Performance of (1) concrete-filled double-skin steel tube with and without core concrete,and (2) concrete-filled steel tubular axially loaded composite columns under close-in blast

Abstract

Composite structural members such as concrete-filled double-skin steel tube (CFDSST) and concrete-filled double steel tubular (CFDST) columns are increasingly being utilized in modern structures owing to their capability to integrate the beneficial properties of constituent materials to carry heavy loads as compared to conventional reinforced concrete columns. Axial compression performance of such composite columns has been extensively investigated and available in the open literature. However, their response under impulsive loadings such as those induced by explosions is not very well studied because not many investigations have been conducted on these columns. Performance of composite compression members under short-duration/high-magnitude blast loading is of considerable interest under the prevailing environment of hi-tech wars, subversive activities, and accidental explosions. The recent devastating accidental Ammonium Nitrate explosion at Beirut port (Lebanon), and the ongoing invasion of Ukraine by Russia raise the concern of researchers and engineers for the safety of structural elements/components. In this study, a 3-D finite element model of axially loaded 2500 mm long CFDSST column of ultra-high-strength concrete (170 MPa) is developed in ABAQUS/Explicit-v.6.15 computer code equipped with Concrete Damage Plasticity (CDP) model, and investigation has been carried out for its blast performance under the 50kg-TNT explosive load at a standoff distance of 1.50 m in free-air. The effects of strain rate on the compressive strength of the concrete are considered as per fib Model Code 2010 (R2010) and UFC-3-340-02 (2008). The non-linear behavior of the steel is also taken into account. Damages in the form of (1) a - concrete crushing on the explosion side of the column and b - concrete cracking on the tension side and their spread over the column length, and (2) yielding of tubes are observed. Computational results are validated with the available experimental observations. To improve the column response, the analysis has been extended to investigate the blast performance of axially loaded CFDSST columns with and without core concrete having an inner steel tube of circular/square cross-section and their response have been compared with the equivalent single skin concrete-filled steel tubular circular/square columns of same axial load capacity.

Keywords

blast loading composite columns concrete-filled double-skin steel tube concrete-filled double steel tubular concrete-filled steel tubular steel tube concrete damage plasticity model finite element analysis damage dissipation energy stresses

Introduction

Over the past 20 years, accidental and man-made explosion incidents have revealed the vulnerability of civilian structures to extreme loadings such as those caused by close-in or contact detonations (Anas, Alam, et al., 2020, 2021, Anas, Ansari, et al., 2020, 2021; Anas et al., 2020a; Anas and Alam, 2021¸ 2021c; Anas et al., 2021c, 2021d., 2021e, 2021f; Byfield et al., 2004; Remennikov and Rose, 2007). Such incidents generate impulsive loading, characterized by their high intensity and very short duration (microsecond to the millisecond), develop blast pressure on structures that can be modeled as an exponential function of time (Hyde, 1992). Variables that affect the intensity of blast loading are as follows: (1) explosive material (type, weight, and shape), (2) medium through which blast shockwave travels, (3) loaded surface (location, orientation, and geometry), (4) blast shockwave, (5) instantaneous rise to peak pressure, (6) exponential decay, (7) peak overpressure, (8) time of positive blast phase, and (9) impulse (Mlakar and Bounds, 2010; Smith and Hetherington, 1994; Smith and Rose, 2002, 2006). Columns are primary load-carrying members of the framed structure which transfer external lateral loads and gravity load of the structure to the foundation. Columns under high intensive loadings such as blast loading may become a local hazard, failure of which can lead to the disproportionate or progressive collapse of the building. Not only the subversive reasons but accidental explosions may also cause the failure of the column(s) or building resulting in a huge loss of economy and human lives. The recent destructive Beirut ammonium nitrate explosion (August 2020) has developed a considerable interest to the structural engineers to have a better understanding of the behavior and resistance of the structural elements under blast loading (Kundu et al., 2021; Landry et al., 2020; Rigby et al., 2020; Sivaraman and Varadharajan, 2021). The Beirut blast resulted in a death toll of 200 in addition to injuries to more than 6000 civilians (Landry et al., 2020; Sivaraman and Varadharajan, 2021). Moreover, collective infrastructural loss due to damage was estimated to the tune of $10–15bn (Sivaraman and Varadharajan, 2021).

Ease of constructability without formwork in lesser time along with higher strength to weight ratio and better ductility than RCC construction of the concrete-filled double-skin steel tube (CFDSST) columns are finding their increasing application in the construction of modern engineering structures (Chang et al., 2013; Ci et al., 2020, 2021). Concrete-filled double-skin steel tube column consists of two concentric steel tubes (outer and inner) without core concrete but with shell concrete between the tubes, Figure 1(a) (Ci et al., 2021; Zhang et al., 2015, 2016a, 2016b). The outer and inner tubes may be of similar or different cross-sections, for example, circular-circular, circular-square, etc. In the present study, axially loaded concrete-filled double steel tubular (CFDST) circular columns with inner steel square/circular tube, and without infilled core concrete subjected to the 50 kg TNT blast load are proposed as a new variant of composite columns. The typical section form of the circular CFDST column consisting of outer and inner tubes, shell as well as core concrete is shown in Figure 1(b). In general, the outer circular tube supports the inner tube against its buckling under axial compression and provides good resistance under blast loading (Pagoulatou et al., 2014).

The study of the blast resistance of conventionally designed structures has become significantly important in recent years in light of the increase in global terrorism (Anas and Alam, 2021a; Anas et al., 2022a, 2022b, 2022c; Anas and Alam, 2022; Anas et al., 2022d, 2022e, 2022f). Conventional structural design principles require loads to be transferred safely to the foundations through defined load paths and in such a way that failure of one component does not lead to failure of a disproportionate part or of the entire structure (Anas et al., 2021d; Anas et al., 2022f). Thus, structural components such as columns are detailed with stringent performance requirements. Columns on the periphery of a building could be exposed to high blast loads from proximate explosions and their failure can lead to progressive or disproportionate collapse (Anas et al., 2021d). Many researchers (Wan and Zha, 2016; Wang et al., 2017; Wu and Hao, 2005; Xiong et al., 2017; Yu et al., 2010; Zhang et al., 2015, 2016a, 2016b; Zhao et al., 2010; Kyei and Braimah, 2017) have identified failure of columns under blast loading as a potential precursor to progressive collapse.

Research significance

Although composite structural members such as CFDSST, CFDST, and single skin concrete-filled steel tubular (CFST) columns are increasingly being utilized in modern structures yet their performance under impulsive loading conditions is found to be not extensively studied (Anas et al., 2021b). Understanding the performance of such composite columns subjected to short-duration/high-magnitude blast loading is vital for improvements of its design under the prevailing environment of Hi-tech wars, subversions, and accidental detonations (Anas et al., 2021b). Recent devastating Beirut explosion and very recent gas pipe explosion in China’s Hubei province are examples of accidental blasts (Anas et al., 2022b, 2022c; Anal and Alam, 2022; 2022d; 2022e; 2022f). Moreover, the world has witnessed small-scale wars out of the conflicts between Russia and Ukraine, Palestine and Israel, in addition to ongoing subversive activism in many other countries involving blasts to damage buildings and other infrastructure (Anas et al., 2021b).

