# Numerical Study of Damage Modes and Damage Assessment of CFST Columns under Blast Loading

Authors: Junhao Zhang; Shiyong Jiang; Bin Chen; Chunhai Li; Hao Qin
Journal: Shock and Vibration
 (2016)

---

## Abstract

Columns of frame structures are the key load-bearing 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 high-fidelity physics-based finite element program LS-DYNA was utilized to investigate the dynamic behavior and damage characteristics of the widely used concrete-filled 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.


---

## Body

## 1. Introduction

Concrete-filled steel tube (CFST) columns have been widely used in engineering structures such as high-rise 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 [1, 2]. With the increase of terrorist bombings in recent years, blast resistance of the structures has become a consideration in their design process [3]. When subjected to blast loads, columns may suffer a loss of bearing capacity to a certain extent due to the damage imparted, which may induce the collapse of the columns and even cause the progressive collapse of the whole structure. In addition, both concrete and steel, of which CFST columns are composed, may respond to blast loads at very high strain rates in the order of 1–100 s−1 or even higher, thus making the dynamic analysis of the CFST columns different from that under static loads and earthquake actions. Therefore, it is of realistic significance to study the dynamic behavior and damage characteristics of CFST columns under blast loading.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 single-degree-of-freedom (SDOF) theory with the test data [4, 5]. Li et al. studied the dynamic behavior of CFST columns through a series of field blast experiments. They analyzed the effects of explosive mass, standoff distance, axial load ratio, concrete strength grade, and steel ratio on the displacement and strain responses of CFST columns which showed global-mode controlled responses in the tests [6]. Remennikov and Uy carried out field tests on the CFST specimens and demonstrated the effects of scaled standoff distance on the mode of response and failure of the specimens under near-field blast loading. It was found that CFST members may suffer severe localized damage due to the highly localized blast impulse when the explosive was located quite close to the test members. The authors also developed a simplified engineering-level model for prediction of the mid-span deflection history of the CFST member [7]. Ngo et al. utilized the coupled Arbitrary Lagrange Euler (ALE) blast wave-structure interaction algorithms and numerically investigated the failure patterns, deformation histories, and energy absorption characteristics of CFST members subjected to near-field blast loading. Two distinct phases of deformation were identified in the study, of which the local deformation that initially occurred rather than the flexural global deformation that followed dominates the energy absorption history of the column specimen [8]. Zhang et al. carried out blast tests and finite element simulations on the axially compressed CFST column members. Results indicated that CFST columns showed good resistance against flexural loads under blast loading. The energies absorbed by local deformation and flexural deformation of the column during the blast loading were also investigated, and it was found that the majority of the energies were absorbed by global deformation when the mode of response was mainly flexural [9]. The authors also investigated the dynamic responses and damage characteristics of the concrete-filled columns with double-skin tubes to blast loads, and the critical parameters that affect the displacement time histories of the columns were analyzed [10].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 LS-DYNA 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.


## 2. Numerical Model Calibration

The high-fidelity physics-based finite element program LS-DYNA 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. [9] was simulated and a comparison was made between the test and numerical simulation results. Figure 1 shows the sketch of test setup of column number S4. The dimensions of the column are 2500 mm (height) × 200 mm (width) × 200 mm (depth), with the tube thickness of 2.8 mm. The yield stress, ultimate stress, Young’s modulus, and elongation of the steel tube are 358.2 MPa, 437.4 MPa, 202.6 GPa, and 21.3%, respectively. The average cubic compressive strength of the infill concrete is 47.4 MPa which is 37.9 MPa if converted to cylindrical compressive strength. During the test, the specimen was firstly placed on a steel frame which was then placed into the test pit. The specimen was simply supported by four rollers (two at each ends); thus the effective span of it was 2300 mm. A steel plate was placed between the roller and the column to avoid stress concentration. The initial axial load (514 kN) was applied to the ends of the column through a pneumatic jack prior to blast loading, and then 50 kg of emulsion explosive (equivalent to 35 kg of TNT) was ignited in the air at a standoff distance (center of explosive to the mid of column front surface) of 1500 mm to generate the blast environment.Figure 1
Test setup (Zhang et al. [9]).
(a)
The steel frame that holds the specimen in place
(b)
The test configuration


