# Axial Compressive Behaviours of Coal Gangue Concrete-Filled Circular Steel Tubular Stub Columns after Chloride Salt Corrosion

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Finite Element Model and Experimental Verification

#### 2.1. Methodology

#### 2.2. Material Constitutive

#### 2.2.1. Steel Tube

_{e}= 0.8f

_{y}/E

_{s}, ε

_{e1}= 1.5ε

_{e}, ε

_{e2}= 10ε

_{e1}, ε

_{e3}= 100ε

_{e1}, A = 0.2f

_{y}(ε

_{e1}− ε

_{e})

^{2}, B = 2Aε

_{e1}, and C = 0.8f

_{y}+ Aε

^{2}

_{e}− Bε

_{e}. f

_{y}and E

_{s}are the yield strength and elastic modulus of the steel tube, respectively.

_{ye}represents the tensile yield strength of the steel with various ρ (unit: MPa). E

_{se}represents the elastic modulus of the steel tube with corrosion exposure. ρ is the corrosion rate (unit: %). The σ-ε relationship of Q345 steel under different ρ is presented in Figure 1.

#### 2.2.2. Concrete

_{0}and σ

_{0}are the peak strain and stress, respectively. ε

_{0}is given by

_{c}is the compressive strength of coal gangue concrete (unit: MPa). λ is the influence of the coal gangue aggregate replacement fraction on strain, and ξ is the hoop coefficient, given by

_{c}is the compressive strength of coal gangue concrete (unit: MPa). f

_{ye}is the yield strength after corrosion, and A

_{c}and A

_{se}are the cross-sectional area of the concrete and steel tube after corrosion, respectively, (unit: mm

^{2}), and

_{bo}/f

_{c}is selected as 1.16, K

_{c}is 0.66667, and 0.0005 is the viscosity parameter [47].

#### 2.3. Finite Element Analysis

#### 2.3.1. Part and Meshing

#### 2.3.2. Interface Properties

_{cnt}). At the same time, the shear stress at the inner surface of the steel tube will always be equal to τ

_{cnt}during the sliding process. τ

_{cnt}is positively correlated with the contacted pressure (p) between the steel tube and concrete surface, and the minimum value is not less than the average interfacial bonding force (τ

_{bond}). The calculation method for τ

_{cnt}and τ

_{bond}is shown in Equation (10), and μ is the cross-sectional friction coefficient, taken as 0.6 in this model.

#### 2.3.3. Boundary Condition

#### 2.4. Experimental Verification

_{u}) were analyzed, aiming at proving the accuracy of the model with experimental values. The equation for the corrosion of steel is based on Equation (11).

_{0}represents the thickness of the tube before corrosion, (mm). t

_{1}represents the thickness of the tube after corrosion (mm).

_{u}; after that, the loading interval was 1/15 N

_{u}, and a rate of 1.0 kN/s was designed during the compression. In the post-peak stage, the loading rate was adopted for displacement control by 0.5 mm/min until the compressive stub column failed [13]. The test was set for displacement control by a loading rate of 1 mm/min until the axial displacement reached 20 mm [49].

#### 2.4.1. Failure Pattern

#### 2.4.2. Load (N)-Displacement (∆) Curve

#### 2.4.3. Ultimate Bearing Capacity

_{f}) and experimental values (N

_{e}) of the peak load of the stub are presented in Table 1. The ratio of numerical values to experimental values is between 0.929 and 1.074, with a mean of 0.990, an SD of 0.033, and a CV of 0.033. It indicates that the finite element method is relatively accurate. N

_{f}represents the numerical values, and N

_{e}represents the experimental values in the References.

## 3. Numerical Investigations

_{cu}) is 30 MPa, yield strength of the steel (f

_{y}) is 345 MPa, replacement rate (r) is 50%, corrosion rate (ρ) is 0, 10%, and 30%, and steel ratio θ is 3%.

#### 3.1. Load (N)-Deformation (∆) Curve

_{u}significantly decreases with corrosion. According to the variation tendency of the N-∆ curve, four characteristic points are defined, namely point A when the concrete is constrained by the steel tube, B at the yield point when the steel tube yields, point C when the specimen reaches the ultimate strength, and point D when N

_{u}reduces and tends to stabilize. The load-displacement curve is divided into five segments by four characteristic points, with the OA section being the elastic stage, the AB section is in the elastic–plastic stage, the BC section is in the plastic strengthening stage, and the CD section is the descending segment.