This research makes significant contributions to the knowledge base of composite tubular columns and provides insight into the core concrete role with circular/square inner steel tube and its influence on the blast performance of the columns. Additionally, this study presents a comparison of blast performance of CFDSST, CFDST, and CFST composite columns and gives a choice to designers to select an appropriate column type against blast loading.

Explosions and mechanism of blast loading

Conventional structural design does not include loading from explosion events (Ahmadi et al., 2021; Ul Anas, Alam, et al., 2021, 2022; Anas, Ansari, et al., 2021; Anas, Shariq, et al., 2022; Anas and Alam, 2021; Sadovskiy, 2004; Shariq et al., 2022; Tahzeeb et al., 2022; TM 5-855-1, 1986; Ul Ain et al., 2021). Thus, few buildings are designed with the requisite resistance against blast loading (Anas et al., 2021b; Anas et al., 2022d; Anas et al., 2022e). Exceptions to this are buildings in petrochemical facilities where explosion hazards exist and high profile buildings such as embassies (Anas et al., 2021d). The explosion process, blast wave evolution and interaction with structures is, thus, not widely understood by the structural engineering community (Anas et al., 2021d).

A chemical explosion is described as the rapid oxidation of explosive material and the release of high amounts of energy in the form of heat and light (Anas et al., 2021d) within a very short period of time. The chemical reaction results in increase in atmospheric pressure and temperature and expansion of the surrounding air (Anas et al., 2021d). The high speed expanding air compresses the leading air into a thin shock front. When the shock front reaches a point in space, remote from the center of explosion, the atmospheric pressure instantaneously increases to the incident pressure value followed by an exponential decay back to atmospheric conditions (Kingery and Bulmash, 1984). The time within which the pressure is above atmospheric characterizes the positive phase and duration of the blast (Anas et al., 2021d). When the shock front impinges on a medium denser than the medium it is propagating in, it is reflected. The peak reflected pressure is higher than the peak incident pressure and depends on the angle of incidence and the magnitude of the incident pressure. The peak reflected pressure can be as high as 8 times the peak incident pressure (Anas et al., 2021d).

Figure 2 shows a typical Friedlander’s form of a blast pressure profile at a point remote from the center of explosion. The time of arrival (t_a) is the time it takes the blast wave to reach the point of interest (Anas et al., 2021d; TM 5-1300, 1990; UFC 3-340-02, 2008; IS 4991, 1968). The atmospheric pressure rises instantaneously to the peak incident pressure (p_s) or peak reflected pressure (p_r) if it impinges on a reflecting surface (Anas et al., 2021d). The reflected pressure is always greater than the incident pressure at the same distance from the explosion. The time during which the pressure is greater than atmospheric is the positive phase of the blast pressure profile with a duration T_s while the time during which the overpressure is below atmospheric is the negative phase of the blast pressure profile with a corresponding duration T_s^- (Anas et al., 2021d), Figure 2. The impulse of the blast is the area under the blast pressure profile (Anas et al., 2021d; TM 5-1300, 1990).

The peak value of the blast pressure (incident and reflected) is a function of the charge mass, standoff distance of the structure from center of explosion, and the angle of incidence to the reflecting surface to the blast wave (Anas et al., 2021d).

Structural response to blast loading

The blast waves generated from an explosion exert a transient dynamic load on structures. The short duration impulsive load and resulting inertial forces generated due to the acceleration of the structure are resisted by internally generated strain energy (Anas, Alam, et al., 2022; Anas et al., 2021; Anas, Shariq, et al., 2022; Anas and Alam, 2021; ASCE/SEI 59-11, 2011; Baker et al., 1983; Shi et al., 2007). The response of structural elements subjected to blast loading can be investigated through field testing or numerical modelling (Anas et al., 2021d). The numerical modelling techniques often employed consist of non-linear dynamic finite element analysis or the simpler single-degree-of-freedom (SDOF) analysis (Anas et al., 2021d). Non-linear finite element numerical modelling techniques provide a less expensive method for investigating the response of structural elements under blast loading in comparison with experimental field testing (Anas et al., 2021d). The numerical modelling also offers opportunity to investigate an extensive number of design parameters pertinent to blast resistance of structures (Anas et al., 2021d). Non-linear finite element analysis, however, presents a different set of challenges including: selection of a suitable problem-specific mesh, ability to examine stability of the solution procedure, and assessing all sources of errors based on modelling assumptions (Anas, Alam, et al., 2020, 2022; Anas, Ansari, et al., 2020; Anas et al., 2020a, 2021a, 2021b, 2021c; Anas, Shariq, et al., 2022; Anas and Alam, 2021).

Review of the previous research works

The need for realizing the dynamic behaviors of RC structures/components under extreme and impulsive loads with short durations such as blast and impact, has been increased with rising subversive blasts on civil structures and infrastructures in recent years (Anas et al., 2022g, 2022h; Anas and Alam, 2022g; Shariq et al., 2022; Tahzeeb et al., 2022a, 2022b; Ul Ain et al., 2022b). Many studies can be found in the literature investigating the blast performance of RC slabs, beams, piers, and bridge superstructures (Alsendi and Eamon, 2020; Anas et al., 2021; Anas and Alam, 2021; Qu et al., 2016). In addition, the performance of CFDSST and CFDST members under axial compression has widely been investigated in the literature, numerically and experimentally both (Zhao et al., 2010; Qian et al., 2011; Chang et al., 2013; Pagoulatou et al., 2014; Wan and Zha, 2016; Ekmekyapar and Al-Eliwi, 2017; Wang et al., 2017; Ahmed et al., 2018, 2019, 2020; Hasan and Ekmekyapar, 2019; Ci et al., 2020, 2021). Important findings of these research are as follows: (1) common failure of the CFDSST short columns include the buckling of the outer steel tube and concrete crushing at the buckling region and (2) circular outer tube performs better by providing more effective encasement to the encased components including core concrete than rectangular/square outer tube. Peng et al. (Peng et al., 2011) tested a total of 18 circular CFDST columns with high-strength concrete under axial compression and evaluated the failure/damage modes. Chang et al. (Chang et al., 2013) conducted axial compression tests on 500 mm long concrete-filled stainless steel–carbon steel tubular (CFSCT) column with core concrete of two different compressive strengths (56.30 MPa and 65 MPa). Thickness of each tube was 4 mm. The outer diameter of the stainless steel tube was 159 mm and the inner carbon steel tube had 108 mm diameter. Stainless steel tube had yield strength 394 MPa, while the carbon steel tube had 200 MPa. It was concluded that the confining of the core concrete is increased by the inner carbon steel tube and makes to improve the strength of the column as compared with the equivalent concrete-filled stainless steel tube (CFST) column. Results were compared and found in close agreement with the predictions of ABAQUS/CAE. Pagoulatou et al. (Pagoulatou et al., 2014) carried out parametric studies to investigate the effect of diameter to thickness ratio (60 and 80), concrete strength (47.40 and 63.40 MPa), and yield strength of the steel (294.50, 370.20, 396.10, 410, and 425 MPa) on the performance of 540 mm long CFDSST columns under axial compressive loads using ABAQUS/CAE software. Steel tubes used were of 3 mm thickness. Results revealed that higher yield strength of the outer tube than the inner tube underwent significant deformation prior to failure of the column, and increased compressive strength of the concrete greatly decreased the deformation. Wan and Zha (Wan and Zha, 2016) experimentally evaluated the axial compression performance of 1300 mm long circular CFDST column and compared its response with the equivalent CFST column. Performance of the CFDST column was found superior. Ekmekyapar and Al-Eliwi (Ekmekyapar and Al-Eliwi, 2017)conducted axial compression tests to investigate the effect of steel tube thickness (3.30, 4.25, and 5.87 mm), concrete strength (30.55 and 68.09 MPa), and yield strength (290, 375, and 355 MPa) on 270 mm long CFDST circular column with outer steel tube diameter 139.70 mm and 88.90 mm. It was concluded that the inner steel tube greatly contributed to ductility and toughness and the gain is more noticeable with high strength core and sandwiched concrete. Xiong et al. (Xiong et al., 2017) compared the axial compression performance of the axially loaded CFDST column of high strength concrete with the CFDST column with ultra-high performance concrete (UHPC), and that with the equivalent CFST column. Results showed that the CFDST column with UHPC gave superior performance. Ahmed et al. (Ahmed et al., 2019) proposed a numerical model to simulate the behavior of circular CFDST columns under quasi-static loading. The results of the proposed model were compared and found in good agreement with the available experimental data. Recently, Ci et al. (Ci et al., 2020) carried out parametric investigations to study the influence of outer/inner tubes’ thickness, concrete strength, hollowness ratio (inner to outer tube diameter), and yield strengths on circular CFDST columns with span to depth ratio ranging from 2 to 5 subjected to the axial compressive loads using the ABAQUS/CAE software. Following conclusions were reported: (1) increase of the concrete strength by 150% increased the ultimate load-carrying capacity (ULC) of the column by 59.29%, (2) increase of the outer tube thickness significantly increased the ULC, (3) higher steel yield strength (450–900 MPa) enhanced the bearing capacity of the column by 64%.

