Research on Damage Assessment of Concrete-Filled Steel Tubular Column Subjected to Near-Field Blast Loading

Concrete-filled steel tubular (CFST) columns are widely used in engineering structures, and they have many different cross section types. Among these, normal solid sections and concrete-filled double-skin steel tubular sections are often used. Although many studies have been conducted on CFST columns with these two section types, no studies have been conducted on their damage assessment under blast loading. In this study, experimental analysis and a numerical simulation method were integrated to evaluate the responses and assess the damage of two concrete-filled steel tubular (CFST) columns with different cross sections subjected to near-field blast loading. ,e results showed that for a scaled distance of 0.14m/kg, plastic bending deformation occurred on the surfaces of the two CFSTcolumns facing the explosive.,e antiexplosion performance of the normal solid-section (NSS) CFST column was better than that of the concrete-filled double-skin steel tubular (CFDST) column. ,e explosion centre was set at the same height as the middle of column, and the distributions of the peak pressure values of the two columns were similar: the peak pressures at the middle points of the columns were the greatest, and the peak pressures at the bottom were higher than those at the top.With the analysis of the duration of the positive pressure, the damage at the middle was themost severe when subjected to blast loading. Using pressure-impulse damage theory and the validated numerical simulations, two pressure-impulse damage evaluation curves for NSS and CFDSTcolumns were established separately by analysing the experimental and simulation data. Finally, based on the two pressure-impulse damage evaluation curves, the two pressure-impulse damage criteria for these two different fixed-end CFSTcolumns were defined based on the deflection of the surfaces facing the explosives. Furthermore, the mathematical formulae for the two different column types were established to generate pressure-impulse diagrams. With the established formulae, the damage of the CFST columns with these two cross section types can be evaluated. Damage to other similar CFST columns with different cross section types due to near-field blast loading can also be evaluated by this method.