#### 3.2. The Stress Distribution of the Steel Tube

_{y}. At point C, the stress on the compressive steel tube still maintains a uniform distribution. Due to the defined reinforced section of the steel after corrosion exposure, compared to point B, when the outer steel tube stress reaches the yield stress, the maximum stress of the steel tube at point C improves, and the yield region of the steel tube also increases. After point D, the cross-section of the column undergoes significant expansion and deformation. Under the same characteristic points, the stress value of the steel tube decreases with the corrosion rate increasing.

## 4. Parameter Analysis

_{cu}), the yield strength of the steel tube (f

_{y}), the replacement rate (r), corrosion rate (ρ), and steel ratio (θ). The ranges of these variations are presented in Table 2. The ultimate bearing capacity of the C-GCFST stub after corrosion exposure (N

_{u}) is analyzed in detail by different variations, as shown in Figure 11.

_{u}is presented in Figure 11a. Other parameters remain unchanged, but the ultimate bearing capacity of the stub decreases as the r of the coal gangue aggregate increases. Taking the corrosion rate of 10% as a sample for analysis, the r of the coal gangue aggregate increases from 0 to 25%, 50%, 75%, and 100% with N

_{u}decreasing by 0.62%, 1.46%, 2.39%, and 3.67%, respectively. And the rate of decline becomes faster and faster. The reason may be that the mechanical and surface characteristics of the coal gangue aggregate are poor compared to the natural aggregate. The compressive properties of the coal gangue concrete gradually decrease as the proportion of the coal gangue aggregate increases, resulting in a reduction in N

_{u}.

_{u}and ρ. For specimens with an r of 0, 25%, 50%, 75%, or 100%, N

_{u}decreases by 5.04%, 5.08%, 5.13%, 5.19%, and 5.28% with the ρ increasing from 10% to 40%, respectively. This is because the specimen is immersed in a solution rich in Cl

^{−}, which causes the external steel tube to electrolyze Fe

^{2+}and Fe

^{3+}, causing the corrosion and thinning of the outer wall for the corroded steel tube, thereby weakening the constrained effective coefficient of the outer steel tube on the restrained concrete and reducing N

_{u}.

_{y}on N

_{u}is presented in Figure 11b. For specimens with a corrosion rate of 10%, N

_{u}increases by 6.28%, 8.77%, 10.49%, and 12.67% with the increase in the f

_{y}of the steel tube from 235 MPa to 345 MPa, 390 MPa, 420 MPa, and 460 MPa, respectively. The reason is that the higher the yield strength of the steel tube, the stronger the constrained effect of the outer steel tube on the core concrete, resulting in an increase in the value of N

_{u}. When the f

_{y}of the steel tube (235 MPa, 345 MPa, 390 MPa, 420 MPa, 460 MPa) is the fixed value, N

_{u}decreases by 2.78%, 5.13%, and 5.72% with the ρ increasing from 10% to 40%, 6.22%, and 7.23%, respectively. This indicates that promoting the f

_{y}of the outer steel tube will not reduce the loss of corrosion on the compressive bearing capacity of the specimen.

_{cu}on N

_{u}is shown in Figure 11c. When the concrete strength grade (20 MPa, 30 MPa, 40 MPa, 50 MPa, 60 MPa) is the fixed value, ρ increases from 10% to 40%, and N

_{u}reduces by 6.66%, 5.16%, 4.16%, 3.47%, and 4.62%, respectively. This indicates that the corrosion rate has a slight effect on the compressive bearing capacity of the columns. The reason is that concrete affords a high contribution rate to the compressive bearing capacity of the columns, and the core concrete is not affected by corrosion.

_{u}is presented in Figure 11d. For specimens with a corrosion rate of 10%, θ is enhanced from 2% to 3%, 4%, and 5%, and N

_{u}is promoted by 9.51%, 19.34%, 29.95%, and 41.24%, respectively. This is because as θ increases, the wall thickness of the used steel tube is thicker at the same diameter. Under the same ρ, the constrained concrete more restrained by a thicker steel tube is found, which can improve N

_{u}. When θ (2%, 3%, 4%, 5%) is the fixed value, N

_{u}decreases by 4.01%, 5.10%, 6.66%, 8.79%, and 11.19% with ρ increasing from 10% to 40%, respectively. It may be because ρ has a more significant destructive effect on the steel tube, and increasing the steel ratio of the specimen is not enough to repair the deficiency of the specimen.