A few studies on the performance of the axially loaded CFDSST columns under blast loading had been performed, namely, by Zhang et al. (2015), (2016a), (2016b). Zhang et al. (Zhang et al., 2015) carried out parametric investigations to study the influence of concrete strength (30, 40, 50, and 60 MPa), outer/inner steel tubes’ thickness, hollowness ratio (0–0.75), support conditions (fixed/pinned), and axial load level (0–50%) on 2500 mm long CFDSST column carrying an axial load of 2500 kN subjected to 20, 40, 60, and 80kg-TNT equivalent loads at 1.50 m standoff distance using the LS-DYNA software equipped with Karagozian and Case Concrete (KCC) damage model. The major finding was that the contribution of the outer steel tube in reducing the maximum displacement was more than the shell concrete and the inner tube under the blast loading. Zhang et al. (Zhang et al., 2016b) tested a total of 10 axially loaded CFDSST columns with ultra-high strength concrete having a clear span of 2500 mm under 17.20, 35.00, and 50.00kg-TNT-equivalent close-in blast loads at 1.50 m standoff distance. The explosive considered was cylindrical-shaped rock emulsion. Five out of 10 columns were of the square cross-section of outer side length 210 mm and inner 110 mm, and the remaining were of circular cross-section with concrete of compressive strength 170 MPa, Table 1. It was found that the circular CFDSST columns performed better than the square ones with regards to maximum displacement and damage.

Table 1.

Detailed information of the blast tests conducted by Zhang et al. (2016), reported in (62).

Cross-section	Label	Clear span, L (mm)	Nominal outer dimensions (D × t_so mm)	Nominal inner dimensions (D × t_io mm)	χ	Emulsion explosive (kg)	TNT equivalent charge (kg)	Axial load (kN)	Maximum displacement (mm)
Square	S1A	2500	210 × 5	110 × 5	0.50	48	35	—	41
	S1B	2500	210 × 5	110 × 5	0.50	70	50	—	49
	S2A	2500	210 × 5	110 × 5	0.50	48	35	1000	36
	S2B	2500	210 × 5	110 × 5	0.50	70	50	1000	—
	S3A	2500	210 × 5	110 × 5	0.50	70	50	1000	41
	S3B	2500	210 × 5	—	—	70	50	1000	50
Circular	C1A	2500	210 × 5	110 × 5	0.50	48	35	—	98
	C1B	2500	210 × 5	110 × 5	0.50	48	35	—	50
	C2A	2500	210 × 5	110 × 5	0.50	48	35	1000	—
	C2B	2500	210 × 5	110 × 5	0.50	24	17.20	—	35
	C3A	2500	210 × 5	110 × 5	0.50	70	50	1000	91
	C3B	2500	210 × 5	—	—	70	50	1000	83

^*Note: LVDT readings were lost for S2B and C2A.

Of particular concern is the circular ultra-high-strength-concrete-steel composite tubular columns. This research investigates the blast performance of the axially loaded CFDSST and CFDST columns having an inner steel tube of circular/square cross-section and their comparison with the equivalent single skin CFST circular/square columns of same axial load capacity is the novelty of the study. One of the five axially loaded circular CFDSST columns, with ultra-high strength shell concrete (i.e., C3A), subjected to maximum 70 kg rock emulsion explosive load (equivalent to 50 kg of TNT), tested by (Zhang et al., 2016b) is considered as a reference column (S-1) in the study. The study undertaken provides insight into the role played by the core concrete with circular/square inner steel tube to improve the blast performance of the columns. Furthermore, the outcomes of the research lead to the advanced application of concrete-steel composite compression members under impulsive blast loading.

Finite element modeling of the columns under blast loading

General description

Altogether six FE models are developed using a high-fidelity physics-based FE software program called ABAQUS/Explicit version 6.15 (release 2020) (ABAQUS, 2020). The first model (S-1) is a 2500 mm long circular CFDSST column with outer and inner steel tubes, each of thickness 5 mm, carrying an axial working load of 1000 kN subjected to 50kg-TNT blast load at 1.50 m standoff distance, as illustrated in Figure 3(a). The second model (S-2) is of an equivalent CFDSST column with a circular outer steel tube but a square inner tube (5 mm) carrying the same axial load, Figure 3(b). The models S-1 and S-2 consist of three parts, that is, outer steel tube, shell concrete, and inner steel tube. The third model (S-3) is a circular CFDST column with the same clear span (2500 mm) and thickness of the tubes (5 mm), carrying an axial working load of 1500 kN calculated in accordance with ACI 318–14 (2014), Figure 3(c). The fourth model (S-4) is obtained by replacing the inner circular steel tube in the third model with the square tube, Figure 3(d). The models S-3 and S-4 consist of four parts, that is, outer steel tube, shell/sandwiched concrete, inner steel tube, and core concrete. The hollow section ratio (χ) of columns S-1 to S-4 is 0.50. It is worth mentioning that the core concrete of the CFDST columns is confined not only by the inner tube but also by the outer steel tube (Ci et al., 2021). The fifth model (S-5) is of an equivalent single skin CFST circular column of same axial load capacity to the third model S-3 with an outer steel tube of thickness 13.50 mm, as shown in Figure 3(e). The sixth model (S-6) is of an equivalent square CFST column to the third model S-3 with an outer tube thickness 13.50 mm carrying an axial load of 1500 kN, Figure 3(f). The finite element models are shown in Figure 4. The time for creating the three-dimensional FE column model is 12min. The slenderness ratio of the columns is 11.90 (<12, that is, short column). The thickness of the shell/sandwiched concrete is 45 mm. Following sections discuss the boundary conditions, element type, mesh selection, surface identification and interaction models, explicit blast analysis, material definition particularly the non-linear response, blast phenomenon, and the typical empirical blast model.