Introduction
Concrete-filled steel tubular (CFST) columns are widely used in engineering structures because of their high bearing capacities, good plasticities, and high flexural stiffnesses, and their static mechanical properties have been researched widely. Since a column is a vertical bearing member, many researchers have focused on the characteristics of CFST columns under axial loading. Huang et al. researched the deformation mechanisms of concrete-filled double-skin steel tubular (CFDST) columns under axial loading and determined the load bearing properties of the inner steel tube, outer steel tube, and concrete [1]. e influences of the cross-sectional parameters on the ultimate bearing capacities of hollow concrete-filled steel tubular columns under axial loading and the effect of the hollow ratio on the stress-strain relation was analysed by Wang et al. [2]. Güneyisi et al. developed an effective prediction model by means of gene expression programming to evaluate the axial load carrying capacities of short CFST columns [3]. Based on the results of tests conducted by various researchers on 213 samples, two theoretical equations were derived for the prediction of the ultimate axial load strengths of CFST columns by Kumar et al. [4]. Li et al. implemented axial compression experiments of short CFST columns with 18 different parameters and proposed a series of formulae to calculate the carrying capacities of these columns [5]. Ou and Shao studied the static strength of a short circular CFST column strengthened with a carbonfibre-reinforced polymer (CFRP) theoretically and established equations for calculating the yield strength and the ultimate strength of this type of column under axial compression [6]. Hossain and Chu developed a modified model to predict the strengths of confined concrete in CSFT columns with different shapes and slenderness values using axial compression experiments [7]. Some scholars have tried to use a static mechanics method (i.e., the singledegree-of-freedom method (SDOF)) to describe the dynamic characteristics of CFST columns [8]. In summary, scholars have conducted many studies on the static mechanical performances of CFST columns. However, due to the frequent occurrence of explosion accidents and terrorist attacks in the world, the possibility of conventional building structures being impacted by explosions is increasing. us, the dynamic characteristics and explosion resistance performance of CFST columns should be more of a focus than ever before. Furthermore, an effective damage assessment method for CFST columns subjected to blast loading is needed. In recent years, researchers have studied the dynamic responses of columns under explosion shocks and achieved many results. e relevant studies can be divided into three categories: (1) Studies of the dynamic bending characteristics of a defective simply supported column made of reinforced concrete or steel subjected to blast loading by numerical simulations and experimental analyses [9][10][11][12]. Hao et al. investigated the elastic-plastic dynamic buckling of steel columns subjected to underground explosions, and the corresponding critical peak particle velocities of ground vibrations were determined for each column [9]. Lim et al. studied the effects of different reinforcing methods in beam-column joints on the blast resistance, and they found that the use of diagonal reinforcement in the joints was the most effective method for enhancing the resistance under blast loads [10]. airy proposed a modified approach to the SDOF analysis method of axially loaded steel columns under blast loads, and this method was proven to be valid [11]. Considering the strain softening behaviour of concrete, Li et al. developed two numerical examples using a nonlocal damage model, and the results indicated that both cases produced objective response in the postpeak stage [12]. (2) Studies of the dynamic responses, antiexplosion performances, failure modes, and the corresponding influence factors of reinforced concrete columns and CFST columns under blasting and impact loads [13][14][15][16][17][18][19][20][21]. A circular concrete-filled steel tubular column had better ductility than a square concrete-filled steel tubular column [23]. Chen et al. conducted a series of blast resistance and load carrying capacity tests on six large-scale reactive-powder concrete-filled steel tubular columns to validate the suitability of the theoretical method that they presented. ey found that the blast resistances of the reactive-powder concrete-filled steel tubular columns were more sensitive to the fire duration than to the scale distance [24]. Zou et al. developed an equivalent single-degree-of-freedom (SDOF) model to predict the residual carrying capacities of firedamaged reactive-powder concrete-filled steel tubular (RPC-FST) columns under axial lateral blast loads [25].
Although researchers have conducted many effective studies on the dynamic responses or failure modes of columns and other members under explosion shocks, studies on how to evaluate the safety of columns subjected to blast loading are still limited [26][27][28], especially CFST columns. Damage assessment of CFST columns subjected to blast loading is related to the safety of many structures. e study of concrete-filled steel tubular columns with different cross sections under near-field blast loading (distances no greater than twenty times the charge radius [29]) is especially important. erefore, it is of great importance to investigate the damage effects of CFST columns under explosion shocks and to establish an effective and convenient damage assessment method.
In this paper, with an explosion experiment and numerical simulations, the dynamic responses of normal solidsection (NSS) CFST and concrete-filled double-skin steel tubular (CFDST) columns subjected to blast loading were numerically simulated based on the experimental results of the two types of CFSTcolumns under blast loading. Focusing on the two key parameters, pressure and impulse, which mainly determine the damage of a target under blast loading, pressure-impulse damage theory is adopted. In this theory, if pressure and impulses coming from explosion shock waves meet the critical damage criterion of the target, it means that the target is damaged. Pressure-impulse damage theory can be described as follows [30]: where P cr is the critical value of the pressure causing a certain amount of damage to the target, I cr is the critical value of the impulse causing a certain amount of damage to the target, and C is a constant that is related to the characteristics and the damage level of the target. Based on pressure-impulse damage theory and considering the deformation characteristics of specimens, an effective damage assessment criterion and corresponding formula for the two CFST column types were also established.

Methods
To evaluate the damage of CFSTcolumns with different cross sections under near-field blast loading, two typical CFST column specimens-one with a normal solid section and one with a composite hollow section (i.e., the CFDST column)were selected and designed. Meanwhile, a near-field blasting experiment was designed and performed so that the dynamic responses and damage of the CFST columns could be investigated thoroughly. e steel pipe was filled with fine-aggregate concrete whose compressive strength was C40. e outer diameter and thickness of the CFDSTcolumn were the same as those of the NSS column. However, there was an inner steel pipe whose outer diameter and thickness were 50 and 3 mm, respectively, inside the CFDST column. Between the outer and inner steel pipes, there was C40 fine-aggregate concrete. e cross sections of the two columns are shown in Figure 1.

Experiment Design and
e bases of the two specimens were designed to be fixed. Steel ribbed plates were welded on the columns and baseplates.
e size of the fillet weld was at least 10 mm to maintain a firm connection. e parameters of the specimens are listed in Table 1.
e specimens are shown in Figure 2. Photographs of the steel specimens are shown in Figure 3, and the corresponding material properties are listed in Table 2.
To avoid local buckling of the column, based on the guidelines for circular hollow steel sections in the standard (Euro code 1994-1-1:2004), the ratio of diameter to thickness should not exceed the following maximum value: where d is the outer diameter of the circular hollow steel section, t is the thickness of the tube wall, and f y is the yield strength of the steel tube. According to equation (2), the diameter-to-thickness ratios of the two specimens were 39 and satisfied this requirement.