### 2.1. Numerical Model

#### 2.1.1. Material Model

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 [11]:(1)
σ
y
=
σ
0
+
β
E
P
ε
e
f
f
P
1
+
ε
˙
C
1
/
P
,where σ
y is the dynamic yield stress, σ
0 is the initial yield stress, β is the hardening parameter (for β equal to 0 and 1, resp., kinematic and isotropic hardenings are obtained as shown in Figure 2); E
P is the plastic hardening modulus, E
P
=
E
E
t
/
(
E
-
E
t
), E is Young’s modulus, and E
t is the tangent modulus; ε
e
f
f
P is the effective plastic strain, ε
˙ is the strain rate, and C and P are Cowper-Symonds strain rate parameters [12]. Material parameters of the steel tube in the study are listed in Table 1.Table 1
Material parameters of the steel tube.
Parameter
Mass density
ρ
1 (kg/m3)
Poisson’s ratioυ
σ
0 (MPa)
E (GPa)
E
t (MPa)
β
C
P
Failure strain(FS)
Value
7850
0.3
358
203
414
0
40.4
5
0.2Figure 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 Johnson-Holmquist-Cook (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 [13]:(2)
σ
∗
=
A
1
-
D
+
B
P
∗
N
1
+
C
ln
⁡
ε
˙
∗
≤
S
M
A
X
,where σ
∗
=
σ
/
f
c
′ denotes the normalized equivalent stress (where σ and f
c
′ are the actual equivalent stress and quasi-static uniaxial compressive strength, resp.), A is the normalized cohesive strength, D is the accumulated damage, B is the normalized pressure hardening coefficient, P
∗
=
P
/
f
c
′ is the dimensionless form of pressure P, N is the pressure hardening exponent, C is strain rate coefficient, ε
˙
∗
=
ε
˙
/
ε
˙
0 is the dimensionless form of strain rate ε
˙ (where ε
˙
0
=
1.0
s
-
1 is the reference strain rate), and S
M
A
X is the normalized maximum strength, as shown in Figure 3.Figure 3
JHC model for concrete modeling.The accumulated damage is expressed as(3)
D
=
∑
Δ
ε
P
+
Δ
μ
P
D
1
P
∗
+
T
∗
D
2
,where Δ
ε
P and Δ
μ
P are the equivalent plastic strain and plastic volumetric strain, respectively; D
1 and D
2 are damage constants, and T
∗
=
T
/
f
c
′ is the dimensionless tensile hydrostatic pressure.The relation between pressure and volumetric strain is defined as(4)
P
=
K
e
μ
,
0
≤
P
<
P
C
P
C
+
K
C
μ
-
μ
C
,
P
C
≤
P
<
P
L
K
1
μ
-
+
K
2
μ
-
2
+
K
3
μ
-
3
,
P
≥
P
L
,where K
e is the elastic bulk modulus, K
e
=
P
C
/
μ
C, and P
C and μ
C are the pressure and volumetric strain when crushing occurs in concrete, μ is the volumetric strain, μ
-
=
μ
-
μ
L
/
1
+
μ
L is the corrected volumetric strain, and P
L and μ
L are the locking pressure and volumetric strain at the beginning of the fully compacted stage (P
≥
P
L); K
1, K
2, and K
3 are material constants of concrete.The reliability of this concrete model in predicting the responses of concrete structures to blast loads has been demonstrated by many researchers [14, 15]. Material parameters of the infill concrete in the simulation are listed in Table 2.Table 2
Material parameters of the infill concrete.
Parameter
Mass density
ρ
2 (kg/m3)
A
B
C
N
f
c
′ (MPa)
S
MAX
Value
2440
0.79
1.60
0.007
0.61
37.9
7.0
Parameter
Shear modulus
G (GPa)
Maximum tensile pressure
T (MPa)
Threshold strain rateEPS0 (s−1)
Plastic strain before fractureEFMIN
Crushing pressure
P
C (MPa)
Crushing volumetric strainU
C
Locking pressure
P
L (MPa)
Value
14.86
4.0
1.0
0.01
16
0.001
800
Parameter
Locking volumetric strainU
L
Damage constant
D
1
Damage constant
D
2
Pressure constant
K
1 (GPa)
Pressure constant
K
2 (GPa)
Pressure constant
K
3 (GPa)
Value
0.1
0.04
1.0
85
−171
208


#### 2.1.2. Finite Element Model and Erosion Algorithm

The Belytschko-Tsay shell element is used in the study to model the steel tube, and the infill concrete is modeled with single-point 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 [16]. A number of simulations are carried out with different erosion criteria, and it is found that using principle tensile strain of 0.01 as the erosion criterion, which is also used by Ngo et al. [8], leads to reliable predictions of the responses of CFST columns.


#### 2.1.3. Sequence of Loads Application and Blast Load Modelling

In order to simulate the real stress state of CFST columns, the linearly increasing axial quasi-static 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 [17], that is, Load Blast Enhanced in LS-DYNA [18]. Compared to other techniques, that is, the Arbitrary Lagrangian Eulerian (ALE) methodology, this model is more computationally efficient to simulate blast loads with a high level of accuracy. While similar to the model Load Blast, it also includes enhancements for treating reflected waves. The loading face of the column is predefined before the generation of blast loads, and the time history of blast loads acting on each segment is calculated through ConWep formula as follows:(5)
P
t
=
P
r
t
cos
2
⁡
θ
+
P
i
t
1
+
cos
2
⁡
θ
-
2
cos
⁡
θ
,where P
(
t
) is the reflected overpressure on the defined load segment at moment t, P
r
t and P
i
t are the normal reflected overpressure and incident overpressure at moment t, respectively, and θ is the angle of incidence of the blast wave.


### 2.2. Model Calibration and Discussion

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 Figure1(b)) at 380 mm from the center of the column was used to calibrate the numerical model. Comparison of the calculated displacement time history with test results is shown in Figure 4. It is found that the peak displacement of numerical results (50.9 mm) is smaller than that in the test (60 mm) while the numerical residual displacement (35.4 mm) is slightly larger than the test value (34 mm). Several factors as follows may account for such discrepancies: (1) the difference between the actual support condition which is not rigid enough and those adopted in the simulation; (2) ignorance of the potential loss of axial loads and reduction of flexural resistance considering the detachment of the column ends from the loading device in the test; and (3) the limitations of material models in depicting the real-time nonlinear behaviors of steel and concrete during test. Although discrepancies exist between the simulation and test values, the largest error with respect to the maximum displacements is within 15.2%. Figure 5 shows the comparison of the damage mode of the column in the test and that from the numerical simulation presented in effective plastic strain contour, and good agreement is observed in between. These results demonstrate that the calibrated numerical model leads to reasonable predictions of the dynamic responses and damage modes of CFST columns to blast loads and can be used for the subsequent study.Figure 4
Comparison of the displacement data from test and that of numerical simulation.Figure 5
Comparison of the column damage mode in the test and that from numerical simulation.
(a)
Test result (Zhang et al. [9])
(b)
Numerical result


