Numerical investigation into dynamic responses of ...

Journal of Loss Prevention in the Process Industries 34 (2015) 10e21

Contents lists available at ScienceDirect

Journal of Loss Prevention in the Process Industries journal homepage: www.elsevier.com/locate/jlp

Numerical investigation into dynamic responses of RC columns subjected for fire and blast Zheng Ruan, Li Chen*, Qin Fang State Key Laboratory of Disaster Prevention & Mitigation of Explosion & Impact, PLA University of Science and Technology Nanjing, Jiangsu 210007, China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 24 February 2014 Received in revised form 10 July 2014 Accepted 10 January 2015 Available online 12 January 2015

Structures may be exposed to fire and blast due to accidents (i.e. explosion of flammable gas in industrial structures) or terrorist attacks during the service life. Performances of RC structures subjected to extreme conditions of fire and blast, thus, have drawn much attention from academia. In this paper, the coupling effect of high temperature and high strain rate in concrete was firstly studied based on the experimental data to improve the damage plasticity concrete model in ABAQUS. Secondly, the transient heat transfer effects in different fire scenarios and following fire resistances of RC columns with constant axial forces were numerically investigated on the basis of the improved concrete model, which are validated by the corresponding test data, and the residual axial loading capacity of RC columns was quantitatively calculated. By incorporating the different merits of implicit algorithm applied to heat transfer analyses and explicit algorithm usually used in blast analyses, a numerical approach to analyze the responses of RC columns subjected to the coupling loadings of fire and blast was finally developed. Mid-span displacements and damage of the RC columns subjected to fire and explosions were quantitatively calculated and discussed. The proposed approach was demonstrated to be effective in predicting the responses of RC structures subjected to coupling loadings of fire and blast. © 2015 Elsevier Ltd. All rights reserved.

Keywords: RC column Coupling effects of high temperature and strain rate Constitutive model Transient heat transfer Fire resistance

1. Introduction Nowadays, safety concerns about blast and fire hazards have been raised significantly in academia ever since the terrorist attack 9.11 in New York (2001). And it also drew much attention from academia about the industrial accidents caused by explosion of flammable gas (i.e. Qingdao pipeline leak explosion on November 22nd 2013, killing 55 people), leading to the effect of high temperature and shock on the industrial structures. Concrete materials are widely used in civil and military buildings all over the world, and are also widely applied in the large scaled industrial constructions e.g. protective shell for the nuclear power station, nuclear fuel, and nuclear waste storage containers and etc. In addition to the normal design loadings, concrete structures may also be exposed to extreme loadings during their service life, such as blast and fire. It has been revealed that concrete is a brittle material and sensitive to the rate of loadings and temperature (Li et al., 2012). High temperatures induce severe micro-structural changes that

* Corresponding author. E-mail address: [email protected] (L. Chen). http://dx.doi.org/10.1016/j.jlp.2015.01.009 0950-4230/© 2015 Elsevier Ltd. All rights reserved.

alter mechanical properties of concrete (Bazant and Kaplan, 1996; Heinfling et al., 1997). And the dynamic inertia effect caused by the strain rate changes the cracking criterion of concrete compared to its static state (Bischoff and Perry, 1991). Thus, it is imperative to consider the blast resistance of the structures under high temperature in the design with the purpose of improving the integrity and collapse resistance of concrete buildings after fire. To ensure structural engineering quality and reliability under impact and high temperature conditions i.e. those encountered in the blast load and fire, the mechanical responses of materials under such loading conditions must be characterized accurately. Chiddister and Malvern (Chiddister and Malvern, 1963) firstly performed the high temperature SHPB experiments (temperatures limited to 550 C) using the first approach of heating specimen. NemateNasser and Isaacs (Nemat-Nasser and Isaacs, 1997) used a UCSD technique hereafter to measure the isothermal flow stress of Ta and TaeW alloys, and the specimen temperature could reach up to 1000 C. However, the research mentioned above has been primarily focused on steel material under the coupling effects of temperature and strain rate. Fang et al. (Fang et al., 2012) designed a special 75 mm diameter Triaxial Static Confining Pressure and High Temperature Split Hopkinson Pressure Bar (TSCPHTeSHPB) to

