# Numerical Investigations on Seismic Behavior of Segmental Assembly of Concrete Filled Steel Tube Piers with External Replaceable Energy-Dissipating Links

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## Abstract

**:**

## 1. Introduction

## 2. Establishment of PSCFST–EREDL

#### 2.1. Model Design

#### 2.2. Constitutive Relationship

- Initial yield strength $\sigma {|}_{0}=0.85{f}_{y}$.
- Maximum bearing strength ${f}_{yu}=2.1{f}_{y}$.
- Kinematic hardening parameters $C=0.02E$.
- Kinematic hardening parameter (M is 0.5 temporarily) $\gamma =C/\left[({f}_{yu}-{\sigma}^{0}\right)M]$.
- Isotropic hardening parameters $Q=({f}_{yu}-{\sigma}^{0})\left(1-M\right)$.
- Isotropic hardening parameters $b=0.5C/Q$.

#### 2.3. Establishment of Finite Element Model

## 3. Model Validation

#### 3.1. Test Introduction

#### 3.2. Comparative Verification

## 4. Finite Element Analysis

#### 4.1. Hysteresis Curve

#### 4.2. Failure Mechanism

#### 4.3. Energy Consumption Capacity

#### 4.4. Cumulative Energy Consumption

#### 4.5. Stiffness Degradation

#### 4.6. Plastic Strain

## 5. Seismic Performance and Influence Parameter Analysis

#### 5.1. Effect of Initial Prestress

#### 5.2. Effect of Steel Yield Strength of EREDL

#### 5.3. Effect of EREDL Thickness

## 6. Analysis of Bending Bearing Capacity of Test Piece

- ${V}_{j}$—shear resistance of joint surface
- ${A}_{j}$—Contact area of joint surface
- $\mu $—Friction coefficient
- ${\sigma}_{n}$—Normal stress value at joint surface.

- ${A}_{k}$—sectional area of the energy dissipator
- ${f}_{v}$—Shear strength of energy dissipator steel
- $n$—Number of energy consumers
- ${\sigma}_{n}$—Provided by axial pressure and prestress
- $\mu $—according to AASHTO American Specification [30], μ is 0.6.

- ${F}_{1}$,${F}_{2}$—force exerted by energy dissipators at different positions on pier segments
- ${F}_{H\tau}$—The shear stress of ${F}_{1}$ in the horizontal direction
- ${F}_{Vt}$—The tensile stress of ${F}_{1}$ in the vertical direction
- ${F}_{3}$—Tension generated by initial prestress and prestressed reinforcement when the pier segment rotates
- $G$—Dead weight of concrete-filled steel tube segments, calculated as 20 kN
- $N$—Axial force
- $b$—Section width of concrete-filled steel tube sections
- $\Delta b$—the relative slip distance between the two segments. According to the finite element simulation results, ∆b is within the loading displacement range of about 6%~12% bending limit state, and the loading displacement value of 9% bending limit state is 0.45 mm.

- $\lambda $—section ratio
- $A$—sectional area of concrete-filled steel tube segments; 4 in this paper × 104 mm
^{2}; - $a$—Axial compression ratio
- ${N}_{0}$—Ultimate bearing capacity of concrete-filled steel tube pier, ${N}_{0}={f}_{c}{A}_{c}+{f}_{y}^{\prime}{A}_{s}=2405.8\text{}kN$p—Initial prestress
- $p$—Initial prestress
- ${\epsilon}_{y}$—Yield strain of energy dissipator steel
- ${E}_{s1}$—EREDL elastic modulus; 1.86 GPa is taken in this paper
- ${E}_{s2}$—Elastic modulus of prestressed reinforcement, 1.95 GPa
- ${A}_{s}$—sectional area of prestressed reinforcement, 139 mm
^{2}.

## 7. Conclusions

- (1)
- When the initial prestress is 600 MPa, the EREDL strength is Q235, and the thickness is 5 mm, the ductility coefficient and residual displacement increase with the increase in initial prestress. When the initial prestress increases from 40.7 kN to 120.0 kN, the ductility factor decreases by about 20.6%. However, the equivalent viscous damping of specimens with different initial prestress is close;
- (2)
- Under the low cycle reciprocating horizontal displacement loading, EREDL–PSCFST piers mainly dissipate the energy with the plastic deformation of EREDL, and the pier damage is mainly concentrated in EREDL during the energy dissipation. EREDL can effectively reduce the damage of the pier steel tube concrete segment. Furthermore, the easy-to-replace EREDL makes the rapid repair of piers after the earthquake possible, and enhances the recoverable function of piers;
- (3)
- In this study, with the increase in EREDL strength in the range of Q120–Q425, the seismic performance of piers has been significantly improved. The bearing and energy capacity of specimens tends to increasing with the EREDL strength increases, however, the residual displacement also increases. Interestingly, with the increasing strength of EREDL, the effect gradually weakened;
- (4)
- The theoretical formula for calculating the flexural capacity of EREDL–PSCFST piers proposed in this paper takes into account the relative slip between segments during loading. The average ratio of the calculated value to the finite element simulation value is 1.009, and the error is basically maintained within 5%. The calculated value is more consistent with the simulated value, which can provide a reference for the calculation of the flexural capacity of EREDL–PSCFST piers in practical engineering.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**Stress-strain curves of concrete. (

