Unified Model for Axial Bearing Capacity of Concrete-Filled Steel Tubular Circular Columns Based on Hoek–Brown Failure Criterion
Abstract
:1. Introduction
2. Database
References | R (%) | fcu (MPa) | fc (MPa) | Number |
---|---|---|---|---|
Liu et al. [3] | 0 | 59.0 | 50.1 | 1 |
Bhartiya et al. [17] | 0 | 42–58.5 | 32.8–43.1 | 4 |
Chen et al. [19] | 100 | 51.7 | 41.5 | 1 |
Zhu et al. [20] | 0 | 47–121.1 | 38–112.1 | 3 |
Wang et al. [21] | 0 | 59.8 | 49.6 | 1 |
Wang et al. [22] | 0 | 85.4 | 73.2 | 1 |
Wang et al. [6] | 0–100 | 45.3–67.1 | 36.9–52.9 | 5 |
Johansson [23] | 0 | 52.3–117.2 | 36.6–93.8 | 2 |
Yuan et al. [24] | 0 | 47.6 | 38.9 | 1 |
Gao et al. [25] | 0 | 59 | 50.1 | 1 |
Chen et al. [26] | 0 | 28.3–52.2 | 19–33.8 | 2 |
Jamaluddin et al. [27] | 0 | 20–115.8 | 13–90 | 22 |
Yan et al. [9] | 0 | 102.4–141 | 89.2–128.1 | 4 |
Lam et al. [28] | 0 | 46.3–109.4 | 37–90 | 2 |
Yang et al. [29] | 0 | 36.9–98.4 | 30.5–102.2 | 3 |
Liu et al. [30] | 0 | 73–97 | 60–89 | 2 |
Tao et al. [31] | 0 | 59.8–61.8 | 50.1–54.8 | 2 |
Summary | 0–100 | 20–141 | 13–128.1 | 57 |
References | L (mm) | D (mm) | t (mm) | L/D | D/t | R (%) | fsy (MPa) | fcu (MPa) | fc (MPa) | Nu (kN) | Number |
---|---|---|---|---|---|---|---|---|---|---|---|
Ding et al. [32] | 450 | 158 | 1.50–2.14 | 2.85 | 74–105 | 0 | 286–308 | 48.5 | - | 815–907 | 2 |
Liu et al. [3] | 688–2748 | 275–1100 | 4.14–16.48 | 2.5 | 54–70 | 0 | 260–281 | 59.0 | 50.1 | 3956–59,361 | 8 |
De Azevedo et al. [4] | 450–560 | 153–178 | 6.56 | 3 | 23–27 | 0–50 | 440–426 | - | 25.2–34 | 2120–2902 | 23 |
Bhartiya et al. [17] | 420–600 | 60–140 | 4.5–5.4 | 3–10 | 13–26 | 0 | 360 | 42–58.5 | 32.8–43.1 | 293–1529 | 22 |
Guler et al. [33] | 400 | 114 | 2.99–6.02 | 3.5 | 19–38 | 0 | 306–314 | - | 115 | 402–1830 | 21 |
Guler et al. [7] | 300 | 76 | 2.48–3.65 | 3.94 | 21–31 | 0 | 278–316 | - | 145 | 752–876 | 12 |
Giakoumelis et al. [34] | 300 | 115 | 3.75–5.02 | 2.62 | 23–30 | 0 | 343–365 | 31.4–104.9 | - | 929–1787 | 13 |
Lyu et al. [5] | 300–600 | 100–200 | 2.89 | 3 | 35–68 | 0–100 | 434 | 51.6–57.2 | - | 1000–3039 | 15 |
Xiong et al. [35] | 210–600 | 114–219 | 3.6–10 | 1.84–2.74 | 18–35 | 0 | 300–428 | - | 51.6–193.3 | 2314–9187 | 18 |
Schneider et al. [36] | 605–616 | 140–141 | 3–6.68 | 4.3 | 21–47 | 0 | 285–537 | - | 23.8–28.2 | 881–2715 | 3 |
Sakino et al. [37] | * | 108–450 | 2.96–6.47 | - | 36–70 | 0 | 279–853 | - | 25.4–85.1 | 941–13,776 | 36 |
Chen et al. [19] | 420–1680 | 138 | 2.71 | 3.05–12.20 | 50–51 | 100 | 299 | 51.7 | 41.5 | 824–1115 | 12 |
Lu et al. [38] | 387–399 | 129–133 | 3–5 | 3 | 27–43 | 0 | 306 | 53.7–76.4 | - | 1068–1774 | 36 |