Experimental Conditions.
To investigate the real dynamic responses and damage of two kinds of CFST columns under blast loading, an explosion experiment under the same constraint conditions was carried out. e basic test parameters were as follows. TNT was selected as the explosive, and 50 kg was used in the experiments. e distance between the explosion centre and column surface was 0.5 m (scaled distance was 0.14 m/kg 1/3 ). e baseplates of the two columns were fixed by highstrength expansion bolts on a precast reinforced concrete board, which was buried in soil. e tops of the two columns Shock and Vibration were fixed by high-strength expansion bolts and professional reaction frames. e professional reaction frames were fixed on the buried reinforced concrete board by high-strength expansion bolts. A schematic diagram for the arrangement of the experiment is shown in Figure 4. To imitate a nearfield explosion, the explosive was placed at half of the column height, and the distance between the explosion centre and column surface was 0.5 m. e corresponding scaled distance was 0.14 m/kg 1/3 . A photograph of the test site is shown in Figure 5.

Experimental Results.
e detonation moment captured using a high-speed camera is shown in Figure 6. e fireball zone was evident. Under the near-field blast loading with a scaled distance of 0.14 m/kg 1/3 , significant plastic deformation occurred on the front middle surfaces of the two kinds of CFSTcolumns. Furthermore, the fireball zone of the near-field explosion created burn marks on the front surfaces of the columns, and no perforations were present. However, significant plastic deformation occurred on the front surfaces of the two columns under the near-field blast loading.
To quantify the plastic deformation, the deflection amounts of the surfaces facing the explosive were measured. e deflection amount of the CFDST column was 195 mm and that of the NSS CFST column was 135 mm. Photographs of the macroscopic deformation of the two columns under the near-field blast loading are shown in Figure 7. Since the plastic deformation of the specimens crushed the inner concrete, concrete fragments would be ejected during the cutting process of the outer steel tube. Due to the safety concerns, the two column specimens were not cut open.

Numerical Simulations.
To investigate the antiexplosion performance thoroughly and establish a scientific damage assessment method for the two kinds of CFST columns, a     Shock and Vibration 5   Shock and Vibration numerical model was established in the LS-DYNA software based on the explosion experiment results, and finite element numerical simulations were carried out.

Constitutive Model of Material.
e CFST columns, air, and explosive were numerically simulated using SOLID164 cell elements [31,32]. e corresponding unit system was mm-ms-MPa.

Constitutive Model of Explosives and Air.
A highenergy explosive combustion model of the high explosive in the LS-DYNA software, * MAT_HIGH_EXPLOSIVE_ BURN, was used to simulate the detonation of the TNT explosive, and the material model * MAT_NULL was used to simulate the air. e parameters of these two constitutive models are shown in Tables 8 and 9, respectively.

State Equation of
Material. In LS-DYNA, the constitutive model and the state equation were used to describe the properties of the fluid materials, i.e., the explosives and air. A constitutive model was chosen to describe the relationship between the stress Δσ ij and strain Δε ij . A state equation was selected to describe the relationship between the volume deformation rate ΔV/V and the pressure ΔP for the air and the explosives.

State Equation of
Explosive. e * EOS_JWL model in LS-DYNA was used to predict the pressure produced in the explosion process, and the predictions were similar to the experimental results. e * EOS_JWL model is based on the   Parameters     Jones-Wilkens-Lee equation of state, which is often used to describe the detonation of explosives [31]: where P is the detonation pressure, V is the relative volume, E is the internal energy per unit volume of the detonation products, and w, A, B, R 1 , and R 2 are material constants. e corresponding parameters of the state equation of the explosive are shown in Table 10.