## 2.1. Numerical Model

### 2.1.1. Material Model

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 [11]:(1)
σ
y
=
σ
0
+
β
E
P
ε
e
f
f
P
1
+
ε
˙
C
1
/
P
,where σ
y is the dynamic yield stress, σ
0 is the initial yield stress, β is the hardening parameter (for β equal to 0 and 1, resp., kinematic and isotropic hardenings are obtained as shown in Figure 2); E
P is the plastic hardening modulus, E
P
=
E
E
t
/
(
E
-
E
t
), E is Young’s modulus, and E
t is the tangent modulus; ε
e
f
f
P is the effective plastic strain, ε
˙ is the strain rate, and C and P are Cowper-Symonds strain rate parameters [12]. Material parameters of the steel tube in the study are listed in Table 1.Table 1
Material parameters of the steel tube.
Parameter
Mass density
ρ
1 (kg/m3)
Poisson’s ratioυ
σ
0 (MPa)
E (GPa)
E
t (MPa)
β
C
P
Failure strain(FS)
Value
7850
0.3
358
203
414
0
40.4
5
0.2Figure 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 Johnson-Holmquist-Cook (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 [13]:(2)
σ
∗
=
A
1
-
D
+
B
P
∗
N
1
+
C
ln
⁡
ε
˙
∗
≤
S
M
A
X
,where σ
∗
=
σ
/
f
c
′ denotes the normalized equivalent stress (where σ and f
c
′ are the actual equivalent stress and quasi-static uniaxial compressive strength, resp.), A is the normalized cohesive strength, D is the accumulated damage, B is the normalized pressure hardening coefficient, P
∗
=
P
/
f
c
′ is the dimensionless form of pressure P, N is the pressure hardening exponent, C is strain rate coefficient, ε
˙
∗
=
ε
˙
/
ε
˙
0 is the dimensionless form of strain rate ε
˙ (where ε
˙
0
=
1.0
s
-
1 is the reference strain rate), and S
M
A
X is the normalized maximum strength, as shown in Figure 3.Figure 3
JHC model for concrete modeling.The accumulated damage is expressed as(3)
D
=
∑
Δ
ε
P
+
Δ
μ
P
D
1
P
∗
+
T
∗
D
2
,where Δ
ε
P and Δ
μ
P are the equivalent plastic strain and plastic volumetric strain, respectively; D
1 and D
2 are damage constants, and T
∗
=
T
/
f
c
′ is the dimensionless tensile hydrostatic pressure.The relation between pressure and volumetric strain is defined as(4)
P
=
K
e
μ
,
0
≤
P
<
P
C
P
C
+
K
C
μ
-
μ
C
,
P
C
≤
P
<
P
L
K
1
μ
-
+
K
2
μ
-
2
+
K
3
μ
-
3
,
P
≥
P
L
,where K
e is the elastic bulk modulus, K
e
=
P
C
/
μ
C, and P
C and μ
C are the pressure and volumetric strain when crushing occurs in concrete, μ is the volumetric strain, μ
-
=
μ
-
μ
L
/
1
+
μ
L is the corrected volumetric strain, and P
L and μ
L are the locking pressure and volumetric strain at the beginning of the fully compacted stage (P
≥
P
L); K
1, K
2, and K
3 are material constants of concrete.The reliability of this concrete model in predicting the responses of concrete structures to blast loads has been demonstrated by many researchers [14, 15]. Material parameters of the infill concrete in the simulation are listed in Table 2.Table 2
Material parameters of the infill concrete.
Parameter
Mass density
ρ
2 (kg/m3)
A
B
C
N
f
c
′ (MPa)
S
MAX
Value
2440
0.79
1.60
0.007
0.61
37.9
7.0
Parameter
Shear modulus
G (GPa)
Maximum tensile pressure
T (MPa)
Threshold strain rateEPS0 (s−1)
Plastic strain before fractureEFMIN
Crushing pressure
P
C (MPa)
Crushing volumetric strainU
C
Locking pressure
P
L (MPa)
Value
14.86
4.0
1.0
0.01
16
0.001
800
Parameter
Locking volumetric strainU
L
Damage constant
D
1
Damage constant
D
2
Pressure constant
K
1 (GPa)
Pressure constant
K
2 (GPa)
Pressure constant
K
3 (GPa)
Value
0.1
0.04
1.0
85
−171
208


### 2.1.2. Finite Element Model and Erosion Algorithm

The Belytschko-Tsay shell element is used in the study to model the steel tube, and the infill concrete is modeled with single-point 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 [16]. A number of simulations are carried out with different erosion criteria, and it is found that using principle tensile strain of 0.01 as the erosion criterion, which is also used by Ngo et al. [8], leads to reliable predictions of the responses of CFST columns.


### 2.1.3. Sequence of Loads Application and Blast Load Modelling

In order to simulate the real stress state of CFST columns, the linearly increasing axial quasi-static 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 [17], that is, Load Blast Enhanced in LS-DYNA [18]. Compared to other techniques, that is, the Arbitrary Lagrangian Eulerian (ALE) methodology, this model is more computationally efficient to simulate blast loads with a high level of accuracy. While similar to the model Load Blast, it also includes enhancements for treating reflected waves. The loading face of the column is predefined before the generation of blast loads, and the time history of blast loads acting on each segment is calculated through ConWep formula as follows:(5)
P
t
=
P
r
t
cos
2
⁡
θ
+
P
i
t
1
+
cos
2
⁡
θ
-
2
cos
⁡
θ
,where P
(
t
) is the reflected overpressure on the defined load segment at moment t, P
r
t and P
i
t are the normal reflected overpressure and incident overpressure at moment t, respectively, and θ is the angle of incidence of the blast wave.