Su et al. [13] | 267–399 | 89–133 | 2.98–3.98 | 3 | 23–34 | 0 | 980–1233 | 35.5–114.9 | - | 1400–4203 | 13 |
Tam et al. [39] | 420–510 | 138–171 | 2.83 | 3 | 49–60 | 0–100 | 340–389 | - | 37.8–41.7 | 1148–1708 | 8 |
Uy et al. [15] | 150–2940 | 51–203 | 1.2–2.8 | 2.95–14.47 | 34–79 | 0 | 259–321 | - | 20–75.4 | 164–1550 | 37 |
Cai et al. [40] | 222–421 | 89–169 | 4.92–12.08 | 2.50 | 14–27 | 0 | 388–460 | - | 39.9–78.7 | 1001–5000 | 40 |
Dai et al. [41] | 899–977 | 298–325 | 7.74–11.94 | 3 | 27–38 | 0 | 242–544 | 40–53.8 | - | 4640–13,200 | 18 |
O’Shea et al. [42] | 578–665 | 165–190 | 0.86–2.82 | 3.5 | 67–192 | 0 | 186–363 | - | 41–108 | 1350–3360 | 15 |
Yang et al. [43] | 342–657 | 114–219 | 2.19–2.86 | 3 | 52–77 | 0–50 | 336–350 | 36.6–42.7 | - | 669–2158 | 15 |
Liew et al. [14] | 210–600 | 114–219 | 3.6–12.5 | 1.84–3 | 13–32 | 0 | 380–779 | - | 51.6–193.3 | 2314–9187 | 25 |
Han et al. [44] | 300–2000 | 100–200 | 3 | 3–10 | 33–67 | 0 | 304 | 58.5 | - | 708–2383 | 17 |
Gupta et al. [45] | 340 | 47–113 | 1.87–2.89 | 3–7.19 | 25–39 | 0–30 | 360 | 25.8–35.7 | - | 145–822 | 72 |
Abed et al. [46] | 250–350 | 114–167 | 3.1–5.6 | 2.15 | 30–37 | 0 | 300 | 53–70 | - | 1042–1873 | 6 |
Yu et al. [47] | 510–650 | 165–219 | 2.72–4.78 | 3 | 35–81 | 0 | 350 | 42.6–77.2 | - | 1560–3400 | 6 |
Ekmekyapar et al. [48] | 300–900 | 114 | 2.74–5.9 | 2.62–7.87 | 19–42 | 0 | 235–355 | - | 56.2–107.2 | 877–1990 | 18 |
Yu et al. [11] | 300–3000 | 100 | 1.9 | 3–30 | 53 | 0 | 404 | 121.6 | - | 288–1170 | 10 |
Yang et al. [10] | 360 | 120 | 1.77 | 3 | 68 | 0–75 | 287 | 55.3–63.4 | - | 768–823 | 7 |
Chan et al. [49] | 250 | 95 | 5.4–7.6 | 2.62 | 13–18 | 0 | 418–476 | 39 | - | 1168–1435 | 6 |
Zhu et al. [20] | 695 | 200 | 6 | 3.48 | 33 | 0 | 451 | 47–121.1 | 38–112.1 | 3503–5099 | 7 |
Wei et al. [12] | 450 | 140 | 2 | 3.21 | 70 | 0 | 268 | 105–125 | - | 1684–1718 | 4 |
Zhou et al. [1] | 525–975 | 141–262 | 2.11–3.04 | 3.72 | 66–97 | 0 | 691–734 | 50.4–53.4 | - | 1550–4302 | 15 |
Xue et al. [50] | 700 | 219 | 3–5 | 3.2 | 44–73 | 0 | 313 | 62.5 | - | 2647–3218 | 3 |
Oliveira et al. [16] | 343–1143 | 114 | 3.35 | 3–10 | 34 | 0 | 287 | - | 32.7–105.5 | 599–1453 | 16 |
Zhu et al. [51] | 995 | 558 | 16.53 | 1.78 | 34 | 0 | 546 | 31.7 | - | 28,830–29,590 | 3 |
Ding et al. [52] | 900 | 300 | 3.76 | 3 | 78–81 | 0 | 311 | 35.5–54.4 | - | 3540–4976 | 4 |
Xiao et al. [53] | 400 | 199 | 4 | 2 | 50 | 0–100 | 465 | 36.7–47.2 | - | 2182–2513 | 5 |
Wan et al. [54] | 1300–3300 | 273–426 | 6.81–7.78 | 3.05–12.09 | 40–55 | 0 | 313–328 | 30.51 | - | 3155–6826 | 2 |