Z. Ruan et al. / Journal of Loss Prevention in the Process Industries 34 (2015) 10e21

study the dynamic mechanical properties of concreteelike material on the effect of the temperature and confining pressure. While the specimen can only be heated up to 80 C, limited by the lower flammable of hydraulic oil. Li et al. (Liu et al., 2011) employed a f 100 mm SHPB device for concrete under each temperature (20 C, 400 C, 600 C and 800 C) and conducted a series of strain rates ranging from 30 s1 to 220 s1. Jia et al. (Jia et al., 2009; Jia et al., 2010, 2008; Tao et al., 2011) experimentally studied the temperature and strain rate effect with SHPB by using a microwave stove for concrete rapidly heated. Huo et al. (He et al., 2010) carried out experimental research on the dynamic behavior of concrete at the high temperatures up to 800 C. Although a lot of efforts have been paid to the SHPB tests on concrete-like material subjected to high strain rates and high temperatures, there is still lacking enough information about the responses of concrete-like materials under the high strain rates and high temperatures experimentally and theoretically. In the field of the responses of engineering structures subjected to blast and fire, Izzuddin and Song (Song et al., 2000; Izzuddin et al., 2000) firstly presented a method for the nonlinear analysis of steel frames subject to fire and blast loading conditions. The integrated approach can therefore be used to study the behavior of steel members and frames subject to scenarios of blast loading followed by fire. Liew and Chen (Richard Liew and Chen, 2004; Chen and Richard Liew, 2005) proposed a mixed element approach and a fiber element approach for analyzing steel frame structures subjected to a localized explosion and following fire. Ma (Ma, 2006) studied the steel frames structural bearing capacity in fire after an impact loading using the commercial software ABAQUS. Wang et al. (Wang et al., 2007) analyzed the deformation of a simply supported steel beam subjected to shock waves in the fire field, and the influence of elevated temperature on Young's modulus of steel was discussed. Sun and Nuo (Sun and Nuo, 2009) deduced the amplitude calculation of steel columns under the action of heat-coupled forces. Fang et al. (Fang et al., 2010, 2013) proposed a numerical approach to investigate deformation and failure of steel beams and columns subjected to combined actions of explosion and fire. Yan et al. (Yan et al., 2010) performed a numerical analysis to study the dynamic responses and failure modes of light steel structural columns caused by fire and blast loading using ANSYS/LSeDYNA. Zhao et al. (Xu et al., 2013) conducted an analysis of steel beams under elevated temperature and blast loadings considering the effects of high temperature and high strain rate on steel elastic modulus, yield strength and other physical properties. What should be mentioned is, all of the research mentioned above has been focused on steel structures. Fang et al. (Fang et al., in press) proposed a numerical approach to investigate deformation and failure of RC beams subjected to explosion and following by fire, and the most of the available research on RC structures are only limited to individual fire or blast loading (Yaozhuang et al., 2008). In this paper, a series of impact tests on concrete under high temperatures were carried out with a specially improved SHPB apparatus, where the coupling effect of high temperature and high strain rate on concrete derived that was introduced to improve the concrete damage plasticity constitutive model in the commercial software ABAQUS. By incorporating the different advantages of the implicit algorithm and the explicit algorithm, an effective numerical analytical approach for RC columns subjected to fire and blast was developed. Further investigations (i.e. the transient heat transfer and fire resistance analyses including residual resistance of RC columns under four different fire exposures) have also been done based on the developed approach.