Boundary conditions, element mesh, contact interaction models, and explicit solver

Steel end plates of thickness 10 mm and yield strength 300 MPa are included in the modeling in order to achieve an equal shortening of the entire section (Chang et al., 2013; Pagoulatou et al., 2014; Peng et al., 2011). Two different boundary conditions are assigned to each column cross-section by considering two reference points, one coupled with the bottom endplate (RP1), and the other with the top endplate (RP2) (ABAQUS, 2020; Pagoulatou et al., 2014; Peng et al., 2011). The reference point RP1, that is, at the center of the bottom endplate, is fixed against all degrees of freedom, while the reference point RP2 is restrained against all types of rotation, and against lateral displacements (x and z directions), that is, no translational degree-of-freedom restraint in the direction of the applied axial compressive load (Zhang et al., 2016b).

Continuum 3-D stress 8-node linear brick with reduced integration and hourglass control explicit element (C3D8R) available in the ABAQUS/CAE library had been proved to be the most effective element for the discretization of the concrete (Chang et al., 2013; Ci et al., 2020, 2021; Pagoulatou et al., 2014; Peng et al., 2011; Qian et al., 2011; Wan and Zha, 2016; Wang et al., 2017). Some researchers had adopted shell elements, while the others considered solid elements for the discretization of the steel tubes (Chang et al., 2013; Ci et al., 2020; Qian et al., 2011). However, the shell element often causes the convergence problem and leads to the failure of the normal operation of the model (Pagoulatou et al., 2014; Peng et al., 2011; Wan and Zha, 2016; Wang et al., 2017). In this paper, the solid element C3D8R is utilized to discretize the concrete, tubes, and endplates. Generally, the average mesh size of 5 mm for concrete, tubes, and endplates is considered following the mesh sensitivity test, that is, convergence analysis, conducted at 0.41 m/kg^1/3 scaled distance. Figure 5 shows the FE mesh of the circular CFDST column S-3.

Surface-to-surface contact interaction model available in the ABAQUS interactions library, with a pressure-over closure model, that is, hard contact model in the normal direction, and a penalty constraint function with Coulomb friction coefficient 0.25 in the tangential direction, is used to model/define the interaction between the tube surface and concrete (ABAQUS, 2020; Chang et al., 2013; Ci et al., 2020; Ci et al., 2021; Pagoulatou et al., 2014; Peng et al., 2011; Qian et al., 2011; Wan and Zha, 2016; Wang et al., 2017). The tube surface is chosen as the master surface, while the concrete surface is chosen as the slave surface (ABAQUS, 2020). Moreover, the ‘hard contact’ and ‘rough friction’ models are used for the plate-tube and plate-concrete interactions (ABAQUS, 2020; Pagoulatou et al., 2014). According to the Coulomb friction model (Wan and Zha, 2016), the surfaces can transfer the shear stress until it is greater than the limit static friction force value ( $τ_{c r i t}$ ) given as in equation (1).

τ_{c r i t} = μ * p \geq τ_{b o n d}

(1)

where

μ

= Coulomb friction coefficient,

p

= confinement stress (MPa), and

τ_{b o n d}

= average surface bond stress (MPa).

In the current study, the blast loading is defined as pressure versus time application, P(t), and subsequently applied to the outer tube surface of the column facing the explosion (Z direction) using the explicit solver solves the equation of motion with increments and modify the stiffness matrix after each increment of load and corresponding displacement considering geometric and material non-linearity (ABAQUS, 2020; Hao et al., 2016). Accuracy of the employed FE software to simulate the explosion effects on the structural components is also discussed in the previously published research by the authors (Anas, Alam, et al., 2020, 2021a, 2021b, 2021c, 2022a, 2022b, Anas, Ansari, et al., 2020, 2021; Anas et al., 2020a; Anas, Shariq, et al., 2022a, 2022b, Anas and Alam, 2021a, 2021b, 2021c, 2022).

Constitutive models for steel and concrete

The structural blast response of the CFDSST or CFDST columns depends on the mechanical properties of the steel and concrete (Chang et al., 2013; Ci et al., 2020, 2021; Wan and Zha, 2016; Zhang et al., 2015, 2016a, 2016b). Elastic-plastic idealization with strain hardening effect is considered for the carbon steel and Von-Mises yield criteria associated with the isotropic strain hardening and flow rule is used to define the steel tube behavior, as illustrated in Figure 6 (Ci et al., 2020; Wan and Zha, 2016; Zhang et al., 2016b). The yield strength, ultimate strength, Young’s modulus, and Poisson’s ratio of the tubes are 300 MPa, 515 MPa, 206 GPa, and 0.30, respectively (Zhang et al., 2016b). Concrete has mass density 2400 kg/m³, elastic modulus 26.60 GPa, and Poisson’s ratio 0.20 (Zhang et al., 2016b). Table 2 lists the dimensions and mechanical properties of the composite columns considered in the study.

Table 2.

Dimensions and mechanical properties of the considered composite columns.

Column no.	Dimensions								Material properties		P_a (kN)	W_TNT (kg)	S (mm)	H (mm)
Column no.	D_o (mm)	t_o (mm)	D_o/t_o	D_i (mm)	t_i (mm)	D_i/t_i	L (mm)	χ	f_c (MPa)	f_y (MPa)	P_a (kN)	W_TNT (kg)	S (mm)	H (mm)
S-1	210	5	42	110	5	22	2500	0.50	170	300	1000	50	1500	1250
S-2	210	5	42	110	5	22	2500	0.50	170	300	1000	50	1500	1250
S-3	210	5	42	110	5	22	2500	0.50	170	300	1500	50	1500	1250
S-4	210	5	42	110	5	22	2500	0.50	170	300	1500	50	1500	1250
S-5	210	13.50	15.56	—	—	—	2500	-	170	300	1500	50	1500	1250
S-6	210	13.50	15.56	—	—	—	2500	-	170	300	1500	50	1500	1250

^*Note: D_o: outer tube diameter (or outer side length); t_o: outer tube thickness; D_i: inner tube diameter (or inner side length); t_i: inner tube thickness; L: clear span of the column; f_c: average 28-days static concrete compressive strength; f_y: yield strength of the tubes; P_a: axial working load; W_TNT: mass of explosive in TNT-equivalent; S: stand-off distance; H: height of burst from the ground surface; χ: D_i/(D_o-2t_o).

