Fiber reinforced polymer (FRP) material is commonly applied in retrofitting structures due to the advantages of high strength and well corrosion resistance. Previous studies indicated that retrofitting with FRP sheet was an effective way for protecting the existing structures to resist the blast loads, but little research made comprehensive comparison study on the blast response of RC columns with different retrofitting strategies. This paper proposed a series of FRP retrofitting strategies and evaluated their effect on blast mitigation using numerical analysis approach. Comparison studies were conducted on the effect of FRP type, FRP thickness, and retrofitting mode on blast mitigation. A finite element model of RC columns retrofitted with FRP under blast loading was developed. The model considered the strain rate effect of steel and concrete and the orthotropic property of FRP composites. The reliability of the proposed model was validated against the data from a field blast test. Based on the verified model, the blast responses of RC columns with different retrofitting strategies were numerically investigated. According to the result analysis, appropriate FRP type, FRP thickness, retrofitting mode, and retrofitting length were recommended.

Blast accidents caused by deliberate terrorist attacks and improper operations occur frequently. The blast accidents and their secondary disasters may bring about casualties and economic losses. Additionally, structures easily damage or even collapse when exposed to severe blast loading. For reducing the damage after explosion, the blast protection of buildings should be taken into consideration in the design phase. Besides, it is an urgent and significant task to retrofit the existing structures for blast mitigation.

In order to enhance the blast resistance of the existing building structures, previous studies provide valuable achievements on the retrofitting strategies with some high strength or high stiffness materials bonding on the surface of the structure, such as fiber reinforced polymer (FRP), steel plates, and aluminium foam. These retrofitting schemes can improve the blast resistance performance of the structures in different degrees [

In this study, a series of retrofitting strategies were proposed for improving the blast resistance of reinforced concrete columns. Different FRP types, FRP thicknesses, and retrofitting modes were considered in the proposed retrofitting designs. The blast responses of these retrofitting strategies were evaluated and compared using the numerical analysis method. First, a finite element model of the RC columns retrofitted with FRP under blast loading was developed with the consideration of strain rate effect. The numerical analysis was conducted by the explicit nonlinear finite element program LS-DYNA. The reliability of the proposed numerical model was verified against the relevant experimental results. Furthermore, a series of RC columns retrofitted with FRP under identical blast condition were numerically investigated based on the verified model. The blast responses of the columns were compared, and the effect of different retrofitting strategies was discussed. The reported findings in this study can serve as available reference for blast mitigation of structural design and retrofitting.

In order to investigate the effect of RC columns with different retrofitting strategies on blast mitigation, this paper presents a series of FRP retrofitting schemes, including different FRP types, FRP thicknesses, and retrofitting modes. In view of broader application in the engineering practice, all the designed columns for this comparative study are of square section. Of all the investigated columns, S-1 is a conventional RC column as a control member. Each column consists of a 300 mm × 300 mm square cross section and a height of 3000 mm. The columns are reinforced with four 20 mm longitudinal bars and 10 mm stirrups. As depicted in Figure

Geometry and reinforcement of the column. (a) Reinforcement configuration. (b) Cross section.

Material properties for steel reinforcement and concrete.

Material | Parameters | Magnitude |
---|---|---|

Steel reinforcement | Mass density | 7830 kg/m^{3} |

Young’s modulus | 208 GPa | |

Poisson’s ratio | 0.3 | |

Yield stress | 450 MPa | |

Concrete | Mass density | 2400 kg/m^{3} |

Compressive strength | 40 MPa | |

Shear modulus | 14.86 GPa |

The retrofitted columns are designed from the following three aspects. Firstly, as the commonly used strengthening materials, CFRP, GFRP, AFRP are selected to be the retrofitting materials for comparative study. Table

Material properties for FRP.

Parameters | Magnitude | ||
---|---|---|---|

CFRP | GFRP | AFRP | |

Mass density | 1580 kg/m^{3} | 1600 kg/m^{3} | 1440 kg/m^{3} |

Young’s modulus-longitudinal direction | 138 GPa | 75.6 GPa | 67 GPa |

Young’s modulus-transverse direction | 9.65 GPa | 17.7 GPa | 4.7 GPa |

Poisson’s ratio | 0.021 | 0.025 | 0.028 |

Shear modulus | 5.24 GPa | 2.8 GPa | 2.0 GPa |

Longitudinal tensile strength | 2280 MPa | 1330 MPa | 1420 MPa |

Transverse tensile strength | 57 MPa | 69 MPa | 36 MPa |

Shear strength | 71 MPa | 70 MPa | 53 MPa |

Four retrofitting modes. (a) Mode A. (b) Mode B. (c) Mode C. (d) Mode D.