11

2. Concrete model considering coupling effect of high strain rate and high temperature 2.1. A new SHPB tests apparatus for concrete under high temperatures Actually, concrete is a composite material composed of coarse aggregate, cement, water and some other additives. Since heterogeneity is the main characteristic of concrete it is very complicated to describe the mechanical behavior of concrete under high temperature and dynamic loadings. However, it is commonly acknowledged that different particular components of concrete can be integrated as a homogeneous material to study dynamic and thermal properties on a macro scale level in the SHPB apparatus (Liu et al., 2011; Tao et al., 2011; He et al., 2010), which is illustrated at the beginning of this paper. Since the temperature gradient may affect the wave propagation along the bar in a significant way, the approach of exposing the specimen to the high temperature environment and keeping the incident and transmission bars away from the heating zone is usually carried out in SHPB tests with heated specimens at elevated temperature. A special SHPB apparatus called MATSHPB (Microwaveeheating Automatic Timeecontrolled Split Hopkinson Pressure Bar) was designed, which is for concrete under high temperatures up to 1300 C. An automatic transmission fast matching bars approach was used in MATSHPB (shown in Fig. 1). The concrete specimen can be promptly sandwiched between the incident bar and transmission bar just after easily rolled through the specially designed slide groove from a microwave oven. The test would be automatically managed by the control circuit just after the specimen reaches the striking position between the incident bar and transmission bar. The striking position, located on a refractory brick where the concrete specimen can be in an exactly fixed position after rolling through the slide groove, is sandwiched between a pair of photoelectric sensors. The cylinders will quickly push the incident and transmission bars into contact with the heated concrete specimen, and will be followed by the impact from the striker bar. The test is automatically processed by the MATSHPB, and the experimental process can be monitored and time-controlled exactly. Generally, six specimens, the mix of which is given in Table 1, have been tested in the MATSHPB apparatus. The size of the cylinder specimen is f 70 mm 35 mm, as shown in Fig. 2a.Some of the test results and data from reference (Tao et al., 2011) are graphically demonstrated in Fig. 3, where sTd stands for the dynamic stress at T temperature, while ss designates the static maximum strength at ambient temperature. 2.2. Improved constitutive model on coupling effect of high strain rate and high temperature To describe the combined effects of high temperature and high strain rate on the strength of concrete, the parameter TDSIF (Temperature and Dynamic Strength Increase Factor), which is the maximum dynamic strength of concrete at T temperature divided by the maximum static strength at ambient temperature, is introduced in this paper. The TDSIF of each tested concrete specimen under different strain rates and corresponding temperatures was obtained from the SHPB test results shown in Fig. 3 and plotted in a two dimensional coordinate system with the abscissa of strain rate and ordinate of TDSIF, as shown in Fig. 4. As per the TDSIFestrain rate curves under different temperature plotted in Fig. 4, an explicit formula for TDSIF accounting for strain rate and temperature is supposed to be fitted. It should be noticed that there are only three data available for each high temperature and strain rates ranging from 30 s1 to

12


Fig. 1. MATSHPB apparatus for concrete at high temperatures. (a) Sketch of the apparatus, (b) Setup of the MATSHPB apparatus (c) Touch switch for controlling striker.

250 s1 due to the difficulty of the SHPB experiments. After the results was carefully compared, it is reasonable to assume that the fitted TDSIF-strain rate curves for different temperature levels are similar to those obtained using the CEB model (CEBeFIP, 1990) in the shape under ambient temperature and can be fitted as an explicit analytical formula using the curve-fitting method in Origin 8.5 that is expressed in Equation (1).

lg 3_ TDSIF ¼ A0 exp þ Y0 t1

(1)

where the parameters A0, t1 and Y0 stand for the different fitting coefficients, respectively. The parameters in Equation (1) can be solved using only three experimental data under each temperature, which are also fitted according to different temperatures as shown in Fig. 5, and expressed in Equations from (2)e(4).