The structural mechanics of concrete structures is paramount important, and concrete identification parameters including the non-linear stress-strain relation under imposing stress conditions and strain hardening/softening make the concrete response more complicated (Hafezolghorani et al., 2017; Imran and Pantazopoulou, 2001; Lee and Fenves, 1998; Lubliner et al., 1989; Tao and Chen, 2015; Yu et al., 2010). Elastic damage models or elastic-plastic laws are inadequate to simulate the response of the concrete. Irreversible or plastic strain cannot be realized using the elastic damage model (Sumer and Aktas, 2015). In the present work, the Concrete Damaged Plasticity (CDP) model, a precise elastoplastic constitutive damage model with isotropic compressive and tensile plasticity to incorporate the inelastic concrete behavior, is employed to model the concrete. Cracking under tension and crushing under compression of the concrete are considered the two common failure mechanisms (ABAQUS, 2020; Hafezolghorani et al., 2017). In general, the model utilizes the yield function, $f (ε^{p l, h}, \bar{σ})$ representing the yield surface in relation to the effective stress $(\bar{σ})$ to determine the damage/failure states (Hafezolghorani et al., 2017; Sumer and Aktas, 2015). The yield surface is linked to equivalent plastic strains under tension and compression (Hafezolghorani et al., 2017). Referring to Figure 7, the concrete response during unloading is weakened by the degradation of the elastic stiffness of the concrete (ABAQUS, 2020). This degradation is described by two scalar damage variables, namely; tension damage (d_t) and compression damage (d_c) which can range from 0 (undamaged) to 1 (fully/total damaged) (ABAQUS, 2020; Hafezolghorani et al., 2017; Lee and Fenves, 1998; Lubliner et al., 1989; Sumer and Aktas, 2015; Yu et al., 2010).

The total strain (ε) has its elastic and plastic components, $ε^{el}$ and $ε^{pl}$ .

ε = ε^{e l} + ε^{p l}

(2)

With this information, the stress tensor (

σ

) is defined as

σ = (1 - d_{i = c, t}) \bar{σ} = E_{0} (ε - ε^{p l})

(3)

Here, d = scalar degradation variable, $\bar{σ}$ = effective stress, $E_{0}$ = initial concrete elastic modulus. Damage behavior of the concrete is governed by stress-cracking strain, and stress-crushing strain response (Hafezolghorani et al., 2017). The elastic stiffness of the concrete is progressively degraded using a single scalar degradation variable, d, calculated based upon a relationship between the damage dissipation energy (D_DE) and the total absorbed energy (Q) imparted (ABAQUS, 2020), given as

Q - D_{D E} = (1 - d) Q

(4)

d = \frac{D_{D E}}{Q}

(5)

D_DE is a mechanical strain-based dissipated energy by the damage (ABAQUS, 2020). During an analysis, once the new strain increment is estimated from the current strain state, and the resultant damage factor, d, found. If D_DE is zero, then d will be zero and the material will remain undamaged (ABAQUS, 2020). Once the D_DE increases, the new stress state is calculated for the degraded concrete stiffness and passed back to ABAQUS/Explicit along with the internal energy for the next increment (ABAQUS, 2020). In general, the calculation of D_DE is primarily dependent upon the strain field, characterization constants, and material volume (Hafezolghorani et al., 2017).

Concrete compressive behavior

In CDP model, the equivalent compressive plastic strain $ε_{c}^{pl, h}$ played a paramount role in describing the relation between the concrete compressive strength and damage parameters (Figure 7(a)) as follows

σ_{c} = (1 - d_{c}) E_{0} (ε_{c} - ε_{c}^{p l, h})

(6)

{\begin{matrix} ε_{c}^{i n, h} = ε_{c} - \frac{σ_{c}}{E_{0}} \\ ε_{c}^{p l, h} = ε_{c} - \frac{σ_{c}}{E_{0}} (\frac{1}{1 - d_{c}}) \end{matrix}

(7)

In ABAQUS, the user provide the $(d_{c} - ε_{c}^{pl,h})$ data. In return, ABAQUS will internally compute the plastic strain as follows

ε_{c}^{p l, h} = ε_{c}^{i n, h} - \frac{σ_{c}}{E_{0}} (\frac{d_{c}}{1 - d_{c}})

(8)

Ideally, the damage parameter is deduced from a material test with ramped loading/unloading cycles as follows

d_{c} = 1 - \frac{E_{u}}{E_{0}}

(9)

In the absence of such data, the damage parameter can be approximated as

d_{c} = 1 - \frac{σ_{c}}{σ_{c u}}

(10)

Concrete tensile behavior

In CDP model, the equivalent tensile plastic hardening strain $ε_{t}^{pl, h}$ is derived (Figure 7(b)) as follows

σ_{t} = (1 - d_{t}) E_{0} (ε_{t} - ε_{t}^{pl, h})

(11)

{\begin{matrix} ε_{t}^{c k, h} = ε_{t} - \frac{σ_{t}}{E_{0}} \\ ε_{t}^{p l, h} = ε_{t} - \frac{σ_{t}}{E_{0}} (\frac{1}{1 - d_{t}}) \end{matrix}

(12)

ε_{t}^{p l, h} = ε_{t}^{c k, h} - \frac{σ_{t}}{E_{0}} (\frac{d_{t}}{1 - d_{t}})

(13)

d_{t} = 1 - \frac{σ_{t}}{σ_{t 0}}

(14)

where

(1 - d_{i = c, t}) E_{0} = E_{u}

is the reduced elastic modulus of the concrete (or unloading stiffness). The elastic and plastic sections are considered in the ABAQUS/CAE software for the input of the considered damage model (ABAQUS, 2020; Chang et al., 2013; Ci et al., 2020; Ci et al., 2021; Hafezolghorani et al., 2017; Wan and Zha, 2016). Young’s modulus, and elastic Poisson’s ratio of the concrete reflect the elastic section while, for the plastic section, the cracking strain-stress data under tension and inelastic strain-stress data under compression are utilized (ABAQUS, 2020; Wan and Zha, 2016). Experimental data of the study conducted by Hafezolghorani et al. (Hafezolghorani et al., 2017) are used to incorporate the concrete plasticity.

Blast loading

Blast-induced impulsive loading is a type of extremely dynamic action on the building structure that applies a high intensity of force over a very short duration and results structural response/damages different from that caused by other quasi-static and less intense dynamic loadings such as those induced by wind, wave, and earthquake, Figure 8(a) (Goel and Matsagar, 2014; Hao et al., 2016; Smith and Hetherington, 1994; Smith and Rose, 2002, 2006). Explosives that may be considered in the structural design include improvised explosive devices (IEDs), standoff IEDs, people-borne IEDs, vehicle-borne IEDs, military weapons (i.e., aerial bombs), and conventional/industrial explosives (TNT/ANFO/RDX/Torpex/Semtex/Composition B/Rock emulsion), which are being increasingly employed to trigger blasts around the world. Blast pressure-time history variation following a detonation is expressed by the empirical-based model proposed by Wu and Hao (Wu and Hao, 2005), given in equation (15), shown in Figure 8(a).