State Equation of
Air. e * EOS_LINEAR_POLYNOMIAL state equation was used to simulate the properties of air in the explosion process [33]. e state equation can be written as follows: where μ � (1/V) − 1, P is the detonation pressure, E is the internal energy per unit volume of the detonation products, and C 0 − C 6 are the parameters of the state equation. For air,  [34,35] and the conditions of the experiments, the air region was defined as follows. e columns were surrounded by a rectangular box filled with air. e box boundaries on the two sides and behind the column were 300 mm from the outer surface of the column. e top boundary of the air was even with the top of the column, and the bottom boundary of the air was even with the ground. A rigid reflecting plane was added at the bottom of the model to simulate the shock wave reflection from the ground. e model geometry is shown in Figure 8.

Finite Element
Model. SOLID164 units were selected to represent all objects, including the columns, air, and explosive, to match closely with the experiment. Using LS-DYNA, a multimaterial, arbitrary Lagrangian-Eulerian finite element method with fluid-structure coupling was adopted to simulate the blast load exerted on the CFST columns. Considering the instantaneity of the blast loading, the surfaces between the steel tube units and infilled concrete units were set as fixed contacts. To determine a reasonable element size to simulate the explosion wave transmission, mesh sensitivity analyses were implemented based on different element sizes of 10, 20, 30, 40, and 60 mm. All mesh sensitivity analysis results (0.5 ms after explosion) are shown in Figure 9. e peak pressures decreased as the element sizes were increased from 10 to 60 mm. Furthermore, the shape of the wave front changed from hemispherical to ellipsoidal when the element sizes were increased from 10 to 60 mm. e results of the mesh sensitivity analysis show that the accuracy of simulation decreased when the element size increased beyond 30 mm. Considering the size effect of the mesh resolution, the efficiency, and the requirement of node sharing [36], the element size was selected as 20 mm. us, the total number of SOLID164 cell units in the finite element model was 534,050, and the total simulation time was set to 20 ms. e finite element model is shown in Figure 10.

Numerical Simulation Results.
e results of the numerical simulations of the CFDST and NSS CFST columns are shown in Figures 11 and 12, respectively. Bending deformation on the front middle surfaces of the two kinds of     CFST columns was evident. e deformation of the composite hollow section was greater than that of the normal solid section. To compare the deformation amounts of the two kinds of CFST columns further, the results of the two columns are shown side by side in Figure 13. Comparing the numerical simulation results with the bending deflection values of the two columns measured in the explosion experiments, the accuracies of the simulations were determined. e front middle surface deformation amounts of the two columns reached stable values after 2 ms in the numerical simulation. As shown in Figure 11, the simulated bending deflection of the CFDST column was 211.21 mm, and the experimental value was 195 mm, corresponding to an error of 7.8%. As shown in Figure 12, the simulated bending deflection of the NSS column was 123.29 mm, and the experimental result was 135 mm, corresponding to an error of 8.7%. e two errors were less than 10%. Comparing Figures 7 and 13, the deformation of the columns in the simulation was much more localized than that in the experiments. e reasons for the errors and differences between the simulation and experimental results are as follows. First, there were differences in the environments. e conditions were ideal in the numerical simulations, but the explosion experiment was affected by factors such as the site conditions (i.e., the sizes of the air regions, the ground reflection conditions, and deviations from ideal adiabatic conditions) and the measurement accuracy of the deflection amounts of the columns. Second, there were differences in the constraint conditions. To implement fixed constraints of the columns, professional reaction frames were used in the explosion experiments, but the bolts used to fix the columns could be deformed or displaced. In the simulations, the fixed constraints of columns were fully implemented. Based on the error, the differences between the experiment and simulation conditions, such as the constraint conditions, the ground reflection conditions, and the ranges of the air regions, were acceptable, and the numerical simulations for the two kinds of CFST columns under the near-field explosion were reasonable. us, the numerical model could be used to perform further damage evaluation research for the two kinds of CFST columns.