T A0 ¼ 0:09437 exp 117:57 t1 ¼ 0:40417 exp

T 274:5

Y0 ¼ 1:1043 0:00148T

concept of isotropic damaged elasticity in combination with isotropic tensile and compressive plasticity to represent the inelastic behavior of concrete. The CDP model assumed that the uniaxial tensile and compressive responses of concrete are characterized by damaged plasticity, as shown in Fig. 6. The material is damaged or degraded due to the elastic stiffness degradation characterized by the variables for tension and compression. However, parameters considering both temperature and strain rate in ABAQUS are still unclear. In this manuscript, these parameters are calibrated by the above TDSIF expression, and some typical parameters are listed in Table 2. The tensile parameters listed in Table 2 are calibrated based on the relationship between compression and tensile strength provided by code for the design of concrete structures (Ministry of Housing and UrbaneRural Construction (MHUC), 2010) due to the limited experimental data available.

(2)

2.3. Verification for the improved CDP model

(3)

Some simplified numerical tests were carried out in order to verify the improved CDP model modified by the TDSIF expression. In the present study, all the numerical simulations of the SHPB test under different temperatures were conducted using the

(4)

where the parameter T stands for temperature. The above TDSIF expression can be introduced to modify the constitutive model of Concrete Damage Plasticity that is designated as CDP in ABAQUS (User's Manual V, 2010). The CDP model used the

Table 1 Mix proportions of concrete (kg/m3). W/B (water cement ratio)

Water

Cement

Flyash

Sand

Stone

0.48

184

326

58

659

1124


13

Fig. 2. Concrete specimens in the MATSHPB tests. (a) Concrete specimen for MATSHPB tests (b) Concrete specimen after test.

commercial software ABAQUS. The concrete specimen was lumped in the C3D8R element model, which was an eightenode hexahedral continuum reduced integrated element. Each node had six degrees of freedom (DOF), three of which were rotational and three of which were rotational. The model size is 70 mm 35 mm, which is exactly the same as the real SHPB tests. The parameters used in the CDP model have been listed in Table 2. The element size should be determined based on the stress wave speed, as the numerical results are highly sensitive to the element size (Zhuang et al., 2005). A convergence test was performed to determine the proper element size. It was carried out by halving the element size in subsequent simulations until the numerical results obtained from simulations with two consecutive element sizes converged, showing that further decreases in element size have an insignificant influence on the numerical results, but this leads to the risk of computer memory overflow and substantially increases the computing time. The final maximum element size used in the study was 0.0089 mm in the axial direction of the cylinder model, which was illustrated in Fig. 7. The simplified displacement loading method that directly applies axial displacement was used in the simulation, as shown in Fig. 7, in order to reduce the computational cost and to precisely simulate the strain rate of the tested specimens. A series of stressestrain curve results obtained in the numerical tests were compared to the experimental data after reasonably smooth disposal, as shown in Fig. 8. It can be inferred that the strength of concrete decreases when subjected to rising temperatures, but increases when subjected to increasing material strain rates. The concrete strain corresponding to peak stress increases with the temperature under the same strain rate. It is clear that the softening effect of temperature on concrete is far greater than the hardening effect of strain rate. The comparison of stressestrain curves between simulations and tests are shown in Fig. 9. It can be noticed that the simulated mechanical characteristics of the concrete affected by strain rate and temperature essentially coincide with those of the tests. 3. Transient heat transfer analysis of RC columns A further numerical simulation was carried out to verify the accuracy of the improved concrete constitutive model in the analytical process of heat transfer. Four different fire loading scenarios (i.e. case A: four fire exposures; case B: three fire exposures; case C: two opposite fire exposures; case D: two adjacent fire exposures) in reference (Wu et al., 2007) are considered in the simulation. The cross-section sizes and reinforcement details of the tested RC column in the reference (Wu et al., 2007) are shown in Fig. 10. “Fire” was the fire exposure state according to the tests, and

the black points marked “1”, “2” and “3” were temperature sensors. The elevated temperature curve of ISO834 was chosen as the fire loading criteria for indoor ambient temperature, which is shown in Fig. 11 and expressed by Equation (5). The elevated temperature curve is also used by Wu (Wu et al., 2007) et al. (2007).