**a**) Compressive stress-strain relationship of concrete. (

**b**) Tensile stress-strain relationship of concrete.

**Figure 9.**Comparison of hysteresis curves and skeleton curves [20]. (

**a**) Hysteresis curve. (

**b**) Skeleton curve.

**Figure 12.**Deformation of specimen R0 during loading; (

**a**) Prophase; (

**b**) Metaphase; (

**c**) $\delta =4\%$.

**Figure 13.**Deformation of specimen R2 during loading; (

**a**) Prophase; (

**b**) Metaphase; (

**c**) $\mathsf{\delta}=4\%$.

Specimen | EREDL | Initial Prestress (MPa) | Ratio of Axial Compression Stress to Strength | Steel Type of EREDL | Thickness of EREDL (mm) |
---|---|---|---|---|---|

UPCC-R0 | NO | 600 | 0.15 | - | - |

UPCC-R1 | YES | 300 | 0.15 | Q235 | 5 |

UPCC-R2 | YES | 600 | 0.15 | Q235 | 5 |

UPCC-R3 | YES | 900 | 0.15 | Q235 | 5 |

UPCC-R4 | YES | 600 | 0.15 | Q120 | 5 |

UPCC-R5 | YES | 600 | 0.15 | Q345 | 5 |

UPCC-R6 | YES | 600 | 0.15 | Q425 | 5 |

UPCC-R7 | YES | 600 | 0.15 | Q235 | 8 |

UPCC-R8 | YES | 600 | 0.15 | Q235 | 10 |

$\mathit{\psi}$ | $\mathit{\u03f5}$ | ${\mathit{f}}_{\mathit{b}0}/{\mathit{f}}_{\mathit{c}0}$ | ${\mathit{K}}_{\mathit{c}}$ | $\mathit{\mu}$ |
---|---|---|---|---|

30 | 0.1 | 1.16 | 0.6667 | 0.0005 |

Test Block | Compressive Strength (MPa) | Tensile Strength (MPa) |
---|---|---|

1 | 42.8 | 2.35 |

2 | 43.1 | 2.43 |

3 | 41.6 | 2.40 |

Average | 42.5 | 2.39 |

Comparative Item | Horizontal Bearing Capacity/kN Side Shift 6.2% | Residual Displacement/mm Side Shift 6.2% | Equivalent Stiffness/(kN·mm ^{−1}) Side Shift 6.2% | Energy Consumption/(kN·mm) Side Shift 6.2% |
---|---|---|---|---|

Experimental values | 74.1 | 5.8 | 1.2 | 12.0 |

Finite element values | 62.6 | 8.2 | 1.0 | 16.2 |

Rate | 0.8 | 1.4 | 0.8 | 1.2 |

Specimen | UPCC-R0 | UPCC-R2 |
---|---|---|

Yield strength (kN) | 50.32 | 97.04 |

Yield displacement (mm) | 24.50 | 9.76 |

Peak load capacity (kN) | 57.40 | 101.56 |

Peak displacement (mm) | 39.70 | 14.65 mm |

Ductility factor | 1.62 | 1.50 |

Specimen | $\mathit{E}$ | ${\mathit{h}}_{\mathit{e}}$ |
---|---|---|

UPCC-R0 | 0.116 | 0.018 |

UPCC-R2 | 0.728 | 0.116 |

Specimen | Initial Prestress (MPa) | Steel Type of EREDL | Thickness of EREDL (mm) |
---|---|---|---|

UPCC-R1 | 300 | Q235 | 5 |

UPCC-R2 | 600 | Q235 | 5 |

UPCC-R3 | 900 | Q235 | 5 |

Specimen | Peak Carrying Capacity | Yield Displacement | Displacement (90% Peak Carrying Capacity)/mm | Ductility Factor $\mathbf{\Delta}\mathit{u}$ |
---|---|---|---|---|

UPCC-R1 | 95.27 | 4.87 | 40 | 8.21 |

UPCC-R2 | 101.56 | 4.9 | 37.04 | 7.56 |

UPCC-R3 | 107.73 | 4.91 | 32.02 | 6.52 |

Specimen | Initial Prestress (MPa) | Steel Type of EREDL | Thickness of EREDL (mm) |
---|---|---|---|