Each investigated column is given a specific number in this study so as to describe the columns in the following parts conveniently. Except the unretrofitted column S-1, all the retrofitted columns in this study are assigned as “XX-X.” The first capital refers to the abbreviation of FRP type, the second capital is the retrofitting layer of FRP, and the last capital represents the retrofitting mode. For example, G3-C is the column retrofitted with 3-layer GFRP material and the retrofitting mode is Mode C.

Numerical simulation is an effective approach to analyzing the blast response of structures. Some data and phenomena that are difficult to be observed from the experiment can be easily obtained in the numerical simulation. Moreover, this method can significantly save the research expenses. A well-known explicit dynamic program, LS-DYNA, is adopted in numerical analysis.

For the material model of both longitudinal bars and stirrups, kinematic hardening plasticity model is chosen to model the steel reinforcement. In LS-DYNA, this model is implemented as keyword MAT_PLASTIC_KINEMATIC (MAT003). The yield stress function of steel is given by

Stress-strain relationship of hardening material.

The strength of steel materials increases under the high strain rate impact. Based on the Cowper–Symonds model [

Currently, the concrete material models that are commonly used in the impact issues mainly include the Johnson–Holmquist–Cook (JHC) model [_{1} and _{2} are damage constants.

Constitutive law of JHC model.

In JHC model, the relationship between pressure and volume is described as equation of state in three response regions as follows. The curve of hydrostatic pressure and volumetric strain is also illustrated in Figure _{1}, _{2}, and _{3} are material constants.

Relationship of hydrostatic pressure and volumetric strain in JHC model.

MAT_ENHANCED_COMPOSITE_DAMAGE (MAT054) in LS-DYNA is applied to model the behavior of FRP composite. This material model can effectively simulate the composite materials especially orthotropic materials. The failure criterion of this material model is based on Chang–Chang model. It includes the failure criteria for the tensile fiber mode, compressive fiber mode, tensile matrix mode, and compressive matrix mode [

The numerical results are affected by the mesh size especially when the nonlinear material models are adopted in simulation [

The press-time history curve of typical blast load is shown in Figure _{A}. Then the press drops gradually to the initial atmospheric press through the positive press duration _{0}. During the time of

Press-time curve of blast loading. (a) Typical blast loading. (b) Simplified blast loading.

The reinforcement bars are modeled with beam elements, concrete is employed with solid elements, and FRP is adopted with shell elements. Separate model is utilized to develop the RC column wrapped with FRP. In order to be consistent with the fixed ends condition in the following blast tests, translational and rotational constraints for

The above-mentioned numerical modeling should be validated against the relevant blast tests. The test implemented in laboratory with simulated blast loading is inappropriate for verification because the strain rate of simulated blast loading is different from the stain of real blast loading in explosion. The available data are limited in the relevant blast test. In this paper, the finite element model is validated against the blast test of RC circular column retrofitted with CFRP carried out by Liu [

The column in the field blast test was a circular section column with a diameter of 400 mm and a length of 3500 mm. The concrete strength grade was C40 and the reinforcement ratio was 0.9%. The column was wholly retrofitted with one-layer CFRP sheet. As to Case 26 in the blast test, the explosive was 2 kg TNT and was detonated at a standoff distance of 1500 mm. The numerical model is generated by the proposed model mentioned above, and the geometry of column and material properties are in accordance with the blast test. Figure ^{1/3}, which is classified as far blast event. One acceleration sensor was set on the backside of the column with a height of 300 mm. Figure

Finite element model of tested column. (a) Rebar. (b) Concrete. (c) FRP.

Deformation of tested column. (a) Test result. (b) Numerical result.

Acceleration history curve of the test point on the column.

Comparison of numerical results and test data.

Test | Simulation | Deviation rate (%) | |
---|---|---|---|

Strain of longitudinal bar | 150 | 144 | −4.0 |

Strain of stirrup | 273 | 261 | −4.4 |

Arrival time of peak pressure | 2.56 ms | 2.299 ms | −10.19 |

Peak pressure | 0.32 MPa | 0.317 MPa | −0.94 |

Moreover, in order to verify the proposed numerical approach further, a finite element model is developed and compared with the results analyzed in [

Comparison of the maximum deflection in the analysis.