## 5. Simplified Design Method

_{0}is the unmodified design strength of the C-CFST columns (N), A

_{sc}is the total cross-section (mm

^{2}), and f

_{sc}is the compressive strength for the C-CFST columns (MPa). f

_{sc}is given by

_{ye}as the yield strength of the steel tube after corrosion, f

_{c}the compressive strength of a concrete cylinder, and θ

_{se}the steel ratio after corrosion exposure. f

_{ye}is given by

_{y}is the yield strength of the uncorroded steel tube. f

_{c}is given by

_{cu}is the compressive strength of a concrete cube. θ

_{se}is given by

_{se}and A

_{c}are the cross-section of the steel tube and concrete after exposure, respectively.

_{d}/N

_{0}and r in Figure 12.

_{f}) and designed values (N

_{d}) of the design strength of the C-GCFST columns with corrosion exposure are shown in Figure 13. The error between N

_{f}and N

_{d}is within 9%, with a mean of 0.990, an SD of 0.001, and a CV of 0.035, which indicates that the predictive effect of this formula is reasonable.

## 6. Conclusions

- (1)
- Compared to the FE and Ref. experimental results, it is said that the failure mode of them was shear failure with bulging outward along the height direction of the specimens. The ratio of numerical to experimental values is between 0.929 and 1.074, with a mean of 0.990 and an SD of 0.033. This indicates that the finite element method is relatively accurate.
- (2)
- When the load exceeds the steel yield strength, as the corrosion rate increases, the specimen will enter various characteristic regions. At the same characteristic points, the stress value of the steel tube decreases with increasing corrosion rate due to the lower bearing capacity of the specimen.
- (3)
- The concrete strength, steel yield strength, and steel ratio are positively correlated with the compressive bearing capacity of the specimen. The increase in the steel yield strength and steel ratio will not reduce the loss from corrosion on the compressive bearing capacity of the stub.
- (4)
- The corrosion rate and replacement rate are negatively correlated with the N
_{u}of the specimen. When the r of the coal gangue aggregate increases from 0 to 100%, N_{u}decreases by 3.67%, 3.84%, 3.92%, and 3.91% due to worse mechanical properties of coal gangue, respectively, within the parameter range of this study. - (5)
- A design method was proposed for predicting the design strength of C-GCFST stub columns with corrosion. The error between the numerical values and designed values is within 9%, which indicates that the predictive effect of this formula is reasonable.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

A_{c} | cross-section area of concrete | N_{d} | modified ultimate bearing capacity with replacement rate |

A_{s} | cross-section area of steel | N_{u} | ultimate bearing capacity |

A_{s}_{e} | cross-section area of steel after exposure | N_{f} | peak load of the numerical model |

A_{sc} | total column cross-section | N_{e} | peak load of the experiment |

D | section diameter of the specimen | μ | cross-section friction coefficient |

L | length of the specimen | r | coal gangue aggregate replacement fraction |

E_{c} | elastic modulus of concrete | μ_{s} | Poisson’s ratio |

E_{s} | elastic modulus of steel tube | t_{0} | thickness of steel tube before corrosion |

E_{se} | elastic modulus of steel tube with corrosion exposure | t_{1} | thickness of steel tube after corrosion |

f_{s}_{c} | compressive strength of the CFST column | θ | steel ratio |

ξ | hoop coefficient of the CFST | RP-2 | bottom point of the model |

f_{c} | compressive strength of the coal gangue concrete cylinder | θ_{se} | steel ratio after corrosion exposure |

f_{cu} | compressive strength of concrete cubes | p | contacted pressure in finite element model |

f_{b0} | compressive strength of concrete under biaxial loading | β | size of the area encompassed by the descending sections and the strain axis |

f_{y} | yield strength of steel tube | Ψ | influence of the coal gangue on descending curvature |

f_{ye} | yield strength of steel tube with corrosion exposure | λ | influence of the coal gangue substitute fraction on strain |

f_{ue} | ultimate strength of steel tube with corrosion rate | τ_{bond} | bonding force in finite element model |

ρ | corrosion rate | τ_{cnt} | critical value in finite element model |

N | axial load | σ | stress |

∆ | axial displacement | σ_{0} | peak stress |

N_{0} | unmodified ultimate bearing capacity | ε | strain |

K_{c} | compressive meridian | ε_{0} | peak strain |

U1, U2, U3 | X-, Y-, Z-axis displacement | ε_{e} | elastic strain |

UR1, UR2, UR3 | X-, Y-, Z-axis angle of rotation | ε_{e1}, ε_{e2}, ε_{e3} | process strain of the compression |