Deformation of Column Surface Facing Explosive.
e results of the in-situ explosion experiments and numerical simulations showed that under the near-field blast loading with a scaled distance of 0.14 m/kg 1/3 , the two kinds of columns were damaged on the surface facing the explosive. Greater plastic deformation occurred on the front middle surfaces of the two kinds of columns. e deflection values of the CFDST column were greater than those of the NSS column, which indicated that the antiexplosion performance of the NSS CFST column was better than that of the CFDST column subjected to the same near-field blast loading for a small-scaled distance.
As the duration of the in-situ explosion experiment was short, the numerical method, which was validated by the comparison above, was used to obtain the typical dynamic parameters of the two different types of CFSTcolumns under blast loading. e displacement-time curves of the bottom, middle, and top regions of the two columns were obtained from the simulations and are shown in Figures 14 and 15. Since the deformation changes of the two columns mainly occurred from 0 to 5 ms, the curves in Figures 14 and 15 only show the results from the first 5 ms. Because the positive direction of the blast wave propagation was defined as the direction perpendicular to the surface of the NSS CFST column facing the explosive, the displacement values of the CFDST column in Figure 14 are negative, and the displacement values of the NSS CFSTcolumn in Figure 15 are positive. Figure 14 shows that for the CFDST column, the deformation amounts at the three positions of the surface facing the explosive were stable after 4 ms. Furthermore, because of the constraints and the explosive position, the maximum deformation occurred in the middle of the column, and the minimum deformation occurred on both ends. e deformation amounts at the middle, top, and bottom were 211.21, 6.38, and 7.53 mm, respectively. e reason the deformation at the bottom was slightly greater than that at the top was related to the reflection of the blast wave from the rigid plane during the simulation (to simulate the reinforced concrete slab buried in soil). erefore, the deformation at the bottom was larger than that at the top due to the increase in the blast wave intensity. Figure 14 shows the process of deformation development. At the top and bottom, the slopes of the curves increased quickly from 0 to 3 ms, after which they slowly increased until becoming stable. In the middle, the slopes of the curves increased quickly from 0 to 0.5 ms, after which they increased slowly and finally became stable. e deformation process for the NSS CFST column is shown in Figure 15, and the deformations of the three positions of the surface facing the explosive were stable after 3 ms. As with the hollow column, the maximum deformation amount was located in the middle of the column, and the minimum deformation amounts were located at both ends. e deformation in the middle, top, and bottom sections were 123.29, 5.56, and 6.14 mm, respectively. e deformation at the bottom was slightly greater than that at the top. e deformation development curves at the top and bottom are shown in Figure 15. e slopes of the curve increased quickly from 0 to 2 ms, after which they increased slowly until becoming stable. At the middle, the slope of the curve increased quickly from 0 to 0.7 ms, after which it increased slowly and finally became stable.
A comparison of the dynamic responses showed that the deformation distributions of the two columns were similar. e maximum was located in the middle of the column, and the minimum was located at the two ends. At the same time, due to the reflection of the rigid plane, the deformation amounts at the bottom points of the two kinds of columns were slightly greater than those at the top points. e difference was that the deformation response time of the CFDST column was shorter than that of NSS CFST column.
To compare the final deformation amounts of the surfaces of the two columns facing the explosive, the values in the top, middle, and bottom regions are summarized in Table 12. From the data in Table 12, the deformation distribution of the surface facing the explosive was approximately symmetric with respect to the blasting centre. e final deformation values of the NSS CFST column were less than those of the CFDST column. is shows that the NSS column was superior to the CFDST column in terms of the antiexplosion performance.

Pressure-Time History Curve.
With the numerical simulation results, the pressure-time history curves at the bottom, middle, and top points of the two kinds of CFST columns were obtained, as shown in Figure 16. With 50 kg of explosives and a scaled distance of 0.14 m/kg 1/3 , the changes of the pressure-time curves at the three positions for the two kinds of columns were relatively consistent. e pressuretime curves at all three positions were characterized by steep  Figure 11: Result of simulation for CFDST column (scaled distance � 0.14 m/kg 1/3 ).     Figure 13: Side-by-side comparison of simulation results for two kinds of CFST columns (scaled distance � 0.14 m/kg 1/3 ). Shock and Vibration rises to peak values within short times after the explosion had initiated and then steep drops, after which they gradually approached zero.
As shown in Figure 16, the periods of positive pressure for both columns were approximately 1.5 ms at the bottom points, 1 ms at the middle points, and 1.5 ms at the top points.
us, the positive pressure durations at the three positions facing the explosive were very similar.
As shown in Figure 16 us, the distribution of the pressure peak values for the two different CFST columns can be summarized as follows. Both middle values were greater than the bottom and top values. e pressure peak values at middle points were about 8 times greater than those at the bottom points and 41 times greater than those at the top points. Based on this analysis, severe damage occurred in the middle of column surface facing the explosive. us, the damage assessment of the two column specimens should focus on the deformation of the middle of the column surface facing the explosive.
Furthermore, the times of the peak pressure for three different positions of the two column types were 0.4 ms at the bottom point, 0.2 ms at the middle point, and 0.3 ms at the top point, which showed that the amount of time for the blast waves to reach the bottom, middle, and top of each column were almost the same. erefore, it was concluded that the blast wave had the strongest effect on the middle points of the two columns. e effect was lower at the bottom points and the smallest at the top points of the columns. e numerical simulation results were consistent with the experimental results.

