model A of PCCP and another model B of CFRP-lined PCCP with one longitudinal CFRP and one hoop CFRP under combined loads are developed by using the ABAQUS/Standard program. Obviously, the hoop CFRP is designed to improve the hoop structural performance of distressed pipe. In the distressed pipe, bending between the broken wire zone without any prestress and the adjacent zone where it is affected by the broken wire zone will cause uneven radial displacement. This displacement may result in transverse gaps between waves of CFRP. As a result, water can bypass the CFRP liner through gaps, rendering the liner ineffective [
CFRP-lined PCCP consists of various FRP layers and PCCP components. Figure
Typical CFRP-lined PCCP.
The internal working pressure
FE model of CFRP-lined PCCP: (a) schematic diagram and (b) detailed drawing.
To prevent the PCCP from cracking under different embankment conditions, the backfilling soil and bedding soil of the pipe can be divided into several zones. In these models, the surrounding soil of PCCP was partitioned into six different areas: the in situ soil, bedding soil zone, backfilling soil zone A, the foundation of the pipe, buffering soil zone, and backfilling soil zone B, as shown in Figure
Soil and entire assembly of FE mesh model: (a) six different zones of surrounding soil and (b) three-dimensional mesh geometry.
In these two models, every component was meshed based on the geometric characteristics. Soil, concrete, and mortar were simulated using three-dimensional eight-node brick elements (C3D8R). An eight-node three-dimensional cohesive element (COH3D8) layer was used to model the CFRP-concrete interface. According to the property of the cohesive element, CFRP could be meshed with C3D8R element. The prestressing wire was simulated using a three-dimensional truss element (T3D2). A four-node, quadrilateral, stress/displacement shell element with reduced integration (S4R) was used to represent the steel cylinder. Furthermore, the C3D8R and S4R elements adopted the total stiffness approach as the hourglass control approach. The concrete core, mortar, prestressing wires, steel cylinder, and soil had 9600, 4800, 28000, 1600, and 21000 elements, respectively. The cohesive element layer and CFRP had 1600 and 3200 elements, respectively. The entire model is shown in Figure
With regard to the boundary conditions, the nodes on the bottom surface of the model were fully fixed, the nodes on the top surface of the model were free, the nodes on the left and right surfaces of the model were specified with no horizontal displacement or rotation because of the vertical consolidation settlement, and the nodes on the front and back surfaces of the model were restricted in the pipeline longitudinal direction. Typical loads such as the weight of soil, pipe, and internal/surge pressure were considered in the model.
Concrete and mortar are both brittle materials and have two main failure mechanisms: tensile cracking and compressive crushing. The concrete damaged plasticity (CDP) model in the ABAQUS material model can be used to present these two failure patterns by accounting for the tensile equivalent plastic strains
Concrete constitutive relationship curves: (a) concrete uniaxial tensile curve and (b) concrete uniaxial compressive curve.
On the other hand, strain softening also decreases the elastic modulus. The reduction of the elastic modulus
In terms of the effective stresses, the yield function takes the following form [
Yield surface in the deviatoric face with different
The plastic flow rule determines the direction and magnitude of plastic deformation. The CDP model utilizes a nonassociated Drucker-Prager hyperbolic function to define potential function
The gross wrapping stress of the prestressing wire
The steel cylinder adopts the von Mises elastoplastic stress-strain relationship with a linear elastic branch and a constant stress after reaching the yield strength.
CFRP is treated as an orthotropic elastic-brittle material. In the fiber direction, once the stress reaches the ultimate tensile strength, CFRP will fracture. The unidirectional fiber laminate thickness, each fiber orientation, and constitutive constants are required as input for the numerical model of the CFRP liner. Regarding the surrounding soils, a modified Mohr-Coulomb model is used to calculate earth loads on PCCP buried pipes.
The concrete core was modeled with a compressive strength of 44.00 MPa and a tensile strength of 3.86 MPa. The mortar coating had a compressive strength and tensile strength of 47.5 MPa and 3.58 MPa, respectively. The uniaxial stress-strain relationships of the concrete and mortar were based upon a current standard [
Material properties of PCCP and soil.