Case | Charge weight (kg) | Standoff distance (m) | Maximum deflection (mm) | Deviation rate (%) | |
---|---|---|---|---|---|

Crawford et al. [ | Present analysis | ||||

1 | 682 | 3.05 | 132 | 146.25 | 10.80 |

2 | 682 | 3.05 | 18 | 19.13 | 6.28 |

3 | 1364 | 6.1 | 88 | 91.47 | 3.94 |

Displacement history curve at midspan of the column in Case 2.

From the above validation and comparison, the proposed finite element proved to be a reliable approach to simulate the performance of RC columns retrofitted with FRP under blast loading. In addition, the verified numerical model is suitable for evaluating the blast response of RC columns retrofitted with FRP in different blast situation or different retrofitting scheme.

Based on the verified finite element model, a series of RC columns retrofitted with different strategies are numerically analyzed. The details of the column and the design of retrofitting schemes are described in Section ^{1/3}. After being solved by LS-DYNA, the numerical results of the numerical models are postprocessed by LS-PrePost, and available data are exported.

Deformation is an important index to measure the blast resistance performance of the structural members. According to the numerical results, the columns mainly suffer flexural deformation. The maximum displacement occurs at the midspan of the member. Therefore, the displacements of midspan of the columns under blast loading are exported to measure the blast performance. Additionally, damage assessment is chosen to evaluate the damage degree of the structure. Based on the Unified Facilities Criteria (UFC 3-340-02), support rotation angle is usually used as a failure criterion for structural members. The support rotation angle is a combination of the maximum deflection of a given column and the length of the column. This angle is usually used in damage assessment of the structure under blast loading and blast resistance design. The support rotation angle

Information and main results of investigated columns.

Column no. | FRP type | FRP thickness (mm) | Retrofitting mode | Max deflection (mm) | |
---|---|---|---|---|---|