Hu et al. [55] | 696 | 232 | 7.96–12.55 | 3 | 18–29 | 0 | 376–442 | - | 48.2–122 | 4846–8917 | 8 |
Wang et al. [21] | 657–1890 | 216–632 | 2.6–11.2 | 3 | 51–83 | 0 | 260–590 | 59.78 | 49.64 | 4030–29,463 | 12 |
Wang et al. [22] | 306–954 | 153–477 | 1.54–11.36 | 2 | 42–99 | 0 | 290–345 | 85.4 | 73.2 | 1823–20,462 | 36 |
Chen et al. [8] | 342 | 108–115 | 2.05–8.03 | 2.98–3.17 | 14–53 | 0 | 252–304 | 70.86 | 130.8–113.2 | 904–1748 | 9 |
Wang et al. [6] | 400–420 | 133–140 | 2.64–4.66 | 3 | 30–50 | 0–100 | 302–335 | 45.3–67.1 | 36.9–52.9 | 1065–1749 | 39 |
Han et al. [56] | 180–750 | 60–250 | 1.87–2 | 3 | 32–125 | 0 | 282–404 | 85.2–90 | - | 312–4800 | 26 |
Johansson [23] | 650 | 159 | 5–10 | 4.1 | 16–32 | 0 | 355–402 | 52.3–117.2 | 36.6–93.8 | 2040–3710 | 6 |
Chang et al. [57] | 288 | 168 | 4.98–8.06 | 3.5 | 21–34 | 0 | 291–369 | - | 34.1 | 1501–2312 | 8 |
Lai et al. [58] | 248–420 | 89–169 | 0.95–10.06 | 2.08–2.96 | 17–116 | 0 | 285–476 | - | 27–125.3 | 456–4358 | 28 |
Huang et al. [59] | 600–900 | 200–300 | 2–5 | 3 | 40–150 | 0 | 266–342 | - | 27.2–31.2 | 2013–3025 | 3 |
Liao et al. [60] | 740 | 180 | 3.8 | 4.11 | 47 | 0 | 360 | 64.1 | - | 2070–2110 | 2 |
Hu et al. [61] | 400 | 202–204 | 1–2 | 1.97 | 102–202 | 0 | 226–242 | - | 35.9–42.2 | 1380–1864 | 3 |
Duarte et al. [62] | 300–500 | 114–219 | 2.7–4.25 | 2.28–3.29 | 40–57 | 0–15 | 284–456 | 25.2–49.5 | - | 484–2888 | 15 |
Summary | 150–3300 | 47–1100 | 0.86–16.54 | 1.78–30 | 13–202 | 0–100 | 186–1233 | 25–125 | 20–193.3 | 145–59361 | 788 |
3. Establishment of a Unified Model for Axial Bearing Capacity
3.1. Axial Bearing Capacity Nu
3.2. Hoek–Brown Failure Criterion
3.3. Ultimate Compressive Strength fcc
3.4. Unified Model for Axial Bearing Capacity
3.4.1. Concrete Strength Conversion
3.4.2. Axial Bearing Capacity Model for CFST Circular Short Columns Nus
3.4.3. Axial Bearing Capacity Model for CFST Circular Long Columns Nul
4. Assessment of Axial Bearing Capacity Model for CFST Circular Columns
4.1. Assessment of Axial Bearing Capacity Model for CFST Circular Short Columns
4.2. Assessment of Axial Bearing Capacity Model for CFST Circular Long Columns
4.3. Assessment of Unified Model for CFST Circular Columns
4.4. Prediction of Axial Bearing Capacity of CFST Columns under High Temperature
5. Conclusions
- (1)
- Most of the existing models are empirical models. On the one hand, there are some limitations in the application of the models. On the other hand, the types of experimental data and the parameter range affect the accuracy of the published models.