## 2.1.1. Material Model

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 [11]:(1)
σ
y
=
σ
0
+
β
E
P
ε
e
f
f
P
1
+
ε
˙
C
1
/
P
,where σ
y is the dynamic yield stress, σ
0 is the initial yield stress, β is the hardening parameter (for β equal to 0 and 1, resp., kinematic and isotropic hardenings are obtained as shown in Figure 2); E
P is the plastic hardening modulus, E
P
=
E
E
t
/
(
E
-
E
t
), E is Young’s modulus, and E
t is the tangent modulus; ε
e
f
f
P is the effective plastic strain, ε
˙ is the strain rate, and C and P are Cowper-Symonds strain rate parameters [12]. Material parameters of the steel tube in the study are listed in Table 1.Table 1
Material parameters of the steel tube.
Parameter
Mass density
ρ
1 (kg/m3)
Poisson’s ratioυ
σ
0 (MPa)
E (GPa)
E
t (MPa)
β
C
P
Failure strain(FS)
Value
7850
0.3
358
203
414
0
40.4
5
0.2Figure 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 Johnson-Holmquist-Cook (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 [13]:(2)
σ
∗
=
A
1
-
D
+
B
P
∗
N
1
+
C
ln
⁡
ε
˙
∗
≤
S
M
A
X
,where σ
∗
=
σ
/
f
c
′ denotes the normalized equivalent stress (where σ and f
c
′ are the actual equivalent stress and quasi-static uniaxial compressive strength, resp.), A is the normalized cohesive strength, D is the accumulated damage, B is the normalized pressure hardening coefficient, P
∗
=
P
/
f
c
′ is the dimensionless form of pressure P, N is the pressure hardening exponent, C is strain rate coefficient, ε
˙
∗
=
ε
˙
/
ε
˙
0 is the dimensionless form of strain rate ε
˙ (where ε
˙
0
=
1.0
s
-
1 is the reference strain rate), and S
M
A
X is the normalized maximum strength, as shown in Figure 3.Figure 3
JHC model for concrete modeling.The accumulated damage is expressed as(3)
D
=
∑
Δ
ε
P
+
Δ
μ
P
D
1
P
∗
+
T
∗
D
2
,where Δ
ε
P and Δ
μ
P are the equivalent plastic strain and plastic volumetric strain, respectively; D
1 and D
2 are damage constants, and T
∗
=
T
/
f
c
′ is the dimensionless tensile hydrostatic pressure.The relation between pressure and volumetric strain is defined as(4)
P
=
K
e
μ
,
0
≤
P
<
P
C
P
C
+
K
C
μ
-
μ
C
,
P
C
≤
P
<
P
L
K
1
μ
-
+
K
2
μ
-
2
+
K
3
μ
-
3
,
P
≥
P
L
,where K
e is the elastic bulk modulus, K
e
=
P
C
/
μ
C, and P
C and μ
C are the pressure and volumetric strain when crushing occurs in concrete, μ is the volumetric strain, μ
-
=
μ
-
μ
L
/
1
+
μ
L is the corrected volumetric strain, and P
L and μ
L are the locking pressure and volumetric strain at the beginning of the fully compacted stage (P
≥
P
L); K
1, K
2, and K
3 are material constants of concrete.The reliability of this concrete model in predicting the responses of concrete structures to blast loads has been demonstrated by many researchers [14, 15]. Material parameters of the infill concrete in the simulation are listed in Table 2.Table 2
Material parameters of the infill concrete.
Parameter
Mass density
ρ
2 (kg/m3)
A
B
C
N
f
c
′ (MPa)
S
MAX
Value
2440
0.79
1.60
0.007
0.61
37.9
7.0
Parameter
Shear modulus
G (GPa)
Maximum tensile pressure
T (MPa)
Threshold strain rateEPS0 (s−1)
Plastic strain before fractureEFMIN
Crushing pressure
P
C (MPa)
Crushing volumetric strainU
C
Locking pressure
P
L (MPa)
Value
14.86
4.0
1.0
0.01
16
0.001
800
Parameter
Locking volumetric strainU
L
Damage constant
D
1
Damage constant
D
2
Pressure constant
K
1 (GPa)
Pressure constant
K
2 (GPa)
Pressure constant
K
3 (GPa)
Value
0.1
0.04
1.0
85
−171
208


## 2.1.2. Finite Element Model and Erosion Algorithm

The Belytschko-Tsay shell element is used in the study to model the steel tube, and the infill concrete is modeled with single-point 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 [16]. A number of simulations are carried out with different erosion criteria, and it is found that using principle tensile strain of 0.01 as the erosion criterion, which is also used by Ngo et al. [8], leads to reliable predictions of the responses of CFST columns.


## 2.1.3. Sequence of Loads Application and Blast Load Modelling

In order to simulate the real stress state of CFST columns, the linearly increasing axial quasi-static 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 [17], that is, Load Blast Enhanced in LS-DYNA [18]. Compared to other techniques, that is, the Arbitrary Lagrangian Eulerian (ALE) methodology, this model is more computationally efficient to simulate blast loads with a high level of accuracy. While similar to the model Load Blast, it also includes enhancements for treating reflected waves. The loading face of the column is predefined before the generation of blast loads, and the time history of blast loads acting on each segment is calculated through ConWep formula as follows:(5)
P
t
=
P
r
t
cos
2
⁡
θ
+
P
i
t
1
+
cos
2
⁡
θ
-
2
cos
⁡
θ
,where P
(
t
) is the reflected overpressure on the defined load segment at moment t, P
r
t and P
i
t are the normal reflected overpressure and incident overpressure at moment t, respectively, and θ is the angle of incidence of the blast wave.


## 2.2. Model Calibration and Discussion

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 Figure1(b)) at 380 mm from the center of the column was used to calibrate the numerical model. Comparison of the calculated displacement time history with test results is shown in Figure 4. It is found that the peak displacement of numerical results (50.9 mm) is smaller than that in the test (60 mm) while the numerical residual displacement (35.4 mm) is slightly larger than the test value (34 mm). Several factors as follows may account for such discrepancies: (1) the difference between the actual support condition which is not rigid enough and those adopted in the simulation; (2) ignorance of the potential loss of axial loads and reduction of flexural resistance considering the detachment of the column ends from the loading device in the test; and (3) the limitations of material models in depicting the real-time nonlinear behaviors of steel and concrete during test. Although discrepancies exist between the simulation and test values, the largest error with respect to the maximum displacements is within 15.2%. Figure 5 shows the comparison of the damage mode of the column in the test and that from the numerical simulation presented in effective plastic strain contour, and good agreement is observed in between. These results demonstrate that the calibrated numerical model leads to reasonable predictions of the dynamic responses and damage modes of CFST columns to blast loads and can be used for the subsequent study.Figure 4
Comparison of the displacement data from test and that of numerical simulation.Figure 5
Comparison of the column damage mode in the test and that from numerical simulation.
(a)
Test result (Zhang et al. [9])
(b)
Numerical result


## 3. Damage Modes of CFST Column under Blast Loading

### 3.1. Column Configuration

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 [19]. As shown in Figure 6, the dimensions of the column are h
(
height
)
×
w
(
width
)
×
d
(
depth
) = 3700 mm × 600 mm × 600 mm, with the tube thickness of 18 mm. Parameters of the steel tube and the infill concrete used in the simulation are the same as those in Section 2. In order to simulate the real life boundary conditions for CFST columns, a column head and a footing are considered in the numerical model. The outer vertical face of the footing and head are constrained against horizontal motions and the bottom face of the footing is constrained against vertical motions [20]. Horizontal distance from the charge center to the column front surface, that is, the standoff distance, is denoted as X. And the vertical distance from the charge center to the ground, that is, the height of burst, is denoted as H
B. The initial dead weight imposed on the column is 35 percent of axial load capacity of the undamaged column, which represents the axial load level of a typical ground floor column in a high-rise building.Figure 6
Sketch of the numerical analysis model.
(a)
Explosion scenario
(b)
Column detailsAs 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 [21](6)
Z
=
X
M
1
/
3
,where Z is the scaled standoff distance and M is the equivalent mass of TNT.