P (t) = {\begin{matrix} P_{o}, & (0 \leq t < t_{A}) \\ P_{o} + P_{r} (\frac{t}{t_{1}}), & (t_{A} \leq t \leq t_{1}) \\ P_{o} + P_{r} (1 - \frac{t - t_{1}}{t_{2}}) . e x p (- \frac{Ψ (t - t_{1})}{t_{2}}), & (t_{1} \leq t) \end{matrix}}

(15)

where P(t) = blast pressure at time “t”, P_O = ambient air-pressure (0.10 MPa), P_r = reflected peak pressure (MPa), t_A = blast shockwave arrival time (ms), t₁ = rising time (ms); t₂ = decreasing time (ms); t^- = time of negative phase (ms); t_d = time of positive phase (ms), and

Ψ

= decay constant. It is worth noting that the nature of the blast wave profile is similar to the flow of high-pressure gas inside and outside of a compressed gas shock tube (Codina and Ambrosini 2018; Gajewski and Sielicki, 2020; Ritzel et al., 2018). Experimental data of Zhang et al. (Zhang et al., 2016b) along with the current blast design provisions given in IS 4991, 1968; ESL-TR 87-57, 1989; TM 5-1300, 1990; DOE/TIC-11268, 1992; and UFC 3-340-02, 2008 have been followed to model the blast history. Figure 8(b) compares the estimated blast pressure-time history to the pressure profile predicted using the ConWep blast code for the considered 50kg-TNT equivalent close-in blast loading. It is observed that the estimated pressure profile is in good agreement with the CONWEP predictions.

*Important Note: For realistic combinations of explosive yield and building dimensions, the rarefaction waves from the edge of an object (or target structure), traveling at the local speed of sound, will reach regions on the surface of the object before the positive phase is complete (Codina and Ambrosini, 2018; Gajewski and Sielicki, 2020; Netten and Dewey, 1997; Ritzel et al., 2018; Wu and Hao, 2005). When this occurs, the pressure load rapidly decreases from the incident pressure to the stagnation pressure. This phenomenon cannot be represented by a simple Friedlander form (Codina and Ambrosini, 2018; Dewey, 2018; Wu and Hao, 2005). Therefore, the experimentally validated typical blast model given by Wu and Hao (2005) has been used in the research work presented herein. Idealized overpressure waveforms (i.e., Friedlander/Modified Friedlander forms) are generally used for the loads with no consideration of edge effects from finite targets (Codina and Ambrosini, 2018).

Explicit dynamic analysis

ABAQUS/Explicit solver, used for the numerical modelling, has the capability of modelling the blast loading based on the semi-empirical blast load calculation code – ConWep (ABAQUS, 2020). Use of the semi-empirical code for blast load calculation precludes the modelling of explosive detonation process and blast wave propagation through air and its interaction with the column (ABAQUS, 2020; Kyei and Braimah, 2017). Moreover, the semi-empirical code has been reported to give satisfactory blast loads compared to computationally expensive computational fluid dynamics based codes (Kyei and Braimah, 2017).

In order to keep numerical simulation within a pure Lagrangian formulation, the blast loading is defined as a pressure profile. The blast loading applied is derived from the experimental data obtained by Zhang et al. (Zhang et al., 2016b), Figure 8(b). A key issue on the mechanical behavior under blast is the strength increase due to high-strain rate. The strain rate influence on the material properties are introduced as Dynamic Increase Factors (DIFs), which are variable with the strain rate (Li et al., 2021). For this analysis, the DIFs according to the CEB-FIB MODEL CODE 2010 (MC2010) (International Federation for Structural Concrete, 2013) are used to determine the effects of strain rate on compressive strength of the ultra-high-strength concrete, Table 3. There is a primary modification from the original CDP model that can be described as follows:

• The stress-strain relationship in compression in the softening phase (after the compressive strength reaches a peak) is calculated according to Ref. (Guo et al., 2017).

• Compressive damage variable (d_c) is calculated according to Ref. (Alfarah et al., 2017).

• Tensile damage variable (d_t) is calculated according to Ref. (Alfarah et al., 2017).

• The ratio between biaxial compression and uniaxial compression is selected as 1.2, reported in Guo et al. (2017).

Table 3.

Dynamic material properties of ultra-high-strength concrete, (62).

Parameter	Static	Dynamic	DIF
Tensile strength, f_t (MPa)	16.90	101.40	6.0
Compressive strength, f_c (MPa)	170.0	510.0	3.0
Elastic modulus, E₀ (GPa)	65.19	195.57	3.0

This process is not fully objective but, the obtained results are in agreement with the conclusions obtained in other research for the concrete specimens, where DIF between 1.50 and 3.0 for the compressive strength and the Young’s modulus (Li et al., 2021). The full details of the modified CDP model are given in (Minh et al., 2021). In general, concrete with a quasi-static compressive strength fc = 170 MPa under a strain rate ε˙ = 10⁴ s⁻¹, the (apparent) DIF is around 6.0 for tension (Li et al., 2021) but 3.0 (Anas et al., 2021b; Li et al., 2021) for compression, reported in (Anas et al., 2022f; Anas et al., 2021b; Anas and Alam, 2021b; Anas et al., 2021d).

The damage behaviors in the concrete are modeled using an erosion parameter (ERODE) on the basis of the maximum principal strain of the concrete material as discussed in the previous study (Pereira et al., 2014). As such, the concrete elements are eliminated from the FE simulation when ERODE has a value greater than 0.99 in ABAQUS (Pereira et al., 2014).

The loading on the columns in the numerical simulations is accomplished in two phases. In the first phase, the axial loading was applied to the top surface nodes as linearly increasing load to the axial load level (Anas et al., 2021d). The load is maintained for a few milliseconds until the internal stress stabilize at the stress corresponding to the axial load level considered in the simulation (ABAQUS, 2020). The static pressure is then maintained throughout the second phase of the loading which involves lateral blast loading on the column (ABAQUS, 2020).

Validation of the numerical model

The finite element model of the circular CFDSST column (S-1) carrying an axial load 1000 kN, subjected to 50kg-TNT equivalent load, has been validated with results from an experimental test program reported by Zhang et al. (Zhang et al., 2016b). Mesh sensitivity analysis is conducted with mesh sizes ranging from 5 mm to 20 mm. The modeled column is subjected to 50 kg of TNT, the same as was used by (Zhang et al., 2016b) in their numerical validation. The explosive is set at a standoff distance of 1.50 m and a height of burst of 1.25 m. Table 4 presents the results from the mesh sensitivity analysis and shows the maximum mid-height displacements, approximate run times, and computer disk space requirements for the different mesh sizes while Figure 9 presents the displacement–time response of column S-1 with the different mesh sizes. The maximum mid-height displacement decreases with increase in the element size. The 5 mm mesh size had a mid-height transverse Z-displacement of 89.64 mm (1.50% lower than experimental) while the 20 mm mesh size showed a lower mid-height displacement of 71.72 mm (21% lower than experimental). The 10 mm and 15 mm meshes resulted in mid-height displacements of 80.67 mm (11% lower than experimental) and 77.08 mm (15% lower than experimental), respectively. Referring to Figure 9, the 5 mm mesh size, with a 1.51% error in maximum displacement, is deemed adequate to highlight the comparative displacement response of the composite column under the considered blast loading. Thus, a mesh size of 5 mm is used for the numerical analysis presented herein.