Damage of Inner Concrete.
To investigate the damage of the concrete filled in the steel tube under near-field blast loading, the * MAT_ADD_EROSION keyword was added to the numerical model based on the ultimate tensile strain of the concrete (which was 0.2 × 10 −2 ). e damage and failure of the concrete filled in the two columns are shown in Figure 17.
For a scaled distance of 0.14 m/kg 1/3 , the concrete in both columns became damaged, especially in the middle region facing the explosive. From the analysis of the damage of the concrete, especially through the comparison of the missing concrete elements in both columns shown in Figure 17, it was determined that there was slightly less damage to the concrete in the CFDST column (left side of figure) than that in the NSS column (right side of figure). Since the two column specimens were not cut open for examination, all the results of the inner concrete damage from the simulation must be calibrated with experimental results in future research [37]. e simulated damage of the inner concrete was based on a predefined concrete constitutive model. Although this was not calibrated with the experimental data, the relative inner concrete damage of the two columns should be comparable because the same constitutive model was used for both.

Damage Assessment Criterion.
Damage assessment plays an important role in the evaluation of the stability and strength of a structural member. At present, the modes of failure for column members can be divided into maximum displacement, maximum stress, maximum strain, and vertical residual bearing capacity [38,39]. e main principle for determining the damage assessment criteria is that the characteristics of the CFST columns related to the criteria should be easily obtained by experimental or numerical simulation methods, and the criteria should be easy to use in practical projects. According to the UFC 3-340-02 standard, under blast loading, the allowable value of the elastic-plastic rotation angle at the support of the structural member is 2° [ 40]. It is known from material mechanics theory that the rotation angle at the support of the column can be converted into deflection at the middle of the column. us, if the deflection of the middle of the column does not exceed 1/60 times the height of the column under the blast loading, the column can be considered to be safe. In this paper, a pressure-impulse damage assessment criterion for the deflection of two CFST columns under the condition of fixedend constraints was established based on the relationship between the deflection and the height of the column.
Two damage assessment criteria for CFST columns can be simply expressed as follows. If the deflection is less than 1/ 60 times the height of the column, the column can be determined to be safe. If the deflection is more than 1/60 times the height of the column, the column can be determined to be unsafe. A schematic of the deflection of the column is shown in Figure 18. e final middle deformation values of the two columns shown in Table 12 can be used as the deflection values.

Establishment of Pressure-Impulse Diagram (P-I Curve)
for Two Different Columns. e established finite element models of the two kinds of CFST columns were adjusted several times to obtain the critical pressure and impulse. After each numerical simulation, the displacement-time curve of the element was obtained by selecting the element located in the geometric centre of the column surface facing the explosive. f denotes the deflection of the column, and L denotes the height of the column. e pressure and impulse data obtained from many numerical simulations were plotted in the pressure-impulse (P-I) plane.
e critical values of the pressure and impulse were determined from the data, which agreed with the condition of f � L/60. e damage diagram, i.e., the P-I curves, for the CFDST column and the NSS CFST column were obtained, as shown in Figures 19 and 20, respectively. e P-I curves established in Figures 19 and 20 show that the P-I plane was divided into two regions. If the P and I data fall to the left of the curve, the deflection of the column is less than L/60, and the deformation is still within the safe range.
us, the column can be judged to be safe. If the combined data of P and I fall to the right of the curve, the deflection of the column is greater than L/60, and the column can be judged to be unsafe. If the P and I data fall on the curve, corresponding to a critical state, the column should be judged to be unsafe. For example, according to the near-field explosion experiment and simulation for the CFDST column, the P and I data (P � 176.05 MPa and I � 22.66 MPa · ms) fell to the right of the curve shown in Figure 19, and thus, the CFDST column could be judged to be unsafe under the blast loading in the experiment. Furthermore, for the NSS CFST column, the P and I data (P � 176.01 MPa and I � 23.37 MPa · ms) also fell to the right of the curve shown in Figure 20. us, the NSS CFST column was in an unsafe state.
To compare the differences between the two P-I curves of the different columns, the curves are plotted in the same coordinate system in Figure 21. e P-I curves of the two columns had the same trends, but the curve of the NSS column was slightly higher than that of the CFDST column.
e results showed that for the NSS CFST column, the probability of the P and I data falling to the left of the curve was slightly higher.
is means that the antiexplosion performance of the NSS CFSTcolumn was better than that of CFDST column.