### 3.2. Possible Damage Modes

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. Table3 presents damage modes of the column according to different blast conditions. It is found that, in general, explosive with a small scaled standoff distance favors a localized damage, whilst shear damage and localized damage occur when the explosive is relatively far from the column. This is because the blast loads are highly intensive when the scaled standoff distance is small, and for very local blast loads acting on the column, failure of the infill concrete and steel tube starts before any considerable overall response can occur and the column surfers a localized damage. However, with the increase of scaled standoff distance, blast loads tend to be well-distributed over the surface of the column, which is inclined to response globally and undergo shear damage and flexural damage. Also, the damage mode is affected by the explosive mass, height of burst. Typical results of these damage modes are shown with effective plastic strain contours in Figures 7–9.Table 3
Possible damage modes of the CFST column.
M (kg)
H
B (m)
Z (m/kg1/3)
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
FlexuralFigure 7
Flexural damage mode of CFST column under blast loading.
(a)
CFST column
(b)
Infill concreteFigure 8
Shear damage mode of CFST column under blast loading.
(a)
CFST column
(b)
Infill concreteFigure 9
Localized damage mode of CFST column under blast loading.
(a)
CFST column
(b)
Infill concreteFigure7 shows the flexural damage mode of the CFST column induced by the detonation of 50 kg of TNT at the scaled standoff distance of 0.18 m/kg1/3 with the height of burst of 1.85 m. In this configuration, when the blast loads acted on the column, the mid-part of it responded immediately with the increment of lateral deformation. Then, the areas near the supports of the column began to deform and rotate. As the global flexural deformation of the column evolved, plastic hinges developed in the mid-part and near the supports of the column where the bending moments were large.Figure8 shows the shear damage mode of the column resulted from 250 kg of TNT detonating on the ground at the scaled standoff distance of 0.33 m/kg1/3. Due to the large shear force and the development of shear deformation near the supports, the infill concrete was sheared off accompanied with the rupture of the steel tube around the cross section of the column. Finally, the column failed in brittle shear before any ductile flexural hinge developed.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.Figure9 shows the localized damage mode of the CFST column caused by the detonation of 50 kg of TNT on the ground with the scaled standoff distance of 0.18 m/kg1/3. When the impulsive shock front of high intensity met the column surface, the stress waves were generated and propagated from the tube front surface towards the concrete infill and the lateral and back surfaces of the tube. Then, the concrete close to the explosion was cracked and crushed, and the front side of the tube which lost the internal support of the concrete fill was squashed with the bulging of its lateral and back sides. As the localized deformation of the column evolved, rupture and local buckling failure of the steel tube took place, yet the global lateral deformation of the column had almost not developed at this moment.It should be mentioned that these damage modes are only typical ones. Sometimes, there exists a combination of these damage modes.


## 3.1. Column Configuration

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 [19]. As shown in Figure 6, the dimensions of the column are h
(
height
)
×
w
(
width
)
×
d
(
depth
) = 3700 mm × 600 mm × 600 mm, with the tube thickness of 18 mm. Parameters of the steel tube and the infill concrete used in the simulation are the same as those in Section 2. In order to simulate the real life boundary conditions for CFST columns, a column head and a footing are considered in the numerical model. The outer vertical face of the footing and head are constrained against horizontal motions and the bottom face of the footing is constrained against vertical motions [20]. Horizontal distance from the charge center to the column front surface, that is, the standoff distance, is denoted as X. And the vertical distance from the charge center to the ground, that is, the height of burst, is denoted as H
B. The initial dead weight imposed on the column is 35 percent of axial load capacity of the undamaged column, which represents the axial load level of a typical ground floor column in a high-rise building.Figure 6
Sketch of the numerical analysis model.
(a)
Explosion scenario
(b)
Column detailsAs 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 [21](6)
Z
=
X
M
1
/
3
,where Z is the scaled standoff distance and M is the equivalent mass of TNT.


## 3.2. Possible Damage Modes

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. Table3 presents damage modes of the column according to different blast conditions. It is found that, in general, explosive with a small scaled standoff distance favors a localized damage, whilst shear damage and localized damage occur when the explosive is relatively far from the column. This is because the blast loads are highly intensive when the scaled standoff distance is small, and for very local blast loads acting on the column, failure of the infill concrete and steel tube starts before any considerable overall response can occur and the column surfers a localized damage. However, with the increase of scaled standoff distance, blast loads tend to be well-distributed over the surface of the column, which is inclined to response globally and undergo shear damage and flexural damage. Also, the damage mode is affected by the explosive mass, height of burst. Typical results of these damage modes are shown with effective plastic strain contours in Figures 7–9.Table 3
Possible damage modes of the CFST column.
M (kg)
H
B (m)
Z (m/kg1/3)
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
FlexuralFigure 7
Flexural damage mode of CFST column under blast loading.
(a)
CFST column
(b)
Infill concreteFigure 8
Shear damage mode of CFST column under blast loading.
(a)
CFST column
(b)
Infill concreteFigure 9
Localized damage mode of CFST column under blast loading.
(a)
CFST column
(b)
Infill concreteFigure7 shows the flexural damage mode of the CFST column induced by the detonation of 50 kg of TNT at the scaled standoff distance of 0.18 m/kg1/3 with the height of burst of 1.85 m. In this configuration, when the blast loads acted on the column, the mid-part of it responded immediately with the increment of lateral deformation. Then, the areas near the supports of the column began to deform and rotate. As the global flexural deformation of the column evolved, plastic hinges developed in the mid-part and near the supports of the column where the bending moments were large.Figure8 shows the shear damage mode of the column resulted from 250 kg of TNT detonating on the ground at the scaled standoff distance of 0.33 m/kg1/3. Due to the large shear force and the development of shear deformation near the supports, the infill concrete was sheared off accompanied with the rupture of the steel tube around the cross section of the column. Finally, the column failed in brittle shear before any ductile flexural hinge developed.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.Figure9 shows the localized damage mode of the CFST column caused by the detonation of 50 kg of TNT on the ground with the scaled standoff distance of 0.18 m/kg1/3. When the impulsive shock front of high intensity met the column surface, the stress waves were generated and propagated from the tube front surface towards the concrete infill and the lateral and back surfaces of the tube. Then, the concrete close to the explosion was cracked and crushed, and the front side of the tube which lost the internal support of the concrete fill was squashed with the bulging of its lateral and back sides. As the localized deformation of the column evolved, rupture and local buckling failure of the steel tube took place, yet the global lateral deformation of the column had almost not developed at this moment.It should be mentioned that these damage modes are only typical ones. Sometimes, there exists a combination of these damage modes.