UPCC-R2 | 600 | Q235 | 5 |

UPCC-R4 | 600 | Q120 | 5 |

UPCC-R5 | 600 | Q345 | 5 |

UPCC-R6 | 600 | Q425 | 5 |

Specimen | Peak Carrying Capacity | Yield Displacement | Displacement (90% Peak Carrying Capacity)/mm | Ductility Factor $\mathbf{\Delta}\mathit{u}$ |
---|---|---|---|---|

UPCC-R2 | 101.56 | 4.90 | 37.04 | 7.56 |

UPCC-R4 | 92.075 | 4.98 | 40 | 8.03 |

UPCC-R5 | 145.67 | 4.98 | 29.78 | 5.98 |

UPCC-R6 | 161.25 | 5.02 | 29.92 | 5.96 |

**Table 11.**Final cumulative energy consumption of each specimen and the increase range of specimen strength and cumulative energy.

Specimen | Cumulative Energy Dissipation (kN·m) | The Increase Range of Strength | The Increase Range of Cumulative Energy |
---|---|---|---|

UPCC-R4 | 11.5 | - | - |

UPCC-R2 | 16.2 | 20.5% | 40.4% |

UPCC-R5 | 19.4 | 76.9% | 68.5% |

UPCC-R6 | 21.4 | 123% | 85.4% |

Specimen | Initial Prestress (MPa) | Steel Type of EREDL | Thickness of EREDL (mm) |
---|---|---|---|

UPCC-R2 | 600 | Q235 | 5 |

UPCC-R7 | 600 | Q235 | 8 |

UPCC-R8 | 600 | Q235 | 10 |

Specimen | Peak Carrying Capacity | Yield Displacement | Displacement (90% Peak Carrying capacity)/mm | Ductility Factor $\mathbf{\Delta}\mathit{u}$ |
---|---|---|---|---|

UPCC-R2 | 101.56 | 4.90 | 37.04 | 7.56 |

UPCC-R7 | 128.79 | 4.93 | 28.17 | 5.71 |

UPCC-R8 | 146.58 | 4.90 | 27.97 | 5.71 |

Model Number | Section Ratio | Axial Compression Ratio | Initial Prestress (MPa) | $\mathbf{Finite}\text{}\mathbf{Element}\text{}\mathbf{Value}\text{}{\mathit{M}}_{\mathit{u},\mathit{\vartheta}}\text{}(\mathbf{kN}\xb7\mathbf{m})$ | $\mathbf{Calculated}\text{}\mathbf{Value}\text{}{\mathit{M}}_{\mathit{u},\mathit{c}}\text{}(\mathbf{kN}\xb7\mathbf{m})$ | ${\mathit{M}}_{\mathit{u},\mathit{\vartheta}}/{\mathit{M}}_{\mathit{u},\mathit{c}}$ |
---|---|---|---|---|---|---|

UPCC-R1 | 2% | 0.15 | 300 | 47.6 | 45.64 | 1.043 |

UPCC-R2 | 2% | 0.15 | 600 | 50.8 | 49.26 | 1.031 |

UPCC-R3 | 2% | 0.15 | 900 | 53.9 | 52.23 | 1.032 |

UPCC-R4 | 2% | 0.15 | 600 | 46.0 | 43.81 | 1.050 |

UPCC-R5 | 2% | 0.15 | 600 | 72.0 | 69.94 | 1.029 |

UPCC-R6 | 2% | 0.15 | 600 | 78.2 | 81.47 | 0.953 |

UPCC-R7 | 3% | 0.15 | 600 | 64.4 | 67.58 | 0.953 |

UPCC-R8 | 4% | 0.15 | 600 | 73.3 | 74.78 | 0.980 |

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## Share and Cite

**MDPI and ACS Style**

Wang, C.; Yin, C.; Zou, Y.; Ping, B.; Wu, X.; Liao, J.; Sun, M.
Numerical Investigations on Seismic Behavior of Segmental Assembly of Concrete Filled Steel Tube Piers with External Replaceable Energy-Dissipating Links. *Materials* **2023**, *16*, 1122.
https://doi.org/10.3390/ma16031122

**AMA Style**

Wang C, Yin C, Zou Y, Ping B, Wu X, Liao J, Sun M.
Numerical Investigations on Seismic Behavior of Segmental Assembly of Concrete Filled Steel Tube Piers with External Replaceable Energy-Dissipating Links. *Materials*. 2023; 16(3):1122.
https://doi.org/10.3390/ma16031122

**Chicago/Turabian Style**

Wang, Chengquan, Chongli Yin, Yun Zou, Boyan Ping, Xi Wu, Juan Liao, and Miaomiao Sun.
2023. "Numerical Investigations on Seismic Behavior of Segmental Assembly of Concrete Filled Steel Tube Piers with External Replaceable Energy-Dissipating Links" *Materials* 16, no. 3: 1122.
https://doi.org/10.3390/ma16031122