Columns of frame structures are the key loadbearing components and the exterior columns are susceptible to attack in terrorist blasts. When subjected to blast loads, the columns would suffer a loss of bearing capacity to a certain extent due to the damage imparted, which may induce the collapse of them and even cause the progressive collapse of the whole structure. In this paper, the highfidelity physicsbased finite element program LSDYNA was utilized to investigate the dynamic behavior and damage characteristics of the widely used concretefilled steel tube (CFST) columns subjected to blast loads. The established numerical model was calibrated with test data in open literatures. Possible damage modes of CFST columns under blast loading were analyzed, and the damage criterion based on the residual axial load capacity of the columns was adopted to assess the damage degree. A parametric study was conducted to investigate the effects of critical parameters such as blast conditions and column details on the damage degree of CFST columns. Based on the numerical simulation data, an empirical equation was proposed to estimate the variation of columns damage degree with the various parameters.
Concretefilled steel tube (CFST) columns have been widely used in engineering structures such as highrise buildings, arch bridges, and factories, as they have advantages of high strength and excellent ductility due to a confinement effect and a changed buckling mode [
Fujikura et al. experimentally investigated the dynamic responses of CFST bridge pier column specimens under blast loading. According to the magnitude of the support rotation, the damage states of the column specimens were categorized into three types, that is, the plastic deformation, onset of fracture, and postfracture. The authors also compared the maximum response of the specimens obtained from the simplified method based on the equivalent singledegreeoffreedom (SDOF) theory with the test data [
The review of these literatures indicates that the mode of response and damage criterion are key issues in understanding the dynamic behavior and damage characteristics of CFST columns subjected to blast loads, as some damage criterions are only applicable to certain damage mode of the columns and different conclusions may be drawn under varied damage modes as stated previously. The objective of this paper is to study the damage modes and damage assessment of CFST columns under blast loading. The numerical model is established using the finite element program LSDYNA and calibrated with correlated experimental studies by other researchers. Possible damage modes of the columns subjected to blast loads are analyzed, and the criterion suitable to assess the degree of the columns damage is adopted accordingly. Parameters that may affect the damage degree of the columns are analyzed in the study; they are blast condition, column dimension, steel ratio, and axial load ratio, which are then incorporated into a proposed equation, capable of estimating the damage degree of CFST columns based on the numerical results.
The highfidelity physicsbased finite element program LSDYNA was used in the paper. To calibrate the employed numerical models for simulating the dynamic responses of CFST columns to blast loads, one of the blast tests on CFST columns conducted by Zhang et al. [
Test setup (Zhang et al. [
The steel frame that holds the specimen in place
The test configuration
Considering the large strain and high strain rate problems involved in analyzing the responses of steel tube under blast loading, the plastic kinematic model, which takes into account the strain hardening and strain rate effects, is adopted for steel simulation. The dynamic yield stress of it is expressed as follows [
Material parameters of the steel tube.
Parameter  Mass density 
Poisson’s ratio 






Failure strain 

Value  7850  0.3  358  203  414  0  40.4  5  0.2 
Plastic kinematic model for steel modeling.
The infill concrete subjected to blast loading may experience large strains, high strain rates, and high pressures. Besides, the collapse of air void, as well as the dilation caused by shearing cracks, plays an important role in the damage evolution of concrete. Thus the JohnsonHolmquistCook (JHC) concrete model is used to simulate the concrete, and the equivalent stress of it is expressed as a function of pressure, strain rate, and damage as follows [
JHC model for concrete modeling.
The accumulated damage is expressed as
The relation between pressure and volumetric strain is defined as
The reliability of this concrete model in predicting the responses of concrete structures to blast loads has been demonstrated by many researchers [
Material parameters of the infill concrete.
Parameter  Mass density 







Value  2440  0.79  1.60  0.007  0.61  37.9  7.0 


Parameter  Shear modulus 
Maximum tensile pressure 
Threshold strain rate 
Plastic strain before fracture 
Crushing pressure 
Crushing volumetric strain 
Locking pressure 


Value  14.86  4.0  1.0  0.01  16  0.001  800 


Parameter  Locking volumetric strain 
Damage constant 
Damage constant 
Pressure constant 
Pressure constant 
Pressure constant 



Value  0.1  0.04  1.0  85  −171  208 
The BelytschkoTsay shell element is used in the study to model the steel tube, and the infill concrete is modeled with singlepoint integration solid elements. A mesh size of 25 mm is selected for the steel tube and infill concrete through a numerical convergence study. It is found that further refinement of element size has little effect on the numerical results but increases the calculation time enormously. A perfect bond between steel tube and infill concrete is assumed in the numerical study since no researches have reported a noticeable debond between the two materials in blast tests. In order to simulate the physical fracture, shear failure, and crushing of the concrete under blast loading, the erosion algorithm is used to account for concrete failure. Considering the strain rate effect on the concrete strength, the erosion criterion based on the principle strain is often used [
In order to simulate the real stress state of CFST columns, the linearly increasing axial quasistatic loads up to the service axial load level are applied to the top of the column prior to blast loading through the implicit solver. To avoid too much oscillation of the column, the time duration for increasing the loads from zero to full service level is 150 ms. Then, the computational algorithm switches from implicit to explicit, and the blast loads are applied over the front surface of the column with the axial loads unchanged.
Blast loads are generated using the ConWep air blast model [
Numerical simulations of the blast test were carried out and the dynamic response and damage mode of column S4 were obtained. Since the recording of LVDT1 at the center of column S4 was missing in the test, the value of LVDT2 (see Figure
Comparison of the displacement data from test and that of numerical simulation.
Comparison of the column damage mode in the test and that from numerical simulation.
Test result (Zhang et al. [
Numerical result
The above calibrated numerical model is utilized herein to simulate dynamic behavior and possible damage modes of CFST column under blast loading. The column is designed based on the specifications provided by Chinese Standard CECS 159: 2004 [
Sketch of the numerical analysis model.
Explosion scenario
Column details
As the blast load parameters are related to both explosive mass and standoff distance, the scaled standoff distance is introduced to consider their combined effects and is defined as [
Three damage modes of the CFST column under blast loading have been observed through a number of simulations; they are flexural damage, shear damage, and localized damage. Table
Possible damage modes of the CFST column.