Material | Density (kg/m3) | Young’s modulus (MPa) | Poisson’s Ratio | Cohesion, c(kPa) | Angle of internal friction, | Dilation, |
---|---|---|---|---|---|---|
Concrete core | 2500 | 27862 | 0.2 | — | — | — |
Mortar coating | 2350 | 25270 | 0.2 | — | — | — |
Prestressing wire | 7850 | 193050 | 0.3 | — | — | — |
Steel cylinder | 7850 | 206850 | 0.3 | — | — | — |
Undisturbed soil zone | 2100 | 250 | 0.32 | 65 | 30 | 0.1 |
Bedding soil zone | 2000 | 160 | 0.34 | 30 | 26 | 0.1 |
Backfilling soil zone A | 2000 | 180 | 0.33 | 35 | 28 | 0.1 |
Foundation of pipe | 2000 | 180 | 0.33 | 35 | 28 | 0.1 |
Buffering soil zone | 2000 | 150 | 0.34 | 20 | 25 | 0.1 |
Backfilling soil zone B | 2000 | 210 | 0.33 | 50 | 30 | 0.1 |
Material properties of CFRP.
E11 | E22 = E33 | G12 = G13 | G23 | ||
| |||||
75.0 GPa | 6.2 GPa | 2.3 GPa | 2.2 GPa | 0.3 | 0.4 |
All components in model A and model B were modeled as independent parts. Then, all parts were assembled together as an entire model. The interactions between components were vital to the composite pipe. The steel cylinder was embedded into the concrete core. Meanwhile, the prestressing wire was also embedded into the mortar coating. Concrete and mortar were completely tied together without considering delamination. The interface between the pipe and soil was modeled by surface-to-surface contact with small sliding, in which the value of the interface friction was 0.35. Through utilizing the temperature-drop method, the prestress was applied to the prestressing wire.
The CFRP-concrete interface has complex relationships, containing ruptures, debonding, and shearing behaviors [
Bilinear constitutive traction-separation response of cohesive element: (a) typical bilinear traction-separation model, (b) damage propagation occurring earlier, and (c) mixed-mode bilinear law.
The initial elastic behavior relates the nominal stresses to the nominal strains across the interface by an elastic constitutive matrix. The nominal stresses are the force components that present the traction variables, and the nominal strains present the separation variables. In a three-dimensional model, the nominal traction stress vector
However, once the damage initiation criterion is met, the interface begins to suffer damage according to the damage evolution law. The following quadratic nominal stress criterion is used to represent the damage initiation criterion:
A scalar damage variable
Actually, interface will often fail as a mixed mode along three directions in which the relative proportions of the normal and shear deformation are quantified. The damage starts propagating even before one of the limit tractions is attained individually, as shown in Figure
The fracture energy is dissipated as a result of the damage process. It is equal to the area under the traction-separation curve. Figure
The simulated procedure covered two phases: progressively pressurizing to 1.12 MPa in 0.1-MPa intervals, followed by a stepwise wire break under the former steady internal load. The maximum design internal load was 1.12 MPa when considering the working pressure and transient pressure. With an increase in the number of broken wires, the internal load bearing capacity of the pipe decreases continuously. When the number of broken wires is high, the distressed pipe can no longer withstand the original pressure. According to previous experience, the steady pressure should be decreased.
In the second phase, a wire break started at the central location in the longitudinal direction of the pipe. Then, the break extended to the spigot end and bell end alternately with five broken wires at a time. The detailed scenario of the broken wires is shown in Figure
Sequence of wire break in second phase.
During a gradual increase in the number of broken wires, the full composite zone without prestress loss can be converted into a broken wire zone. The pipe was divided into three zones along the longitudinal length to present distinct states during the wire-break phase. As shown in Figure
Three distinct zones during wire-break period.
