# Quantifying Effect of Post-Tensioned Bars for Precast Concrete Shear Walls

^{1}

^{2}

^{3}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Constitutive Modeling of Concrete

#### 2.1. The KCC Model with Mat-Concrete Damage (MAT072R3)

#### 2.2. The CDP Model with Mat-CDP Damage (MAT273)

#### 2.3. The Winfrith Model with Mat-Winfrith Damage (Mat085)

## 3. Analytical Methodology Validation

#### 3.1. Experimental Investigation

#### 3.2. Constitutive Material Models

#### 3.3. Contact and Boundary Conditions

## 4. Numerical Analysis and Comparison with Experimental Results

#### 4.1. Analysis of PT 2D Wall under Pushover Analysis

#### 4.1.1. Geometric and Finite Element (FE) Model

#### 4.1.2. Effect Type of Mesh Size Element

#### 4.1.3. Effect Type of Concrete Element

#### 4.1.4. Effect of Strain Rate

#### 4.1.5. Failure Behaviour

#### 4.2. Analysis of 3D Wall under Pushover Analysis

#### 4.2.1. Hysteresis and Backbone Curves

#### 4.2.2. Failure Behaviour

## 5. Effect of PT Bars for Reinforced Concrete Walls

#### 5.1. Effect of PT Bars for PT 2D Wall

#### 5.1.1. Effect of PT Quantities

#### 5.1.2. Effect of PT Diameter

#### 5.1.3. Effect of PT Yield Strength

#### 5.2. Effect of PT Bars for PT 3D Wall

#### 5.2.1. Effect of PT Quantities

#### 5.2.2. Effect of PT Diameter

#### 5.2.3. Effect of the PT Yield Strength

## 6. Conclusions

- 1.
- All three material models investigated in this study could predict an acceptable peak strength for both PT 2D and 3D walls. The Winfrith model was the best prediction in three models based on the outstanding capability to generate the details of a crack’s location as well as its dimensions. Additionally, not only could it accurately predict the failure position of concrete as compared to the experimental, but the Winfrith model could also identify the regions of maximum flexural stresses in rebars.
- 2.
- The strain rate did not significantly influence the force–displacement relationships for KCC and CDP models but the Winfrith model was converse and the RATE = 1 was appropriate for this model for 2D walls. All three models have a profound effect with the strain rate and the RATE = 1 provided reasonable prediction for the Winfrith model for 3D walls. Because the mesh size of 25 mm and type of element of ELFORM = 1 were suitable for predicting the peak load and minimizing computational time, they were chosen for the numerical simulation.
- 3.
- The number of PT had the greatest influence on lateral strength bearing capacity; yield strength had a negligible effect for PT 2D walls. Based on the numerical simulations, the PT quantity (2X4Y), the PT diameter (15.2 mm) and the yield strength (${f}_{y}$ = 1860 MPa) were selected to efficiently enhance the bearing capacity of lateral strength for PT 3D walls.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 8.**The structural damage reproduced from the finite element model for the PT 2D wall. (

**a**) KCC model. (

**b**) CDP model. (

**c**) Winfrith model.

**Figure 13.**The structural damage reproduced from the finite element model for the 3D wall. (

**a**) KCC model. (

**b**) CDP model. (

**c**) Winfrith model.

Specimen | ${\mathit{E}}_{\mathit{s}}$ | ${\mathit{f}}_{\mathit{c}}$ | $\mathit{\rho}$ | $\mathit{\nu}$ |
---|---|---|---|---|

(MPa) | (MPa) | $\left(\mathbf{g}/{\mathbf{mm}}^{3}\right)$ | ||

Pakiding et al. [49] | 200,000 | 43.4 | 0.0023 | 0.2 |

PT 2D wall | ||||

Beyer et al. [50] | 200,000 | 45.0 | 0.0023 | 0.2 |

3D wall |

Specimen | Bar | ${\mathit{E}}_{\mathit{s}}$ | $\mathit{\rho}$ | $\mathit{\nu}$ | ${\mathit{f}}_{\mathit{y}}$ | ${\mathit{f}}_{\mathit{u}}$ |
---|---|---|---|---|---|---|