## 4. Damage Assessment of CFST Columns under Blast Loading

### 4.1. Damage Criterion

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 deformation-based 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. [20] and is expressed as(7)
D
c
=
1
-
P
r
e
s
i
d
u
a
l
P
m
a
x
,where D
c is the damage degree of CFST columns, P
r
e
s
i
d
u
a
l is the residual axial load capacity of the column after blast loads, and P
m
a
x is the maximum axial load capacity of the column prior to blast loading. Values of D
c vary between 0 (i.e., no loss of capacity) and 1.0 (i.e., complete loss of capacity). Note that, in the paper by Shi et al. [20], the maximum axial load capacity of an undamaged column is calculated with the provided equation from the standard design code, which however may lead to the values of D
c below 0 in some cases. Therefore, both P
r
e
s
i
d
u
a
l and P
m
a
x are determined from numerical simulation in this study. Here P
r
e
s
i
d
u
a
l
/
P
m
a
x is also termed as the residual capacity index (RCI) used by Wu et al. [22] and Crawford et al. [23] to assess the damage level of steel reinforced concrete (SRC) columns and reinforced concrete (RC) columns subjected to blast loads.It is noted that if the ratio of the service axial load to maximum axial load capacity of the column is denoted asn, then a column whose D
c is greater than (
1
-
n
) is considered as failed or collapsed, since its residual axial load capacity is not sufficient for the service axial load.


### 4.2. Steps for Damage Assessment of CFST Columns

Step 1 (derivation ofP
m
a
x).
During this step, the linearly increasing axial load is applied on the column head until the column collapses; thenP
m
a
x is determined as the maximum axial load that the column can withstand.Step 2 (derivation ofP
r
e
s
i
d
u
a
l).
Three substeps as follows are required to obtainP
r
e
s
i
d
u
a
l: (1) before blast loading, a linearly increasing axial load up to the service axial load is imposed on the column; (2) blast loads are applied over the front face of the column with the service axial load being constant, and calculation is stopped when the damaged column approaches static equilibrium; (3) a linearly increasing axial load is imposed on the top of the damaged column until it collapses; then P
r
e
s
i
d
u
a
l is determined as the peak of the axial load that the damaged column can bear.Step 3 (determination ofD
c).
Substitute the values ofP
m
a
x and P
r
e
s
i
d
u
a
l into (7) to obtain D
c.


### 4.3. Parameters Studied

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 Table4, in which a contrast case is generated by changing one of the parameters considered in the benchmark case while keeping other parameters unchanged. Note that, in each case, varied scaled standoff distances are considered so that the effects aforementioned parameters on the damage degree of columns within different blast loading regimes can be assessed.Table 4
Parameters used in the numerical parametric study.
Parameters
Z (m/kg1/3)
H
B (m)
M (kg)
d (m)
w (m)
Steel ratioα
∗
Axial load ration
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
∗
α = A
s/A
c; A
s and A
c are the cross-sectional areas of steel tube and infill concrete, respectively.


#### 4.3.1. Effect of Scaled Standoff DistanceZ

The numerical simulation results show thatD
c of CFST columns decreases with the increasing scaled standoff distance, regardless of other parameters. This is because column damage is affected by the peak overpressure and impulse of the blast wave [21], and both of them drop with the rising scaled standoff distance, which results in a small degree of column damage.


#### 4.3.2. Effect of Height of BurstH
B

It is difficult to characterize the effect ofH
B on the damage degree of the column. On one hand, when H
B nears zero, the initial blast wave is immediately reflected and reinforced by the ground. On the other, the mid-height of the column is expected to surfer the most severe damage due to lack of transverse support. Consequently, as shown in Figure 10, surface burst results in severer damage to the column than that caused by explosion at column mid-height (H
B
=
1.85 m) especially when the standoff distance is small. The effects of H
B on the damage degree of the column are insignificant at large scaled distances, because both the overpressure and impulse on the column are relatively small in these cases.Figure 10
Effects of height of burst on the damage degree.


#### 4.3.3. Effect of Explosive MassM

Figure11 shows the effects of explosive mass on the damage degree of the column. Inspections of the figure show that D
c rises with M for the same scaled standoff distance, indicating that CFST column is impulse-sensitive since explosive with larger mass has relatively more impulse for the column.Figure 11
Effects of explosive mass on the damage degree.


#### 4.3.4. Effects of Column Widthw and Depth d

Effects of column depth and width onD
c are shown in Figure 12. Compared with the reference column (w
=
0.6 m, d
=
0.6 m), columns with larger width and depth tend to have lower damage degrees, because expanding column width and depth produces a larger cross section for attenuation of the stress waves density and contributes to enhancement of the shear resistance as well as flexural strength of the column. However, it is found that columns with the same cross section area but different width and depth have varied damage degrees and that, compared with increasing the column width, increment of the column depth is more effective in reducing the column damage degree. This is because enlarging the column width simultaneously results in a rise of blast loads acting on the column, which balances out the enhancement of column blast resistance to some extent.Figure 12
Effects of width and depth on the damage degree.


#### 4.3.5. Effect of Column Steel Ratioα

As shown in Figure13, D
c drops with the rising steel ratio. This is expected because increasing α means a larger steel area and better confinement of infill concrete, which will enhance the shear and bending strength of the column as well as its resistance to localized damage.Figure 13
Effects of steel ratio on the damage degree.


#### 4.3.6. Effect of Column Axial Load Ration

Effects of axial load ratio onD
c are shown in Figure 14. Inspection of the figure reveals that axial load ratio has dual influences on column damage. When the scaled standoff is small, the column with a larger axial load ratio has lower damage degree. This is because the column under small scaled standoff is likely to suffer localized damage and shear damage, and a higher axial load will restrain the cracking and crushing of concrete, which enhances the resistance of the column to localized damage and shear damage. In contrast, at a large scaled standoff distance, the column with larger axial load ratio has higher damage degree. The reason is that, with the increase of the scaled standoff distance, the column tends to suffer flexural damage which is related to its moment capacity and ductility. The larger the moment capacity and ductility are, the lower the damage degree is. For the CFST column studied in this section, the axial load ratio at the maximum moment capacity is 0.22, which is derived by the methods from Choi et al. [1]. According to the axial load-bending moment (P-M) interactions, the moment capacity of the CFST column will decrease when n rises from 0.35 to 0.60. Moreover, a rising axial load will reduce the ductility of the CFST column.Figure 14
Effects of axial load ratio on the damage degree.