Damage mode 

50  0  ≤0.21  Localized 
0.22–0.24  Shear  
≥0.26  Flexural  


250  0  ≤0.25  Localized 
0.30–0.48  Shear  
≥0.52  Flexural  


50  1.85  ≤0.16  Localized 
≥0.18  Flexural 
Flexural damage mode of CFST column under blast loading.
CFST column
Infill concrete
Shear damage mode of CFST column under blast loading.
CFST column
Infill concrete
Localized damage mode of CFST column under blast loading.
CFST column
Infill concrete
Figure
Figure
As discussed above, flexural damage and shear damage of the column are due to the deformation and internal force of the whole member induced by the blast loads. On the contrary, localized damage of the CFST column is dominated by the deformation and failure of the concrete infill and steel tube in the vicinity of the explosion, whilst other parts of the column remain almost elastic and the global deformation of the column is small.
Figure
It should be mentioned that these damage modes are only typical ones. Sometimes, there exists a combination of these damage modes.
As discussed previously, the CFST column subjected to blast loads may undergo flexural damage, shear damage, and localized damage; thus the damage criterion for the column should be chosen carefully and the appropriate one is expected to be applicable to all the possible damage modes of the column. In this paper, the damage criterion based on the residual axial load capacity is adopted for CFST columns due to the following reasons: (1) the structure column is primarily designed to carry the axial load and the axial load capacity of it reflects both its global properties and material characteristics; (2) the commonly used deformationbased damage criterions, that is, the support rotation, lateral deflection, and ductility, may not be appropriate for the evaluation of localized damage of the column; and (3) the residual axial load capacity of the columns is an explicit metric of the damage imparted and it also provides information in assessing the collapse possibility of a blast damaged column.
The damage index adopted herein is based on the index from Shi et al. [
It is noted that if the ratio of the service axial load to maximum axial load capacity of the column is denoted as
During this step, the linearly increasing axial load is applied on the column head until the column collapses; then
Three substeps as follows are required to obtain
Substitute the values of
In this section, effects of several key parameters on the damage degree of CFST columns are analyzed. These parameters include the scaled standoff distance, height of burst, explosive mass, column depth, column width, column steel ratio, and axial load ratio, as listed in Table
Parameters used in the numerical parametric study.
Parameters 





Steel ratio 
Axial load ratio 

Benchmark case  0.18–0.50  0  50  0.6  0.6  0.13  0.35 


Contrast cases  0.15–0.90  1.85  250, 500  0.9, 1.2  0.9, 1.2  0.16, 0.19  0.50, 0.65 
The numerical simulation results show that
It is difficult to characterize the effect of
Effects of height of burst on the damage degree.
Figure
Effects of explosive mass on the damage degree.
Effects of column depth and width on
Effects of width and depth on the damage degree.
As shown in Figure
Effects of steel ratio on the damage degree.
Effects of axial load ratio on
Effects of axial load ratio on the damage degree.
The parametric study revealed the significance of parameters affecting the damage degree of CFST columns. Through the multivariable regression analysis, an empirical equation is proposed in terms of various parameters to predict the damage degree and is expressed as follows:
The comparisons of the proposed equation with the analytical results are shown in Figures
Comparison of analytical results with the proposed curves.
This paper presents a 3D numerical model to investigate the damage modes and damage assessment of CFST columns. Based on the numerical analysis results, the following conclusions can be drawn.
CFST columns under blast loading may undergo the global flexural damage and shear damage as well as localized damage. Flexural damage and shear damage of the column are mainly attributed to the deformation and internal force of the whole member, whilst the localized damage is dominated by the failure of infill concrete and steel tube in the vicinity of the explosion.
The damage criterion based on the residual axial load capacity is adopted for assessing the degree of CFST columns damage to blast loads. Through parametric studies, it is found that the damage degree of CFST columns decays nearly exponentially with the increasing scaled standoff distance. For the same scaled standoff distance, surface burst results in severer damage to the column than that caused by explosion at column midheight, and the damage degree increases with the rising explosive mass and decreases with column depth and width and steel ratio. Increasing the axial load enhances the resistance of the column against localized damage and shear damage, while the effects of axial load on flexural damage depend on the axial loadbending moment (PM) interactions of the column.
An equation is derived by fitting the results of parametric studies to estimate the damage degree of CFST columns. Typical examples confirm that the proposed equation well represents the variation of the column damage degree. However, future experiments can be conducted for investigating the effects of other parameters on the damage degree of CFST columns.
The authors declare that there is no conflict of interests regarding the publication of this paper.
The research described in this paper was financially supported by Achievement Transfer Program of Institutions of Higher Education in Chongqing under Grant no. KJZH14220.