S-1 | — | — | — | 36.71 | 1.40 |

C1-A | CFRP | 0.17 | Mode A | 28.56 | 1.09 |

C1-B | CFRP | 0.17 | Mode B | 31.57 | 1.21 |

C1-C | CFRP | 0.17 | Mode C | 31.09 | 1.19 |

C1-D | CFRP | 0.17 | Mode D | 32.44 | 1.24 |

C2-A | CFRP | 0.34 | Mode A | 23.91 | 0.91 |

C3-A | CFRP | 0.51 | Mode A | 20.79 | 0.79 |

C3-B | CFRP | 0.51 | Mode B | 23.17 | 0.88 |

C3-C | CFRP | 0.51 | Mode C | 22.93 | 0.88 |

C3-D | CFRP | 0.51 | Mode D | 23.85 | 0.91 |

C4-A | CFRP | 0.68 | Mode A | 18.08 | 0.69 |

C5-A | CFRP | 0.85 | Mode A | 17.90 | 0.68 |

A1-A | AFRP | 0.17 | Mode A | 33.82 | 1.29 |

A1-B | AFRP | 0.17 | Mode B | 35.74 | 1.36 |

A1-C | AFRP | 0.17 | Mode C | 35.13 | 1.34 |

A1-D | AFRP | 0.17 | Mode D | 35.96 | 1.37 |

A2-A | AFRP | 0.34 | Mode A | 29.55 | 1.13 |

A3-A | AFRP | 0.51 | Mode A | 25.76 | 0.98 |

A3-B | AFRP | 0.51 | Mode B | 27.69 | 1.06 |

A3-C | AFRP | 0.51 | Mode C | 27.03 | 1.03 |

A3-D | AFRP | 0.51 | Mode D | 28.04 | 1.07 |

A4-A | AFRP | 0.68 | Mode A | 22.79 | 0.87 |

A5-A | AFRP | 0.85 | Mode A | 22.03 | 0.84 |

G1-A | GFRP | 0.17 | Mode A | 31.73 | 1.21 |

G1-B | GFRP | 0.17 | Mode B | 34.61 | 1.32 |

G1-C | GFRP | 0.17 | Mode C | 34.15 | 1.30 |

G1-D | GFRP | 0.17 | Mode D | 35.12 | 1.34 |

G2-A | GFRP | 0.34 | Mode A | 26.93 | 1.03 |

G3-A | GFRP | 0.51 | Mode A | 23.11 | 0.88 |

G3-B | GFRP | 0.51 | Mode B | 24.98 | 0.95 |

G3-C | GFRP | 0.51 | Mode C | 24.27 | 0.93 |

G3-D | GFRP | 0.51 | Mode D | 25.86 | 0.99 |

G4-A | GFRP | 0.68 | Mode A | 20.92 | 0.80 |

G5-A | GFRP | 0.85 | Mode A | 20.38 | 0.78 |

The mass of explosive in the numerical analysis is relatively small, and the scaled distance is 0.4 m/kg^{1/3}. The blast event is identified as the intermediate class, so the given columns all suffer slight damage based on the results of support rotation angle. As a whole, the retrofitting of FRP material can reduce the deformation and damage of the columns under blast loading. However, under the same blast condition, the dynamic responses of columns retrofitted with different strategies are not uniform. It is necessary to find out the effect of different retrofitting strategies on blast mitigation. The details are discussed from the following aspects.

The RC columns retrofitted with different thicknesses of FRP were initially reported to simulate the blast resistance of RC columns retrofitted with different layers of FRP material. Figure

Displacement history curve at midspan of the column retrofitted with different FRP thicknesses. (a) CFRP. (b) AFRP. (c) GFRP.

The blast responses of RC columns retrofitted with different types of FRP material were also studied. For expressing the blast mitigation effect of FRP materials, the unretrofitted column S-1 was also included in the comparative study. Figure

Damage distribution of columns retrofitted with different types of FRP (left view). (a) S-1. (b) A1-A. (c) C1-A. (d) G1-A.

Displacement history curve at midspan of the column retrofitted with different FRP types.

In addition to full FRP retrofitting, three local retrofitting methods are also designed in this paper. The details of the four retrofitting strategies are described in Section

Displacement history curve at midspan of the columns retrofitted with different modes. (a) CFRP. (b) AFRP. (c) GFRP.

Maximum deflection of the columns retrofitted with different modes. (a) CFRP. (b) AFRP. (c) GFRP.

According to the above research, Mode C exhibits the best blast resistance performance among all partial retrofitting modes. In Mode C, the influence of retrofitting length on blast mitigation is further studied. As can be seen from Figure

Design of retrofitting length.

Maximum displacement of columns retrofitted with different retrofitting lengths.

In this paper, the dynamic response of reinforced concrete columns retrofitted with FRP is investigated using the numerical analysis approach. The main findings are summarized as follows.

A finite element model of RC columns retrofitted with FRP under blast loading is developed. The strain rate effect of concrete and steel and orthotropic property of FRP material are considered in the finite element model. The proposed model is validated against the relevant test data. The numerical analysis corresponds well with the previous results.

A series of RC columns retrofitted with FRP are numerically analyzed using this reliable finite element model. The retrofitted columns are designed with different FRP types, FRP thicknesses, and retrofitting modes. Compared with conventional RC column, retrofitting with FRP can effectively mitigate the damage and deformation of the columns under blast loading.

The deformation of the column decreases with the increase of FRP thickness, but not in the same proportion. The blast mitigation effect weakens with the increase of the FRP material. In the investigated cases, when the thickness of FRP is above 0.68 mm, adding the thickness of FRP has little effect in terms of improving the blast resistance of the column. Thus the maximum thickness for FRP retrofitting suggested in this study is 0.68 mm (namely, 4 layers).

In the three FRP types studied, CFRP is the best retrofitting material for improving the blast resistance of RC columns. GFRP is recommended as the retrofitting material if the cost of material is considered.

A full retrofitting mode and three local retrofitting modes are designed in this study. The full retrofitting mode performs the best in terms of blast mitigation while the material amount is more than others. Among the three local retrofitting modes, retrofitting at both two ends and middle part of the column is suggested. 400∼700 mm retrofitting length for each section is regarded as the proper length for this retrofitting mode.

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that they have no conflicts of interest regarding the publication of this paper.

This study was financially supported by the National Natural Science Foundation of China (NSFC) (Grant no. 51878056), the Social Development Foundation for Science and Technology Planning Project of Shaanxi Province (Grant no. 2019SF-256), and the Fundamental Research Funds for the Central Universities, CHD (Grant nos. 300102280203 and 300102289105).