### 4.4. Empirical Equations for Determining the Damage Degree of CFST Columns

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:(8)
D
c
=
-
15.05
ln
⁡
M
50
+
16.50
w
0.6
-
32.42
d
0.6
-
1316.25
α
+
153.49
n
+
250.11
e
-
6.48
l
n
M
/
50
+
5.33
w
/
0.6
-
10.91
d
/
0.6
-
3.73
-
12.30
α
+
12.92
n
+
26.81
Z
.The comparisons of the proposed equation with the analytical results are shown in Figures15(a)–15(f). The scatters denote the analytical results, and the solid lines represent the proposed equation. Observation of these figures shows that the proposed curves are close to the analytical results for most cases. The effects of height of burst on the damage degree of CFST columns are not reflected by (8) due to the lack of blast data in the lower height of the column which are limited in the ConWep model and will be supplemented in the further studies.Figure 15
Comparison of analytical results with the proposed curves.
(a)
(b)
(c)
(d)
(e)
(f)


## 4.1. Damage Criterion

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 deformation-based 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. [20] and is expressed as(7)
D
c
=
1
-
P
r
e
s
i
d
u
a
l
P
m
a
x
,where D
c is the damage degree of CFST columns, P
r
e
s
i
d
u
a
l is the residual axial load capacity of the column after blast loads, and P
m
a
x is the maximum axial load capacity of the column prior to blast loading. Values of D
c vary between 0 (i.e., no loss of capacity) and 1.0 (i.e., complete loss of capacity). Note that, in the paper by Shi et al. [20], the maximum axial load capacity of an undamaged column is calculated with the provided equation from the standard design code, which however may lead to the values of D
c below 0 in some cases. Therefore, both P
r
e
s
i
d
u
a
l and P
m
a
x are determined from numerical simulation in this study. Here P
r
e
s
i
d
u
a
l
/
P
m
a
x is also termed as the residual capacity index (RCI) used by Wu et al. [22] and Crawford et al. [23] to assess the damage level of steel reinforced concrete (SRC) columns and reinforced concrete (RC) columns subjected to blast loads.It is noted that if the ratio of the service axial load to maximum axial load capacity of the column is denoted asn, then a column whose D
c is greater than (
1
-
n
) is considered as failed or collapsed, since its residual axial load capacity is not sufficient for the service axial load.


## 4.2. Steps for Damage Assessment of CFST Columns

Step 1 (derivation ofP
m
a
x).
During this step, the linearly increasing axial load is applied on the column head until the column collapses; thenP
m
a
x is determined as the maximum axial load that the column can withstand.Step 2 (derivation ofP
r
e
s
i
d
u
a
l).
Three substeps as follows are required to obtainP
r
e
s
i
d
u
a
l: (1) before blast loading, a linearly increasing axial load up to the service axial load is imposed on the column; (2) blast loads are applied over the front face of the column with the service axial load being constant, and calculation is stopped when the damaged column approaches static equilibrium; (3) a linearly increasing axial load is imposed on the top of the damaged column until it collapses; then P
r
e
s
i
d
u
a
l is determined as the peak of the axial load that the damaged column can bear.Step 3 (determination ofD
c).
Substitute the values ofP
m
a
x and P
r
e
s
i
d
u
a
l into (7) to obtain D
c.


## 4.3. Parameters Studied

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 Table4, in which a contrast case is generated by changing one of the parameters considered in the benchmark case while keeping other parameters unchanged. Note that, in each case, varied scaled standoff distances are considered so that the effects aforementioned parameters on the damage degree of columns within different blast loading regimes can be assessed.Table 4
Parameters used in the numerical parametric study.
Parameters
Z (m/kg1/3)
H
B (m)
M (kg)
d (m)
w (m)
Steel ratioα
∗
Axial load ration
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
∗
α = A
s/A
c; A
s and A
c are the cross-sectional areas of steel tube and infill concrete, respectively.


### 4.3.1. Effect of Scaled Standoff DistanceZ

The numerical simulation results show thatD
c of CFST columns decreases with the increasing scaled standoff distance, regardless of other parameters. This is because column damage is affected by the peak overpressure and impulse of the blast wave [21], and both of them drop with the rising scaled standoff distance, which results in a small degree of column damage.


### 4.3.2. Effect of Height of BurstH
B

It is difficult to characterize the effect ofH
B on the damage degree of the column. On one hand, when H
B nears zero, the initial blast wave is immediately reflected and reinforced by the ground. On the other, the mid-height of the column is expected to surfer the most severe damage due to lack of transverse support. Consequently, as shown in Figure 10, surface burst results in severer damage to the column than that caused by explosion at column mid-height (H
B
=
1.85 m) especially when the standoff distance is small. The effects of H
B on the damage degree of the column are insignificant at large scaled distances, because both the overpressure and impulse on the column are relatively small in these cases.Figure 10
Effects of height of burst on the damage degree.


### 4.3.3. Effect of Explosive MassM

Figure11 shows the effects of explosive mass on the damage degree of the column. Inspections of the figure show that D
c rises with M for the same scaled standoff distance, indicating that CFST column is impulse-sensitive since explosive with larger mass has relatively more impulse for the column.Figure 11
Effects of explosive mass on the damage degree.


### 4.3.4. Effects of Column Widthw and Depth d

Effects of column depth and width onD
c are shown in Figure 12. Compared with the reference column (w
=
0.6 m, d
=
0.6 m), columns with larger width and depth tend to have lower damage degrees, because expanding column width and depth produces a larger cross section for attenuation of the stress waves density and contributes to enhancement of the shear resistance as well as flexural strength of the column. However, it is found that columns with the same cross section area but different width and depth have varied damage degrees and that, compared with increasing the column width, increment of the column depth is more effective in reducing the column damage degree. This is because enlarging the column width simultaneously results in a rise of blast loads acting on the column, which balances out the enhancement of column blast resistance to some extent.Figure 12
Effects of width and depth on the damage degree.


