# Numerical Study of the Performance of Existing Prestressed Cylindrical Concrete Pipes Strengthened with Reinforced Concrete or Carbon-Reinforced Fiber Polymer Jackets—Part B

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## Abstract

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## 1. Introduction

**a**) hydraulic internal pressure and/or (

**b**) three-edge vertical load bending. All important details describing the applied loading, the resulting displacement and strain response, and the structural damage observed during this experimental sequence are included in Part A and, due to space limitations, are not duplicated here. The objective of this part of the study (Part B) was to apply commercially available software in an effort to numerically simulate the measured behavior of the tested specimens. This was done using the exact dimensions, technical details, mechanical properties of the various materials and laboratory conditions in applying the load and measuring the response of the tested specimens. Therefore, the numerical simulation is also a step towards proving the validity of such a numerical approach to realistically approximate the observed behavior. Among the tested specimens, one represented the prototype pipeline whereas three specimens represented three different retrofitting schemes; two of these retrofitting schemes employed carbon reinforcing fiber polymer (CFRP) jackets (either internally or externally for the pipe) and the third retrofitting scheme employed an external reinforced concrete (RC) jacket [1]. Because such pipelines have been in operation for many decades, it is of interest to be able to examine their current safe performance as well as to investigate the effectiveness of specific retrofitting schemes to ensure their desired performance in the future. Several researchers have conducted experimental testing supplemented with numerical simulations. Zarghamee et al. [2,3] carried out nonlinear simulations of prestressed concrete pipes subjected to water pressure and dead loads. The numerical simulation used composite shell elements combined with a constitutive law which included compressive crushing, tensile softening, and cracking. External radial pressure was used to simulate the prestress. The prestress loss was simulated by removing this external pressure either from the entire model or from a certain length of the pipe. For a PCCP with a diameter of 6300 mm, it was shown that the principal mode of failure was the failure of wires rather than the compressive crushing of the concrete. For relatively small diameter pipes (equal to 1850 mm), the dominant mode of failure was the rupture of the internal steel membrane. The performance of PCCP under combined internal and external loads was studied numerically by Hajali et al. [4]. They focused on the effect of broken wires and the performance of the joint regions. Five-layer composite elements were utilized in this numerical simulation, representing the inner concrete, the steel membrane, the outer concrete, the prestressing wires and the external coating, assuming perfect bonds between these layers. Nonlinear concrete material laws were assumed for each layer based on the tensile strength and compressive strength for either the concrete or steel. The full interaction between the pipe modulus was assumed at their joint regions. A sensitivity analysis was performed to study the effect of the number and respective location of broken prestressing wires. The effect of prestress loss was also investigated by Gomez et al. [5] using a 3D model to predict the response of the pipe with different numbers of broken wires under dead load and internal water pressure. The concentration of failed wires in one section was found to be the most unfavorable scenario. The effectiveness of retrofitting by applying FRP sheets depended on the percentage of failed wires.

## 2. Description of the Numerical Simulation Used

#### 2.1. Description of the Numerical Methodology Used

#### 2.2. Particulars of the Loading Process

## 3. Obtained Numerical Results

#### 3.1. Numerical Simulation of the Pipe with the Prestressed Wires Removed

_{t}) prior to the descending branch (Figure 4b). When the internal pressure is increased further than 2.5 bar and up to 5.7 bar the numerically predicted response develops a larger radial expansion than the corresponding measured values, possibly due to the mentioned plateau. The maximum pressure reached during the numerical simulation (6.1 bar) is also higher than the one reached during testing (5.2 bar). In Figure 6a,b the numerically predicted radial axial stresses response of the steel membrane is shown for internal pressure amplitudes equal to 4.0 bar and 5.7 bar, respectively. For internal pressure equal to 4.0 bar the steel membrane is predicted to reach yield at four narrow zones indicated with red colour whereas for internal pressure equal 5.7 bar the whole steel membrane is beyond yield. This agrees with the predicted and observed radial expansion versus internal pressure variation response shown in Figure 5a, which indicates a nonlinear behavior similar to the constitutive material law adopted for the steel membrane based on laboratory testing (see Figure 3, Part A, [1]).

**Figure 5.**(

**a**) Internal hydraulic pressure versus radial expansion response. Measured and numerically predicted (

**b**) The numerical simulation of the zones with concentrated large concrete plastic strains.

**Figure 6.**The numerically predicted radial axial tensile stress distribution for the steel membrane. (

**a**) For internal pressure amplitude equal to 4.0 bar. (

**b**) For internal pressure amplitude equal to 5.7 bar.

#### 3.2. Numerical Simulation of the Pipe with All the Prestressing Wires Fully Active

#### 3.3. The Pipe with an Internal FRP Jacket and the Prestressing Wires Fully Active

#### 3.4. Numerical Simulation of the Pipe with an External FRP Jacket and the Prestressing Wires Fully Active

#### 3.5. Numerical Simulation of the Pipe with an External Reinforced Concrete (RC) Jacket and the Prestressing Wires Fully Active

## 4. Numerical Simulation of the Prestress Defect

#### Comparison of the Observed and Numerically Predicted Prestress Defect

## 5. Validity of the Obtained Numerical Results—Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 7.**(

**a**) The numerical simulation of the zones with concentrated large concrete plastic strains. (

**b**) The damaged internal concrete after the end of the hydraulic pressure test for specimen 10.

**Figure 8.**(

**a**) Initial and alternative constitutive law assumed for the tensile behavior of the concrete. (

**b**) Internal hydraulic pressure versus radial expansion response resulting from the initial and the alternative concrete constitutive laws.