Table 4.

Mesh sensitivity analysis.

Finite element size (mm)	Number of nodes	Number of elements	Maximum transverse mid-height Z-displacement of S-1 column (mm)	Computational time (x10³ ms)	Disk space used (GB)
20.0	329,728	127,300	71.72 (21)	995	0.69
15.0	431,787	254,600	77.08 (15)	1985	2.07
10.0	549,547	381,900	80.67 (11)	3300	4.14
5.0	785,067	636,500	89.64 (1.50)	6613	13.80
Experimental	—	—	91.0	—	—

^*Entries in parenthesis are percentage decrease in maximum displacements.

The deformed shape of the column depicted in Figure 10 is matching quite closely with that captured by Zhang et al. (Zhang et al., 2016b), which approves the application of the employed software to predict the performance of the concrete-steel composite column. The difference in the computational and available test results is attributed to the following reasons: (1) approximation involved in the idealization of the boundary conditions and concrete modeling, and (2) disregard of the suction phase of the blast shockwave and weather effects (wind, temperature, and humidity).

Load-carrying mechanism

Figure 11 shows the variation of compressive stresses in the outer steel tube, inner tube, and shell concrete of the reference CFDSST circular column S-1. Prior to the arrival time of the blast pressure under axial working load, compatibility of axial displacement exists and stress in the outer and inner tube is of equal magnitude, while in the shell concrete, the stress is much less. However, the moment the blast pressure strikes the column S-1, the bond between the outer tube and shell concrete as well as between shell concrete and inner tube fails, and the tubes and concrete start responding independently followed by a linear increase in the compressive stresses in the outer tube, shell concrete, and inner tube reach their peak values. The outer tube attains maximum stress of 341.22 MPa, while the inner tube 311.01 MPa at mid-height of the column, which are more than their yield strength (300 MPa). It is observed that the inner tube attains its maximum value of stress earlier than the outer tube. The stress in shell concrete reaches its peak value of 41.10 MPa. Stresses in steel tubes and concrete ascend to their peak value during the rising time of the blast wave, that is, 0.05 ms, and start degrading with the descending blast pressure. Minimum degraded stresses are 217.05, 96.20, and 18.92 MPa, respectively, in outer, inner tube, and shell concrete. Until now the timing of the stresses in the three components of the CFDSST column is almost the same. As the blast pressure decreases to a value of 4.50 MPa, each component of the column starts responding independently from each other with their hardening. Duration of the gain of the stress of shell concrete and inner steel tube during hardening is the same, while that of the outer tube is much less. The rate of stress gain in steel tubes is quite close to each other; however, it is much low in the shell concrete. It is worth noting that the gain in the inner tube is higher than the gain in the outer tube. Strength recovered in the inner tube becomes almost equal to its peak stress, while the outer tube possesses even less than its yield strength, much less than the peak stress it has attained earlier. As the blast pressure further goes below 4.50 MPa, the stresses in tubes become almost constant (up to 60 ms), while re-degradation takes place in shell concrete.

Analysis results and discussions

Figure 12 shows the estimated damage dissipation energy versus maximum displacement plots. The maximum D_DE corresponding to the maximum displacement of the reference column S-1 is 789.17 J, Table 5 and Figure 12. The column buckles displaying maximum displacement near mid-height level, Figure 13(a). Maximum principal compressive stresses of 341.22 and 311.01 MPa are developed in the outer and inner steel tubes, respectively, Figure 14 and Table 6. The shear stress distributions for CFDSST, CFDST, and CFST composite columns are shown in Figure 15, Figure 16, and Figure 17, respectively. The inner tube confines the shell concrete and supports the outer tube as most of the central part of the inner tube experiences the same maximum shear stress (300 MPa) as that of the outer tube of column S-1, Figure 15(a). The shell concrete on the explosion face of the column (S-1) experiences maximum shear stress of 42.77 MPa, Figure 15(a) and Table 6. On the explosion face, the concrete gets crushed wherever the shear stress exceeds ≈21.38 MPa, Figure 18(a). While on the tension side, predominant flexure-shear cracks with an average crack depth 48 mm appear more at the bottom than at top of the column (S-1), Figure 19(a). The shear stress between the cracks is ≈14.26 MPa. It is noted that the fringe levels in Figure 19 are associated with the extent of damage to the reinforced concrete column with fringe level value of 0.0 indicative of no damage and level 1.0, extensive damage and loss of strength and stiffness of concrete. The initiation of softening behaviour in the concrete corresponds to a fringe level value of approximately 0.50. Erosion can be described as the deletion of an element from the numerical calculation when a predefined limit is reached. When the element undergoes extreme deformations in the case of erosion algorithm’s absence, this may cause “lock-up” which leads to numerical instabilities. To avoid highly distorted elements and to simulate fracture debris, in addition to the concrete CDP that includes both strength and stiffness softening, once an element reaches a principal strain of 0.003729, the element is taken to be so badly damaged that it is deleted from the model, Figure 18. Exposed element surfaces caused by deletion are bound by new contact surfaces, which prevent elements undergoing large plastic displacements from penetrating others and allow fragmented pieces to collide.

Table 5.

Summary of maximum displacements and damage energy.

Column no.	Maximum transverse mid-height Z-displacement (mm) at different nodes													Maximum D_DE (J)
Column no.	*N1	*N2	*N3	*N4	*N5	*N6	*N7	*N8	*N9	*N10	*N11	*N12	*N13	Maximum D_DE (J)
S-1	89.64	87.43	87.88	88.33	88.78	87.15	86.97	86.61	86.07	85.88	85.34	85.16 (^c6)	82.52	789.17
S-2	79.73 (^a12)	76.99 (^a12)	77.38	77.76	78.15	76.60	76.54	76.22	75.74	75.58	75.11	74.91 (^c6)	72.62	1069.64 (^a36)
S-3	75.41 (^a17)	72.04 (^a18)	72.11	72.31	71.55	70.88	70.33	69.44	68.05	68.02	67.97	67.78 (^c10)	65.51	703.01 (^a11)
S-4	62.27 (^a31;^b22)	58.08 (^a34;^b25)	58.13	58.21	57.50	57.28	57.04	56.67	56.14	55.86	55.64	55.01 (^c12)	53.22 (^a36;^b27)	649.90 (^a18;^b39)
S-5	81.31 (^a10)	73.31 (^a16)	—	—	—	—	—	—	—	—	—	—	—	1103.98 (^a40)
S-6	83.26 (^a8)	74.78 (^a14)	—	—	—	—	—	—	—	—	—	—	—	3983.07 (^a405)

S-1 and S-2 are CFDSST columns; S-3 and S-4 are CFDST columns; S-5 and S-6 are circular and square CFST columns.

*N1 Node at mid-height of the outer face of the outer exposed tube.

*N2 Node at mid-height of the outer tube in contact of shell concrete.

*N3 to N11 Nodes within the shell/sandwiched concrete.

*N12 Node at mid-height of the inner tube in contact of shell concrete.

*N13 Node at mid-height of the inner face of the inner tube or Node at mid-height of the inner tube in contact of concrete core.