Type | (MPa) | $\left(\mathbf{g}/{\mathbf{mm}}^{3}\right)$ | (MPa) | (MPa) | ||

Pakiding et al. [49] | #1 | 200,000 | 0.00783 | 0.3 | 519 | 744 |

PT 2D wall | #2 | 200,000 | 0.00783 | 0.3 | 473 | 742 |

#3 | 200,000 | 0.00783 | 0.3 | 473 | 742 | |

#4 | 200,000 | 0.00783 | 0.3 | 441 | 683 | |

#5 | 200,000 | 0.00783 | 0.3 | 1675 | 2038 | |

Beyer et al. [50] | #6 | 200,000 | 0.00783 | 0.3 | 519 | 744 |

3D wall | #7 | 200,000 | 0.00783 | 0.3 | 518 | 681 |

_{c}is the concrete compressive strength, $\rho $ is the mass density, $\nu $ is Poisson’s ratio, E

_{s}is Young’s modulus, f

_{y}and f

_{u}are the rebar yield stress and ultimate strength, respectively.

Model | Mesh Size | ELFORM | Strain Rate | |||||||
---|---|---|---|---|---|---|---|---|---|---|

12.5 mm | 25 mm | 50 mm | $-\mathbf{2}$ | $-\mathbf{1}$ | 1 | 2 | a | b | c | |

KCC | 1558 (0.2%) | 1588 (1.7%) | 1711 (9.6%) | 1612 (3.3%) | 1600 (2.5%) | 1588 (1.7%) | 1578 (1.1%) | 1650 (5.7%) | 1590 (1.9%) | - |

CDP | 1586 (1.6%) | 1617 (3.6%) | 1698 (8.8%) | 1602 (2.6%) | 1624 (4.1%) | 1617 (3.6%) | 1632 (4.5%) | 1640 (5.1%) | 1620 (3.8%) | - |

Winfrith | 1589 (1.8%) | 1607 (2.9%) | 1714 (9.8%) | 1617 (3.5%) | 1617 (3.5%) | 1608 (3.0%) | 1595 (2.2%) | 1720 (10.2%) | 1610 (3.1%) | 1790 (14.7%) |

Test | 1561 (kN) | 1561 (kN) | 1561 (kN) |

**Table 4.**The maximum lateral force of the hysteresis diagram of 3D walls for the X Direction (Unit: kN).

Model | Mesh Size | ELFORM | Strain Rate | |||||||
---|---|---|---|---|---|---|---|---|---|---|

12.5 mm | 25 mm | 50 mm | $-\mathbf{2}$ | $-\mathbf{1}$ | 1 | 2 | a | b | c | |

KCC | 459.9 (0.2%) | 450.9 (1.8%) | 482.6 (5.1%) | 495.7 (8.0%) | 500.9 (9.1%) | 450.9 (1.8%) | 508.0 (10.7%) | 450.9 (1.8%) | 468.6 (2.1%) | - |

CDP | 464.7 (1.2%) | 472.0 (2.8%) | 487.9 (6.3%) | 527.3 (14.8%) | 526.9 (14.8%) | 472.0 (2.8%) | 511.2 (11.4%) | 512.1 (11.6%) | 464.7 (1.3%) | - |

Winfrith | 484.1 (5.5%) | 474.6 (3.4%) | 512.6 (11.7%) | 539.9 (17.6%) | 542.1 (18.1%) | 474.6 (3.4%) | 569.4 (24.1%) | 420.0 (8.5%) | 474.6 (3.4%) | 512.1 (11.6%) |

Test | 459.0 kN | 459.0 kN | 459.0 kN |

**Table 5.**The maximum lateral force of the hysteresis diagram of 3D walls for Y Direction (Unit: kN).

Model | Mesh Size | ELFORM | Strain Rate | |||||||
---|---|---|---|---|---|---|---|---|---|---|

12.5 mm | 25 mm | 50 mm | $-\mathbf{2}$ | $-\mathbf{1}$ | 1 | 2 | a | b | c | |

KCC | 401.4 (2.0%) | 412.7 (4.9%) | 404.3 (2.7%) | 452.2 (14.9%) | 456.7 (16.1%) | 412.7 (4.9%) | 450.2 (14.4%) | 412.7 (4.9%) | 404.3 (2.7%) | - |