### 4.3.5. Effect of Column Steel Ratioα

As shown in Figure13, D
c drops with the rising steel ratio. This is expected because increasing α means a larger steel area and better confinement of infill concrete, which will enhance the shear and bending strength of the column as well as its resistance to localized damage.Figure 13
Effects of steel ratio on the damage degree.


### 4.3.6. Effect of Column Axial Load Ration

Effects of axial load ratio onD
c are shown in Figure 14. Inspection of the figure reveals that axial load ratio has dual influences on column damage. When the scaled standoff is small, the column with a larger axial load ratio has lower damage degree. This is because the column under small scaled standoff is likely to suffer localized damage and shear damage, and a higher axial load will restrain the cracking and crushing of concrete, which enhances the resistance of the column to localized damage and shear damage. In contrast, at a large scaled standoff distance, the column with larger axial load ratio has higher damage degree. The reason is that, with the increase of the scaled standoff distance, the column tends to suffer flexural damage which is related to its moment capacity and ductility. The larger the moment capacity and ductility are, the lower the damage degree is. For the CFST column studied in this section, the axial load ratio at the maximum moment capacity is 0.22, which is derived by the methods from Choi et al. [1]. According to the axial load-bending moment (P-M) interactions, the moment capacity of the CFST column will decrease when n rises from 0.35 to 0.60. Moreover, a rising axial load will reduce the ductility of the CFST column.Figure 14
Effects of axial load ratio on the damage degree.


## 4.3.1. Effect of Scaled Standoff DistanceZ

The numerical simulation results show thatD
c of CFST columns decreases with the increasing scaled standoff distance, regardless of other parameters. This is because column damage is affected by the peak overpressure and impulse of the blast wave [21], and both of them drop with the rising scaled standoff distance, which results in a small degree of column damage.


## 4.3.2. Effect of Height of BurstH
B

It is difficult to characterize the effect ofH
B on the damage degree of the column. On one hand, when H
B nears zero, the initial blast wave is immediately reflected and reinforced by the ground. On the other, the mid-height of the column is expected to surfer the most severe damage due to lack of transverse support. Consequently, as shown in Figure 10, surface burst results in severer damage to the column than that caused by explosion at column mid-height (H
B
=
1.85 m) especially when the standoff distance is small. The effects of H
B on the damage degree of the column are insignificant at large scaled distances, because both the overpressure and impulse on the column are relatively small in these cases.Figure 10
Effects of height of burst on the damage degree.


## 4.3.3. Effect of Explosive MassM

Figure11 shows the effects of explosive mass on the damage degree of the column. Inspections of the figure show that D
c rises with M for the same scaled standoff distance, indicating that CFST column is impulse-sensitive since explosive with larger mass has relatively more impulse for the column.Figure 11
Effects of explosive mass on the damage degree.


## 4.3.4. Effects of Column Widthw and Depth d

Effects of column depth and width onD
c are shown in Figure 12. Compared with the reference column (w
=
0.6 m, d
=
0.6 m), columns with larger width and depth tend to have lower damage degrees, because expanding column width and depth produces a larger cross section for attenuation of the stress waves density and contributes to enhancement of the shear resistance as well as flexural strength of the column. However, it is found that columns with the same cross section area but different width and depth have varied damage degrees and that, compared with increasing the column width, increment of the column depth is more effective in reducing the column damage degree. This is because enlarging the column width simultaneously results in a rise of blast loads acting on the column, which balances out the enhancement of column blast resistance to some extent.Figure 12
Effects of width and depth on the damage degree.


## 4.3.5. Effect of Column Steel Ratioα

As shown in Figure13, D
c drops with the rising steel ratio. This is expected because increasing α means a larger steel area and better confinement of infill concrete, which will enhance the shear and bending strength of the column as well as its resistance to localized damage.Figure 13
Effects of steel ratio on the damage degree.


## 4.3.6. Effect of Column Axial Load Ration

Effects of axial load ratio onD
c are shown in Figure 14. Inspection of the figure reveals that axial load ratio has dual influences on column damage. When the scaled standoff is small, the column with a larger axial load ratio has lower damage degree. This is because the column under small scaled standoff is likely to suffer localized damage and shear damage, and a higher axial load will restrain the cracking and crushing of concrete, which enhances the resistance of the column to localized damage and shear damage. In contrast, at a large scaled standoff distance, the column with larger axial load ratio has higher damage degree. The reason is that, with the increase of the scaled standoff distance, the column tends to suffer flexural damage which is related to its moment capacity and ductility. The larger the moment capacity and ductility are, the lower the damage degree is. For the CFST column studied in this section, the axial load ratio at the maximum moment capacity is 0.22, which is derived by the methods from Choi et al. [1]. According to the axial load-bending moment (P-M) interactions, the moment capacity of the CFST column will decrease when n rises from 0.35 to 0.60. Moreover, a rising axial load will reduce the ductility of the CFST column.Figure 14
Effects of axial load ratio on the damage degree.


## 4.4. Empirical Equations for Determining the Damage Degree of CFST Columns

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:(8)
D
c
=
-
15.05
ln
⁡
M
50
+
16.50
w
0.6
-
32.42
d
0.6
-
1316.25
α
+
153.49
n
+
250.11
e
-
6.48
l
n
M
/
50
+
5.33
w
/
0.6
-
10.91
d
/
0.6
-
3.73
-
12.30
α
+
12.92
n
+
26.81
Z
.The comparisons of the proposed equation with the analytical results are shown in Figures15(a)–15(f). The scatters denote the analytical results, and the solid lines represent the proposed equation. Observation of these figures shows that the proposed curves are close to the analytical results for most cases. The effects of height of burst on the damage degree of CFST columns are not reflected by (8) due to the lack of blast data in the lower height of the column which are limited in the ConWep model and will be supplemented in the further studies.Figure 15
Comparison of analytical results with the proposed curves.
(a)
(b)
(c)
(d)
(e)
(f)


## 5. Conclusions

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 mid-height, 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 load-bending moment (P-M) 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.



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*Source: 3972791-2016-01-05.xml*