For each component, strains at the pipe crown, pipe springline, and pipe invert in four sections (S1, S2, S3, and S4 stand for monitoring sections 1, 2, 3, and 4, respectively) were acquired, as shown in Figure
Arrangement of monitoring point on each component.
Without any broken wires, all components of the pipe remain in the elastic domain. The internal load is mainly withstood by prestressing wires. The strains of the concrete, steel cylinder, wire, and mortar in model A are remarkably close to those in model B. CFRP reaches a peak stress of 11.8 MPa under an internal flow pressure of 1.12 MPa, which is much lower than the ultimate strength. CFRP does not play a role in relieving the deformation of the pipe. Owing to the earth pressure, the deformation at the crown, invert, and springline is different. For CFRP, the inner concrete core, and the steel cylinder, the strains at the springline are greater than those at the crown and invert. By contrast, the strains at the springline are lower than those at the crown and invert for the outer concrete core, wire, and mortar. The reason for this phenomenon is that the external part of the pipe wall at the springline and the interior part of the pipe wall at the crown and invert are tensile, while the opposite parts at these hoop locations are compressive under external loads [
Typical deformation of PCCP under external load (prestressing wire is not present).
Strain curves of CFRP during phase of wire break.
S1 is always in the broken wire zone. Figure
Stress in CFRP at end of phase of wire break.
S2 is in the transition zone when the number of broken wires is less than 70 and in the broken wire zone when the number exceeds 75. The impact that the broken wires have on the transition zone decreases successively with an increase in distance. Like the strain of CFRP at S1, the strain at S2 also rises rapidly at a lower rate. The strains at the crown, invert, and springline for S3 stay at a relatively low level, illustrating light damage for S3. S4 is in the full composite zone prior to reaching 160 broken wires. The strain starts growing slightly as the number of broken wires increases further, which indicates that S4 turns into a transition zone. During the entire phase of the wire break, S4 experiences little damage.
In terms of the seriously damaged areas S1 and S2, the strain of CFRP at the crown is greater than that at the invert and springline, stating the crown would fail first as the number of broken wires increases. In other words, the crown is the most seriously damaged part, and CFRP best contributes to its material properties. The three peak values on each curve can be attributed to the decline of the internal flow pressure.
The inner concrete core at S1 experiences compressive plastic damage at 45 broken wires. The higher the number of broken wires, the greater the damage. Since the CDP model does not reflect cracks on concrete directly, 11 times the tensile strain of concrete is taken as the onset of a visual crack [
Number of broken wires required to cause onset of visual crack for inner concrete core.
Component | S1 | S2 | ||||
---|---|---|---|---|---|---|
Crown | Springline | Invert | Crown | Springline | Invert | |
Model A | 125 | 130 | 125 | 160 | 170 | 175 |
Model B | 130 | 165 | no visual crack | 165 | no visual crack | no visual crack |
Proportion of improvement | 4.00% | 26.92% | no value | 3.13% | no value | no value |
Strain curves of inner concrete core during phase of wire break: (a) strain at S1, (b) strain at S2, and (c) strain at S3 and S4.
Strain curves of steel cylinder during phase of wire break: (a) strain at S1 and (b) strain at S2.
These results indicate that CFRP causes a stress redistribution and decreases the strain of the inner concrete core. This effect can be seen as protecting the concrete. Regarding the proportion of improvement, the invert shows the strongest increasing trend, followed by the springline and crown. This demonstrates that CFRP has the best rehabilitation effect on the invert, followed by the springline and the crown of the inner concrete core.
Regarding S2, Table
The strain of the steel cylinder at S1 and S2 shows a rapidly rising rate when the number of broken wires is over 45, which indicates it undertakes part of the internal pressure. Owing to the compressive prestrain provided by prestressing wires, the yield strain of the cylinder is 1377
Number of broken wires required to yield the steel cylinder.