T ¼ T0 þ 345lgð8t þ 1Þ

(5)

where T0( C) is the initial temperature, and T( C) is the ambient temperature subjected to fire after t minutes.

3.1. Modeling of the reinforced concrete columns As showed in Fig. 10, the geometrical model of the tested reinforced concrete column was developed in the commercial software ABAQUS 6.10 exactly according to the experiment geometrical size.

3.2. Mesh and boundary description The element model of reinforced concrete columns is shown meshing on the geometrical model in Fig. 12. As it is shown, concrete is lumped into a 3D eightenode hexahedral continuum element called DC3D8, which is a diffusive heat transfer element. Each node has one degree of freedom (DOF), i.e., one rotational DOF for the temperature field. The element is formulated with trilinear shape functions (constant strain), and the constitutive equations are evaluated based on the state of the element at the vertex. A 2enode heat transfer link element with linear integration named DC1D2 was employed for steel reinforcement. The reinforcement and concrete were combined by the command named “Embedded” in ABAQUS. The temperature load of the curve in Fig. 11 was uniformly applied to the fire exposures of each column. The size effect of grid was also carried out with the convergence test mentioned in Section 2.3, which shows that further decrease in element size only has a slight influence on the numerical results, but leads to the risk of computer memory overflowing and substantially increasing the computing time. However, the heat transfer analysis, without considering stress wave speed, was quite different from the SHPB test in concrete specimen simulation, as the SHPB test is sensitive to the element size. The final maximum element size used in this study was 75 mm 75 mm 75 mm for rigid RC columns and 15 mm for steel reinforcing bars. There is a total of 708 of elements in the model. The heat and mechanical characteristics of the node at the neighboring concrete element and reinforcement element were merged.

14


where l is the heat conduction coefficient, r is the density of the heat transfer material, c is the heat capacity, and x and y are the directions perpendicular to the axial direction of the column. Some simulation parameters for heat transient analysis of reinforcement are listed in Table 3. The heat transfer characteristic and the heat capacity of concrete can be expressed according to EC4 (European Committee for Standardization, 1994) as follows:

lc ¼ 0:012

cc ¼ 4

T 120

T 120

2

2

T þ2 0:24 120

T þ 900 þ 80 120

(7)

(8)

where the applicable scope is 20 C T 1200 C; lc is the heat conduction coefficient; cc is the heat capacity and T is the temperature. The density of concrete in the study was taken as a constant value 2400 kg/m3, and the heat expansion coefficient ac was defined as (Lie and Denham):

ac ¼ ð0:008T þ 6Þ 106

(9)

The expressions about the elastic module of concrete are defined as:

Ec;T ¼ 0:0011T þ 0:83 Ec

(10)

Ec,T is the elastic module under T temperature, Ec is the elastic module under 20 C (Guo and Li, 1991), the applicable temperature scope of which is 60 C T 700 C. The stressestrain curve of concrete under different temperature is determined by Equation (11).

8 2 3 > < 2:2x 1:4x þ 0:2x ; x 1 y¼ x > ;x>1 : 0:8ðx 1Þ2 þ x

(11)

where ¼ 3 3pT , y ¼ f s ; c;T

Fig. 3. Stress ratio-strain curves under different temperatures and strain rates in tests. (a) Test data using MATSHPB apparatus, (b) Test data from reference Tao et al. (2011), (c) Test data contrast between MATSHPB test and test in reference Tao et al. (2011).

3.3. Material model and calibrated parameters related It was supposed that all four fire exposures to the rectangular column were heated in a consistent way along the longitudinal direction of the column, so the transient heat transfer analysis of the RC column could be disposed as a 2D problem. The heat conduction equation can be expressed as follows:

vT 1 v vT v vT ¼ l þ l vt cr vx vx vy vy

(6) Fig. 4. Relationship between TDSIF and strain rate of concrete under different temperatures.