CDP | 375.5 (4.6%) | 386.8 (1.7%) | 378.9 (3.7%) | 363.6 (7.6%) | 364.2 (7.4%) | 386.8 (1.7%) | 393.2 (0.1%) | 376.6 (4.3%) | 386.8 (1.7%) | - |

Winfrith | 429.5 (9.1%) | 418.8 (6.4%) | 454.3 (15.5%) | 452.3 (14.9%) | 454.6 (15.5%) | 418.8 (6.4%) | 439.4 (11.7%) | 362.6 (7.9%) | 418.8 (6.4%) | 450.9 (14.6%) |

Test | 393.5 kN | 393.5 kN | 393.5 kN |

PT Quantities | KCC Model | CDP Model | Winfrith Model | |||
---|---|---|---|---|---|---|

Values (kN) | Errors (%) | Values (kN) | Errors (%) | Values (kN) | Errors (%) | |

Three PT | 1834.1 | 15.5 | 1809.8 | 11.9 | 1850.7 | 15.2 |

Two PT | 1588.3 | - | 1616.8 | - | 1606.8 | - |

One PT | 1502.1 | −5.4 | 1466.5 | −9.3 | 1514.8 | −5.7 |

Non-PT | 1433.9 | −9.7 | 1288.8 | −20.3 | 1376.8 | −14.3 |

PT Diameters | KCC Model | CDP Model | Winfrith Model | |||
---|---|---|---|---|---|---|

Values (kN) | Errors (%) | Values (kN) | Errors (%) | Values (kN) | Errors (%) | |

17.8 mm | 1754.8 | 10.5 | 1873.4 | 15.9 | 1732.6 | 7.8 |

15.2 mm | 1588.3 | - | 1616.8 | - | 1606.8 | - |

12.7 mm | 1520.9 | −4.2 | 1553.3 | −3.9 | 1551.2 | −3.5 |

9.5 mm | 1460.5 | −8.1 | 1496.2 | −7.5 | 1406.3 | −12.5 |

Yield Strength | KCC Model | CDP Model | Winfrith Model | |||
---|---|---|---|---|---|---|

Values (kN) | Errors (%) | Values (kN) | Errors (%) | Values (kN) | Errors (%) | |

${f}_{y}=1570$ MPa | 1520.3 | −4.3 | 1546.8 | −4.3 | 1551.8 | −3.4 |

${f}_{y}=1675$ MPa | 1588.34 | - | 1616.8 | - | 1606.8 | - |

${f}_{y}=1860$ MPa | 1621.9 | 2.1 | 1652.3 | 2.2 | 1625.2 | 1.1 |

${f}_{y}=1960$ MPa | 1645.8 | 3.6 | 1665.3 | 2.9 | 1646.1 | 2.4 |

PT Quantities | KCC Model | CDP Model | Winfrith Model | |||
---|---|---|---|---|---|---|

Values (kN) | Errors (%) | Values (kN) | Errors (%) | Values (kN) | Errors (%) | |

0X0Y | 450.9 | - | 472 | - | 474.6 | - |

1X0Y | 587.1 | 30.2 | 605.1 | 28.2 | 626 | 31.9 |

2X0Y | 645.5 | 43.2 | 665 | 40.1 | 674.9 | 42.2 |

3X0Y | 687.9 | 52.5 | 710.2 | 50.5 | 710.5 | 49.7 |

0X2Y | 625.9 | 38.8 | 652.3 | 38.2 | 659.5 | 38.9 |

0X4Y | 640.8 | 42.1 | 650.4 | 37.8 | 652.9 | 37.6 |

0X6Y | 641.9 | 42.4 | 648.6 | 37.4 | 649 | 36.7 |

1X2Y | 637.9 | 41.5 | 634.3 | 34.4 | 649.3 | 36.8 |

2X4Y | 748.8 | 66.1 | 779.5 | 65.1 | 766.5 | 61.5 |

3X6Y | 775.1 | 71.9 | 805.4 | 70.6 | 792.2 | 66.9 |

PT Quantities | KCC Model | CDP Model | Winfrith Model | |||
---|---|---|---|---|---|---|

Values (kN) | Errors (%) | Values (kN) | Errors (%) | Values (kN) | Errors (%) | |