^aPercentage decrease with respect to reference column S-1.

^bPercentage decrease w. r.t column S-2.

^cPercentage decrease w. r.t Node N-1.

Table 6.

Computed stresses in the material(s) of the columns.

Column no.	Maximum compressive stress (MPa) at mid-height				Maximum shear stress (MPa) in concrete of the column at mid-height
Column no.	Outer tube (N1)	Shell/Sandwiched concrete (N2)	Inner tube (N12)	Concrete core (N13)	Shell/sandwiched concrete (N2)	Core concrete (N13)
S-1	341.22	42.17	311.01 (^c9)	—	42.77	—
S-2	284.88 (^a17)	41.04 (^a3)	325.33 (^c-14)	—	36.45	—
S-3	288.14 (^a16)	37.51 (^a11)	236.81 (^c18)	30.78 (^d18)	23.83	20.00 (^d16)
S-4	278.04 (^a19;^b2)	36.78 (^a13)	195.65 (^c30)	32.05 (^d13)	22.10	11.98 (^d46)
S-5	311.17 (^a9)	—	—	48.26	—	20.27
S-6	319.82 (^a6)	—	—	67.39	—	28.78

^aPercentage decrease with respect to reference column S-1.

^bPercentage decrease w. r.t column S-2.

^cPercentage decrease in compressive stress in inner tube w.r.t. Outer one.

^dPercentage decrease in stress in concrete core w.r.t. Sandwiched concrete.

From the blast analyses’ conducted, the following observations are worth mentioning:

• Maximum mid-height transverse displacement of column S-2 reduces by 12% with the replacement of the circular inner steel tube with square one of the equivalent cross-sectional area with respect to the reference circular CFDSST column S-1, Table 5 and Figure 20. It is worth mentioning that the maximum radial displacement along the thickness of the outer circular tube is 2.74 mm, while that in the inner square tube is 2.29 mm and in the shell concrete, it is 2.08 mm, Table 5 and Figure 21. The shell concrete of the column S-2 attains maximum shear stress 36.45 MPa which is less in comparison to column S-1 (42.77 MPa), but it is distributed over the larger length of the column, while in the S-1 column, the shear stresses are over lesser part of the column, Figure 15(b). The maximum compressive stresses in the outer circular and inner square tubes of the column S-2 are 284.88 and 325.33 MPa, respectively, shows the yielding of the inner tube, Figure 14(b). The shear stress distribution of concrete along with the stresses in the steel tubes increases the maximum D_DE of column S-2 by 36% with lesser maximum displacement with respect to column S-1, Figure 12 and Tables 5 and 6. Therefore, it shows that column S-2 performs better displaying lesser maximum displacement by spreading the damage over a larger part of the column than column S-1.

• CFDST column S-3 with core concrete not only reduces the maximum mid-height displacement by 17% but also maximum D_DE by 11% with respect to column S-1 (without concrete core), Table 5. Maximum compressive stresses in the outer tube, inner tube, and core concrete are found within their yield stress; however, the shell concrete attains maximum compressive stress of 38.51 MPa and maximum shear stress of 35.75 MPa, Figure 14(c) and Figure 16(a). It is worth noting that the core concrete is doubly confined by both inner and outer tubes, which in turn supports the tubes and shell concrete on explosion as well as tension sides and makes the stresses less severe resulting in less displacement and damage than CFDSST columns without core concrete, Figures 12, and 13 and Figures 18 and 19.

• Circular CFDST column S-4 with inner square tube and core concrete decreases the maximum mid-height transverse displacement by 31% with respect to S-1 column; however, the percentage reduction with respect to S-3 column is 17%, Table 5 and Figure 13. The maximum D_DE of column S-4 also reduces by 18% in comparison to reference column S-1, Figure 12. Maximum compressive and shear stresses in the outer tube, sandwiched concrete, inner tube, and core concrete of the column S-4 are lesser than those induced in the column S-3; however the compressive stress in the sandwiched concrete is more than 30 MPa, Table 6 and Figure 14(d). The core concrete with the inner square tube is more effective in controlling the stresses and damage thereby reducing the D_DE and maximum displacement to their lowest values of 649.90 J and 62.27 mm, Table 5 and Figures 18 and 19.

• Concrete filled in CFST columns with a single tube, namely, S-5 and S-6 is not as effectively confined as the shell concrete of the CFDSST column, and core and shell/sandwiched concrete of the CFDST column, get damaged over the larger part of the column thereby reducing the maximum displacements to 81.31 and 83.26 mm, respectively, which are less than the maximum displacement of the reference column S-1 (90.60 mm) but more than the displacements of columns S-2, S-3, and S-4, Table 5, Figure 13, Figure 18, and Figure 22. The column S-6 being square in cross-section is highly vulnerable to blast loading, suffers maximum damage of D_DE 3983.07 J, and is therefore found to be the most poorly performing column under blast loading, Figure 12.

• From the above discussion, the performance of the CFDST columns is found better than the CFDSST and CFST columns under the considered blast loading. However, the CFDST column S-4 gives the most superior blast response with regards to displacement and damage.

Conclusions

This paper presents a numerical study on 2500 mm long circular CFDSST column carrying axial compression subjected to 50kg-TNT blast loading at a scaled distance of 0.41 m/kg^1/3 in free-air. Factors including concrete plasticity, cracking, strain rate effects, elastic-plastic idealization with strain hardening effect for steel, and the interactions between tube surface with concrete are considered in the dynamic analysis. The feasibility and accuracy of the employed commercial software are verified by comparing the computational results with the experimental ones in the open literature. The load-carrying mechanism is explained. Conclusions are as follows:

(a) Comparing the blast performance of the CFDSST columns S-1 and S-2, the column S-2 with circular outer and square inner tube performs better with regards to mid-height displacement and less severe damage over a larger part of the column than the column S-1 with circular outer and inner tubes.

(b) The core concrete of CFDST column S-4 with inner square tube is more effective in controlling the stresses and damage as compared to CFDST circular column S-3, thereby reducing the D_DE and maximum displacement to their lowest values of 649.90 J and 62.27 mm. The core concrete being doubly confined by both inner and outer tubes supports the tubes and shell concrete on the explosion side to develop lower stresses than CFDSST columns without core concrete resulting in less displacement and damage.

(c) Concrete filled in the CFST columns with a single tube, namely, S-5 and S-6 is not as effectively confined as the concrete of the CFDSST or CFDST columns, which gets damaged over the larger part of the column. The column S-6 of square cross-section being more vulnerable to blast loading suffers maximum damage of D_DE 3983.07 J (≈5 times the D_DE of column S-1), and is therefore found to be the most poorly performing column.

(d) CFDST column S-4 with outer circular and inner square tube shows the most superior performance under the considered 50kg-TNT-equivalent blast load with regards to mid-height displacement and damage.

The findings of the present study are useful to structural engineers as well as the sectional committee for drafting the standard for Code of Practice of concrete-steel composite compression members subjected to blast loading. The authors recommend additional research with a higher grade of steel and steel fiber reinforced concrete (SFRC) as shell and core concrete.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iDs

S.M. Anas

Mehtab Alam

Notations/symbols/units

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