Component | S1 | S2 | ||||
---|---|---|---|---|---|---|
Crown | Springline | Invert | Crown | Springline | Invert | |
Model A | 115 | 130 | 170 | 130 | 170 | no yield |
Model B | 120 | 160 | no yield | 135 | no yield | no yield |
Proportion of improvement | 4.35% | 23.08% | no value | 3.85% | no value | no value |
At the end of the second phase, the yielding areas of the cylinder are counted, as shown in Table
Area of yielding cylinder and relevant proportions.
Model | Area of yielding cylinder | Area of cylinder in broken wire zone | Area of entire cylinder | | | |
---|---|---|---|---|---|---|
Model A | 19.75 | 32.85 | 65.71 | 49.99% | 60.12% | 30.06% |
Model B | 15.03 | 32.85 | 65.71 | 51.39% | 40.51% | 20.25% |
The outer concrete core at S1 also exhibits large tensile plastic damage at 45 broken wires. Tensile plastic damage commences at the springline and spreads to the crown and invert with broken wires. Compared to the strain curves in Figure
Number of broken wires required to cause onset of visual crack for outer concrete core.
Component | S1 | S2 | ||||
---|---|---|---|---|---|---|
Crown | Springline | Invert | Crown | Springline | Invert | |
Model A | 90 | 110 | 175 | 125 | 135 | no visual crack |
Model B | 90 | 110 | no visual crack | 125 | 135 | no visual crack |
Proportion of improvement | 0.00% | 0.00% | no value | 0.00% | 0.00% | no value |
Strain curves of outer concrete core during phase of wire break: (a) strain at S1 and (b) strain at S2.
The broken wires are no longer used in the numerical analysis after breakage, which results in no strain in the broken wires, as shown in Figure
Strain curves of prestressing wire during phase of wire break.
Strain curves of mortar during phase of wire break: (a) strain at S1 and (b) strain at S2.
Similar to the concrete core, mortar has a strain that corresponds to the onset of a visual crack. 8 times the tensile strain of mortar is taken, which works out 1133
Number of broken wires required to cause onset of visual crack for mortar coating.
Component | S1 | S2 | ||||
---|---|---|---|---|---|---|
Crown | Springline | Invert | Crown | Springline | Invert | |
Model A | 70 | 90 | 85 | 95 | 115 | 115 |
Model B | 70 | 90 | 90 | 95 | 115 | 120 |
Proportion of improvement | 0.00% | 0.00% | 5.88% | 0.00% | 0.00% | 4.35 |
Typical visual crack in mortar.
Before onset of a visual crack, CFRP takes little effect on the mortar. As shown in Figures
In this paper, two contrasting three-dimensional FE models were established to evaluate the rehabilitation effect of CFRP-lined PCCP during a phase of internal load increase and a phase of wire break considering combined loads. A conceptual zone was introduced to analyze the structural performance of all components in different zones. The state of the pipe was investigated by examining two critical indicators: visual cracking of the concrete and mortar, and the yielding of the steel cylinder. The following conclusions were drawn from this study: In terms of the PCCP during the phase of wire break, components at the crown fail first, followed by the springline and invert. CFRP has a distinct rehabilitation effect on various components. The farther the distance from the component to CFRP, the worse the rehabilitation effect provided by CFRP. Namely, CFRP clearly reduces the development of cracking in the inner concrete core and relieves the yield of the steel cylinder while having little effect on the outer concrete, prestressing wire, or mortar. For the same component, CFRP also has a different rehabilitation effect at different locations. The deformation relieved by CFRP is the largest at the invert, then at the springline, and was smallest at the crown. Meanwhile, a one-hoop CFRP layer diminishes the area of a yielding steel cylinder of 4.72 m2. CFRP only has a clear effect on distressed PCCP. Moreover, CFRP works more effectively with an increase in the number of broken wires. For a full composite zone and transition zone, CFRP has no effect.
The figures and tables data used to support the findings of this study are included within the article. In addition, the finite element models are available from the corresponding author upon request.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
This work was supported by the Beijing Municipal Science and Technology Commission (no. Z141100006014058) and the Science and Technology Service network program (STS) project (no. KFJ-STS-ZDTP-037) of the Chinese Academy of Sciences.