3X0Y | 420.2 | 1.8 | 385.9 | −0.2 | 425.3 | 1.6 |

0X2Y | 585.1 | 41.8 | 560.4 | 44.9 | 585.3 | 39.8 |

0X0Y | 412.7 | - | 386.8 | - | 418.8 | - |

1X0Y | 415.3 | 0.7 | 384.4 | −0.6 | 420.6 | 0.4 |

2X0Y | 414.2 | 0.4 | 386.1 | −0.6 | 423.2 | 1.1 |

0X4Y | 740.8 | 79.5 | 692.8 | 79.1 | 759.9 | 81.4 |

0X6Y | 787.8 | 90.9 | 748.8 | 93.6 | 814 | 94.4 |

1X2Y | 585.5 | 41.9 | 548.2 | 41.7 | 584.4 | 39.5 |

2X4Y | 736.5 | 78.5 | 692.4 | 79 | 758.3 | 81.1 |

3X6Y | 795.6 | 92.8 | 750.3 | 93.4 | 826.5 | 97.3 |

PT Diameters | KCC Model | CDP Model | Winfrith Model | |||
---|---|---|---|---|---|---|

Values (kN) | Errors (%) | Values (kN) | Errors (%) | Values (kN) | Errors (%) | |

9.5 mm | 541.4 | −18.3 | 567.4 | −10.5 | 574.6 | −7.7 |

12.7 mm | 611.3 | −7.7 | 612.4 | −3.5 | 583.1 | −6.3 |

15.2 mm | 662.4 | - | 634.3 | - | 622.2 | - |

17.8 mm | 670.3 | 1.2 | 645.4 | 1.7 | 663.9 | 6.7 |

PT Diameters | KCC Model | CDP Model | Winfrith Model | |||
---|---|---|---|---|---|---|

Values (kN) | Errors (%) | Values (kN) | Errors (%) | Values (kN) | Errors (%) | |

9.5 mm | 562.9 | −10.7 | 449.9 | −19.8 | 486.4 | −16.8 |

12.7 mm | 588.5 | −6.7 | 500.6 | −10.8 | 538.6 | −7.8 |

15.2 mm | 630.5 | - | 561.1 | - | 584.4 | - |

17.8 mm | 649.5 | 3.0 | 601.4 | 7.2 | 640 | 9.5 |

Yield Strength | KCC Model | CDP Model | Winfrith Model | |||
---|---|---|---|---|---|---|

Values (kN) | Errors (%) | Values (kN) | Errors (%) | Values (kN) | Errors (%) | |

1570 MPa | 615.1 | −3.6 | 619.4 | −2.3 | 632.8 | −2.5 |

1675 MPa | 637.9 | - | 634.3 | - | 649.3 | - |

1860 MPa | 678.1 | 6.3 | 690.3 | 8.8 | 678.8 | 4.5 |

1960 MPa | 694.5 | 8.9 | 701.6 | 10.6 | 702.6 | 8.2 |

Yield Strength | KCC Model | CDP Model | Winfrith Model | |||
---|---|---|---|---|---|---|

Values (kN) | Errors (%) | Values (kN) | Errors (%) | Values (kN) | Errors (%) | |

1570 MPa | 565.3 | −3.5 | 528.9 | −3.5 | 558.7 | −4.4 |

1675 MPa | 585.5 | - | 548.2 | - | 584.4 | - |

1860 MPa | 630.5 | 7.7 | 579.4 | 5.7 | 622.8 | 6.6 |

1960 MPa | 645.3 | 10.2 | 593.9 | 8.3 | 640 | 9.5 |

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## Share and Cite

**MDPI and ACS Style**

Bao, Q.T.; Lee, K.; Kim, S.-J.; Shin, J.
Quantifying Effect of Post-Tensioned Bars for Precast Concrete Shear Walls. *Sustainability* **2022**, *14*, 6141.
https://doi.org/10.3390/su14106141

**AMA Style**

Bao QT, Lee K, Kim S-J, Shin J.
Quantifying Effect of Post-Tensioned Bars for Precast Concrete Shear Walls. *Sustainability*. 2022; 14(10):6141.
https://doi.org/10.3390/su14106141

**Chicago/Turabian Style**

Bao, Quoc To, Kihak Lee, Sung-Jig Kim, and Jiuk Shin.
2022. "Quantifying Effect of Post-Tensioned Bars for Precast Concrete Shear Walls" *Sustainability* 14, no. 10: 6141.
https://doi.org/10.3390/su14106141