RP-1 | top point of the model |

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**Figure 3.**The numerical and experimental failure pattern of the typical C-CFST stub columns. (

**a**) C3.0-0-20; (

**b**) C4.5-0-20; (

**c**) Q235-20-0; (

**d**) Q345-20-0; (

**e**) SCGA-100-2.75; (

**f**) SCGA-100-3.5; (

**g**) SCGA-100-4.5; (

**h**) S40-50-c; (

**i**) S40-100-c.

**Figure 4.**The compared numerical and experimental N-∆ curves of the C-CFST stub after chloride salt corrosion. (

**a**) C3.0-0-10 and C4.5-0-10; (

**b**) C3.0-0-20 and C4.5-0-20; (

**c**) C3.0-0-30 and C4.5-0-30; (

**d**) Q235-5-0 and Q345-5-0; (

**e**) Q235-10-0 and Q345-10-0; (

**f**) Q235-20-0 and Q345-20-0.

**Figure 5.**The compared numerical and experimental N–∆ curves of the C-GCFST stub at room temperature. (

**a**) SCGA-50-2.75 and SCGA-50-3.75; (

**b**) SCGA-100-2.75 and SCGA-100-3.75; (

**c**) SCGA-50-4.5 and SCGA-100-4.5; (

**d**) S40-50-a and S60-50-a; (

**e**) S40-50-b and S60-50-b; (

**f**) S40-50-c and S60-50-c; (

**g**) S40-100-a and S60-100-a; (

**h**) S40-100-b and S60-100-b; (

**i**) S40-100-c and S60-100-c.

**Figure 7.**Mises stress distribution of the steel tube at point A. (

**a**) ρ = 0; (

**b**) ρ = 10%; (

**c**) ρ = 30% (unit: Pa).

**Figure 8.**Mises stress distribution of the steel tube at point B. (

**a**) ρ = 0; (

**b**) ρ = 10%; (

**c**) ρ = 30% (unit: Pa).

**Figure 9.**Mises stress distribution of the steel tube at point C. (

**a**) ρ = 0; (

**b**) ρ = 10%; (

**c**) ρ = 30% (unit: Pa).

**Figure 10.**Mises stress distribution of the steel tube at point D. (

**a**) ρ = 0; (

**b**) ρ = 10%; (

**c**) ρ = 30% (unit: Pa).

**Figure 11.**The influence of variations on Nu: (

**a**) replacement rate; (

**b**) the yield strength of the steel tube; (

**c**) concrete strength; and (

**d**) steel ratio.

No. | D (mm) × L (mm) × t (mm) | ρ (%) | E_{s} (GPa) | f_{ye} (MPa) | f_{ue} (MPa) | μ_{s} | N_{f} (kN) | N_{e} (kN) | N_{f}/N_{e} | Ref. |
---|---|---|---|---|---|---|---|---|---|---|