**Figure 9.**The numerically predicted radial axial stress distribution after applying the prestress force. (

**a**) For the concrete volume. (

**b**) For the steel membrane.

**Figure 10.**Measured and numerically predicted for specimen 7: (

**a**) the resulting radial axial stress distribution at the prestressing wires after applying the prestress force. For the concrete volume; and (

**b**) internal hydraulic pressure versus radial expansion response.

**Figure 11.**The predicted radial axial stress and plastic strain distribution for internal hydraulic pressure of 14.6 bar: (

**a**) at the steel membrane; (

**b**) at the prestressing wires; and (

**c**) plastic strains for the concrete volume.

**Figure 12.**Measured and numerically predicted for specimen 5: (

**a**) the predicted radial axial stress distribution of the concrete volume for internal hydraulic pressure equal to 14.4 bar; and (

**b**) internal hydraulic pressure versus radial expansion response.

**Figure 13.**Internal hydraulic pressure of 14.4 bar: (

**a**) steel membrane below yield stress; (

**b**) near the yield stress of the prestressing wires; and (

**c**) the steel membrane below yield (120 MPa).

**Figure 14.**Internal hydraulic pressure of 18.5 bar: (

**a**) steel membrane below yield stress; (

**b**) near the yield stress of the prestressing wires; and (

**c**) the steel membrane below yield (120 MPa).

**Figure 15.**Measured and numerically predicted for specimen 3: (

**a**) the predicted radial axial stress distribution of the concrete volume for internal hydraulic pressure equal to 14.6 bar; and (

**b**) internal hydraulic pressure versus radial expansion response.

**Figure 16.**Internal hydraulic pressure of 14.6 bar: (

**a**) steel membrane below yield stress; (

**b**) near the yield stress of the prestressing wires and (

**c**) the steel membrane below yield (120 MPa).

**Figure 17.**Internal hydraulic pressure of 15.0 bar: (

**a**) steel membrane below yield stress; (

**b**) near the yield stress of the prestressing wires; and (

**c**) the steel membrane below yield (120 MPa).

**Figure 18.**Measured and numerically predicted for specimen 1: (

**a**) pipe with external RC jacket; (

**b**) top right predicted plastic strain distribution of the concrete volume for internal hydraulic pressure equal to 14.6 bar; and (

**c**) internal hydraulic pressure versus radial expansion response.

**Figure 20.**Internal pressure 24 bar: (

**a**) steel membrane; (

**b**) prestressing wires; and (

**c**) steel of RC jacket.

**Figure 21.**Numerical predictions of the internal versus radial expansion response for all specimens.

**Figure 22.**Measured and numerically predicted including the effect of the numerically simulated defect for specimen 7. The initiation of the loading cycle whereby 20 wires were cut is indicated by the gray square.

**Figure 23.**Measured and numerically predicted including the result of the numerically simulated defect for specimen 5 (internal CFRP jacket). The initiation of the loading cycle whereby 20 wires were cut is indicated by the gray square.

**Figure 26.**Numerically predicted response for all the original and the jacketed specimens having 20 prestressing wires removed.

Name and description of specimen tested in the laboratory (see Part A) | Num. model |

Specimen 10, Pipe with all prestressing wires removed | Yes |

Specimen 7, Pipe with all prestressing wires active. | Yes |

Specimen 5. Pipe with all prestressing wires active and an internal CFRP jacket | Yes |

Specimen 3. Pipe with all prestressing wires active and an external CFRP jacket | Yes |

Specimen 1. Pipe with all prestressing wires active and an external RC jacket | Yes |

Specimen 7, Pipe with 32 prestressing wire active and 20 wires removed | Yes |

Specimen 5, Pipe with internal CFRP jacket. 32 prestressing wires active and 20 removed | Yes |

Only Numerical model. Pipe with external CFRP jacket. 32 prestressing wires active and 20 wires removed | |

Only Numerical model. Pipe with external RC jacket. 32 prestressing wires active and 20 wires removed |

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**MDPI and ACS Style**

Katakalos, K.; Melidis, L.; Manos, G.; Soulis, V.
Numerical Study of the Performance of Existing Prestressed Cylindrical Concrete Pipes Strengthened with Reinforced Concrete or Carbon-Reinforced Fiber Polymer Jackets—Part B. *Fibers* **2022**, *10*, 93.
https://doi.org/10.3390/fib10110093

**AMA Style**

Katakalos K, Melidis L, Manos G, Soulis V.
Numerical Study of the Performance of Existing Prestressed Cylindrical Concrete Pipes Strengthened with Reinforced Concrete or Carbon-Reinforced Fiber Polymer Jackets—Part B. *Fibers*. 2022; 10(11):93.
https://doi.org/10.3390/fib10110093

**Chicago/Turabian Style**

Katakalos, Konstantinos, Lazaros Melidis, George Manos, and Vassilios Soulis.
2022. "Numerical Study of the Performance of Existing Prestressed Cylindrical Concrete Pipes Strengthened with Reinforced Concrete or Carbon-Reinforced Fiber Polymer Jackets—Part B" *Fibers* 10, no. 11: 93.
https://doi.org/10.3390/fib10110093