- (2)
- There is a linear relationship between cylinder and cube compressive strength, and the ratio is approximately 0.82.
- (3)
- The ultimate compressive strength was established by the Hoek–Brown failure criterion, considering the section size, diameter–thickness ratio, and concrete strength. At the same time, the vertical and transverse stress components of steel tubular are determined by the von Mises yield criterion. Therefore, from this point of view, the steel corresponding to the ultimate compressive strength may not reach the yield strength.
- (4)
- Based on the ultimate compressive strength established by the Hoek–Brown failure criterion, the axial bearing capacity model for CFST short columns can accurately predict 681 test data, and AV and IAE are 1.008 and 0.093, compared with other existing models. It also fully shows that it is reasonable based on superposition theory and limit equilibrium theory. At the same time, the axial bearing capacity model can accurately predict the data of 107 CFST long columns, and AV and IAE are 1.031 and 0.108. The axial bearing capacity for CFST short and long columns can be predicted at the same time since the proposed model is a unified model. The prediction results of the proposed unified model are 1.012 and 0.094, respectively, which shows that the proposed model is accurate.
- (5)
- The proposed model also predicts the axial bearing capacity of CFST columns under high temperatures, and the AV and IAE are 1.007 and 0.100. On the one hand, it shows that the proposed model can be used to predict the axial bearing capacity of CFST columns under high temperatures. On the other hand, it also shows that the establishment process and confinement mechanism of the proposed model are correct and reasonable.
- (6)
- From the assessment results of the models, the calculation model for axial bearing capacity established by the superposition theory and limit equilibrium theory and the stress component of steel tube based on von Mises yield criterion is reasonable and reliable.
Funding
Data Availability Statement
Conflicts of Interest
References
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References | Models | Comments |
---|---|---|
Han [63] | fck: characteristic value of compressive strength ξ: confinement index | |
Liu et al. [3] | Ditto | |
Giakoumelis et al. [34] | Ditto | |
Sakino et al. [37] | | Dc: diameter of the core concrete column k = 4.1, λ = 0.27. |
Lu et al. [38] | Vf: volume percentage of steel fiber | |
Xiao et al. [53] | Ditto | |
Hu et al. [55] | Ditto | |
Wang et al. [22] | Ditto | |
Chen et al. [8] | Ditto | |
Han et al. [56] | Ditto | |
Chang et al. [57] | Ditto | |
Oliveira et al. [64] | Ditto | |
Yu et al. [65] | Ditto | |
Lai et al. [66] | Ditto |
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Zhou, Z. Unified Model for Axial Bearing Capacity of Concrete-Filled Steel Tubular Circular Columns Based on Hoek–Brown Failure Criterion. Buildings 2023, 13, 2408. https://doi.org/10.3390/buildings13102408
Zhou Z. Unified Model for Axial Bearing Capacity of Concrete-Filled Steel Tubular Circular Columns Based on Hoek–Brown Failure Criterion. Buildings. 2023; 13(10):2408. https://doi.org/10.3390/buildings13102408
Chicago/Turabian StyleZhou, Ziao. 2023. "Unified Model for Axial Bearing Capacity of Concrete-Filled Steel Tubular Circular Columns Based on Hoek–Brown Failure Criterion" Buildings 13, no. 10: 2408. https://doi.org/10.3390/buildings13102408