Mathematical Formula for Pressure-Impulse Diagram (P-I Curve).
To provide a clear mathematical interpretation for the P-I curves of the two columns, the P-I curves in Figures 19  and 20 were fitted with mathematical formulae. rough the analysis of the data, I and P were found to follow an approximately natural logarithmic relationship. us, the P-I curves of the two columns can be expressed as follows: where P is the peak pressure of the blast wave, I is the impulse of the blast wave, and A, B, and C are three real constants, which are related to the damage of the columns. e fitting results of equation (5) are shown in Figures 22  and 23. Figures 22 and 23 show that the curves drawn by the fitting formula were in good agreement with the numerical simulation results. erefore, generalizing equation (5), the damage assessment criteria for the two kinds of CFST columns with deflection values of the surface facing the explosion were established. For example, according to the analyses and data in this paper, taking the deflection f � L/60 as the safety criterion, the deflection value was calculated as 30 mm. Based on equation (5), the following fitted equation was determined, which can be used to determine the damage of the CFDST column: where A � 138.45, B � 70.63, and C � −0.5. Equation (7) was similarly determined, and it can be used to determine the damage of the NSS CFST column: P � 149.03 − 70.63 ln(I − 0.5), where A � 149.03, B � 70.63, and C � −0.5.

Shock and Vibration
Equations (6) and (7) are suitable for the explosion damage assessment of the CFDST section and NSS CFST columns, respectively, under the fixed-end constraints and design parameters presented above (only for the two specimens). Similarly, the fit pressure-impulse (P-I) curves in Figures 22 and 23 can be used to evaluate the safety of these two CFST column cross sections with the design parameters presented above. e corresponding P-I curves and formulae for other CFST columns with different constraints and design parameters (e.g., with different cross sections)     subjected to near-field blast loading can be deduced using the methods summarized in this paper.

Conclusions
In this paper, the dynamic responses and damage assessment of normal solid-section and CFDST columns subjected to near-field blast loading were studied by means of an explosion experiment and numerical simulations. e following conclusions were obtained.
(1) From the bending deformation values and the P-I curves, which were obtained by experiments and numerical simulations, the deformation of the NSS CFST column was smaller than that of the CFDST column under the same near-field blast loading because of the high filling ratio of concrete. e antiexplosion performance of the NSS column was better than that of the CFDST column under the conditions described above.
(2) Under the same blast loading conditions, when the blast centre was equal to the middle height of the column, the blast shock wave caused the most intense damage at the middle points of the two columns, and the amount of damage at the bottom points of the two columns was greater than those at the top points. (3) Based on the analysis of the structural differences between the two columns, the inner concrete damage of the CFDST column subjected to the same blast loading was lower than that of the NSS CFST column because the inner steel tube of the CFDST column increased the overall stiffness of the column. (4) Damage assessment criteria for the CFDST section and NSS CSFT columns were established based on pressure-impulse damage theory. With the damage assessment criterion, the P-I curves and mathematical formulae were derived based on the ratio between the deflection and the height of the column facing the explosive under the fixed constraints. Furthermore, the safety performance of other different CSFT column cross sections subjected to near-field blast loading can be evaluated using this damage assessment criterion.
Data Availability e experimental and numerical simulation data used to support the findings of this research are included within the manuscript.

Conflicts of Interest
e authors declare that there are no conflicts of interest regarding the publication of this paper.