C3-0-10 | 90 × 300 × 3.0 | 10 | 152 | 359 | 431 | 0.282 | 623 | 623 | 1.011 | [22] |

C3-0-20 | 20 | 134 | 288 | 339 | 0.296 | 570 | 577 | 0.987 | ||

C3-0-30 | 30 | 122 | 229 | 325 | 0.283 | 549 | 548 | 1.002 | ||

C4.5-0-10 | 90 × 300 × 4.5 | 10 | 145 | 339 | 403 | 0.266 | 833 | 816 | 1.021 | |

C4.5-0-20 | 20 | 140 | 305 | 336 | 0.279 | 750 | 745 | 1.007 | ||

C4.5-0-30 | 30 | 128 | 258 | 318 | 0.309 | 713 | 691 | 1.031 | ||

Q235-5-0-1/2 | 90 × 270 × 1.78 | 5 | 208 | 242 | 474 | - | 384 | 383 | 1.003 | [29] |

Q235-10-0-1/2 | 10 | 208 | 242 | 474 | - | 369 | 381 | 0.969 | ||

Q235-20-0-1/2 | 20 | 208 | 242 | 474 | - | 341 | 354 | 0.965 | ||

Q345-5-0-1/2 | 90 × 270×1.90 | 5 | 210 | 359 | 531 | - | 490 | 511 | 0.960 | |

Q345-10-0-1/2 | 10 | 210 | 359 | 531 | - | 474 | 485 | 0.978 | ||

Q345-20-0-1/2 | 20 | 210 | 359 | 531 | - | 447 | 464 | 0.963 | ||

SCGA-50-2.75 | 140 × 420 × 2.75 | - | 198 | 278 | 346 | 0.258 | 1207 | 1246 | 0.969 | [13] |

SCGA-100-2.75 | - | 198 | 278 | 346 | 0.258 | 1139 | 1179 | 0.966 | ||

SCGA-50-3.75 | 140 × 420 × 3.75 | - | 205 | 285 | 364 | 0.252 | 1347 | 1384 | 0.973 | |

SCGA-100-3.75 | - | 205 | 285 | 364 | 0.252 | 1213 | 1306 | 0.929 | ||

SCGA-50-4.50 | 140 × 420 × 4.50 | - | 201 | 338 | 420 | 0.262 | 1614 | 1657 | 0.974 | |

SCGA-100-4.50 | - | 201 | 338 | 420 | 0.262 | 1535 | 1549 | 0.991 | ||

S40-50-a | 156 × 450 × 3.0 | - | 201 | 282 | 459 | 0.28 | 1425 | 1327 | 1.074 | [49] |

S40-100-a | - | 201 | 282 | 459 | 0.28 | 1232 | 1201 | 1.026 | ||

S60-50-a | - | 201 | 282 | 459 | 0.28 | 1734 | 1630 | 1.064 | ||

S60-100-a | - | 201 | 282 | 459 | 0.28 | 1443 | 1420 | 1.016 | ||

S40-50-b | 158 × 450 × 4.0 | - | 206 | 295 | 465 | 0.28 | 1577 | 1659 | 0.951 | |

S40-100-b | - | 206 | 295 | 465 | 0.28 | 1330 | 1368 | 0.972 | ||

S60-50-b | - | 206 | 295 | 465 | 0.28 | 1828 | 1865 | 0.980 | ||

S60-100-b | - | 206 | 295 | 465 | 0.28 | 1600 | 1672 | 0.957 | ||

S40-50-c | 159 × 450 × 4.5 | - | 204 | 317 | 477 | 0.29 | 1744 | 1718 | 1.015 | |

S40-100-c | - | 204 | 317 | 477 | 0.29 | 1511 | 1540 | 0.981 | ||

S60-50-c | - | 204 | 317 | 477 | 0.29 | 1957 | 2039 | 0.960 | ||

S60-100-c | - | 204 | 317 | 477 | 0.29 | 1782 | 1812 | 0.984 | ||

Mean value | 0.990 | |||||||||

SD | 0.033 | |||||||||

CV | 0.033 |

_{s}represents the elastic modulus. f

_{ye}and f

_{ue}represent the yield strength and ultimate strength. μ

_{s}represents Poisson’s ratio. N

_{f}represents the numerical value of the ultimate strength. N

_{e}represents experimental ultimate strength. SD represents the standard deviation. CV represents the coefficient of variation. Mean value represents the mean value of all N

_{f}/N

_{e}.

Parameter | Ranges | Default |
---|---|---|

f_{cu} (MPa) | 20, 30, 40, 50, 60 | 30 |

f_{y} (MPa) | 235, 345, 390, 420, 460 | 345 |

θ (%) | 1, 2, 3, 4, 5 | 2 |

r (%) | 0, 25, 50, 75, 100 | 50 |

ρ (%) | 10, 20, 30, 40 | — |

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© 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Zhang, T.; Wang, H.; Zheng, X.; Gao, S.
Axial Compressive Behaviours of Coal Gangue Concrete-Filled Circular Steel Tubular Stub Columns after Chloride Salt Corrosion. *Materials* **2024**, *17*, 2782.
https://doi.org/10.3390/ma17112782

**AMA Style**

Zhang T, Wang H, Zheng X, Gao S.
Axial Compressive Behaviours of Coal Gangue Concrete-Filled Circular Steel Tubular Stub Columns after Chloride Salt Corrosion. *Materials*. 2024; 17(11):2782.
https://doi.org/10.3390/ma17112782

**Chicago/Turabian Style**

Zhang, Tong, Hongshan Wang, Xuanhe Zheng, and Shan Gao.
2024. "Axial Compressive Behaviours of Coal Gangue Concrete-Filled Circular Steel Tubular Stub Columns after Chloride Salt Corrosion" *Materials* 17, no. 11: 2782.
https://doi.org/10.3390/ma17112782