15

Table 2 Simulation thermalemechanical parameters for compressive and tensile properties of concrete specimen. Temp/ C Compressive Inelastic yield stress/Pa strain

Strain Damage rate parameter

Inelastic strain for damage parameter

200 200 200 200 200 200 200 200 200 200 200

50 50 50 50 50 50 50 50 50 50 50

0 2.42E-05 7.28E-05 0.000146 0.000244 0.000368 0.000517 0.000692 0.000893 0.00112 0.00138

6910531 15343070 21839140 27527530 32390230 36409210 39566460 41843950 43223650 43687560 42985750

0 2.52E-05 7.61E-05 0.000153 0.000258 0.00039 0.000549 0.000738 0.000956 0.001204 0.00149

0 0.001113 0.002224 0.003335 0.004446 0.005557 0.006667 0.007778 0.008889 0.01 0.0636

Temp/ C Tensile Cracking Strain Damage Cracking strain yield Stress/Pa strain rate parameter for damage parameter

Fig. 5. Fitting curves for coefficients in the Equation (1) under different temperatures.

fc;T 1 ¼ fc 1 þ 2:4 ðT 20Þ6 1017 3 pT 3p

(12)

¼ 1 þ 0:0015 T þ 5 106 T 2

200 200 200 200 200 200 200 200 200 200 200

2219996 4052000 8090601 11999100 15323640 16884230 13718740 10279050 7963514 6434976 5384621

0 9.00E-05 0.00018 0.000271 0.000365 0.000469 0.000599 0.000731 0.000856 0.000977 0.001095

50 50 50 50 50 50 50 50 50 50 50

0 0.001111 0.003333 0.005556 0.007778 0.01 0.155908 0.317192 0.445457 0.540347 0.610679

0 9.00E-05 0.00018 0.000271 0.000365 0.000469 0.000599 0.000731 0.000856 0.000977 0.001095

(13)

where fc,T, fc is the strength of concrete under T temperature and ambient temperature, respectively; and 3 pT, 3 p is the strain corresponding to peak stress in compression under T temperature and ambient temperature, respectively (Li, 1994). Some typical thermal parameters of concrete calibrated in the simulation are listed in Table 4. 3.4. Temperature loads calculation Implicit heat transfer procedure is employed for the analysis, and a total heat transfer process for 250 min is calculated. Fig. 12 shows the node temperature field distribution (NT11) at 250 min obtained from the numerical simulation. The simulated temperature time histories of heat sensor 3 under different fire exposures are shown in Fig. 13, which basically agree with the test recording. The errors are probably caused by spalling effects in the columns. Owing to the low waterecement ratio in the tests, spalling in the high strength concrete material would cause irregular shapes in the temperatureetime curves (Kodur and Sultan, 2003). However,

spalling is not considered in the numerical analysis.

4. Fire resistance analysis of RC columns The investigation into the residual strength of RC columns after fire loads are carried out based on the study in Section 3, as it uses the same finite element model as that of the transient heat transfer analysis. The data transmission approach is applied in the analysis. Hence, the element size in the residual strength analysis is the same as the element size used in the numerical model for transient heat transfer. The element DC3D8, used in the transient heat transfer analysis is changed to C3D8R for the residual strength analysis. C3D8R is a three dimensional solid 8enode linear reduction with hourglass control, and each node in C3D8R element has three translation DOFs. The element for reinforcement, DC1D2, has been changed into the truss element T3D2, which is a 3eD truss stress/ displacement element with 2enode linear integration. Each node consists of three translation DOFs. The mechanical properties of materials of RC column are also listed in Tables 2e4. In the FE

Fig. 6. Response of concrete to uniaxial loading in tension (a) and compression (b).

16


Fig. 10. Configuration for the reinforcement and the temperature measuring.

Fig. 7. FE model for concrete specimen.

Fig. 11. Curve for ISO834.

Fig. 8. Simulation stressestrain curves under different temperatures and strain rates.

model, nodes on the bottom surface of the column are constrained for translational movements along the X, Y and Zeaxis, but the three rotational DOFs are free; on the top surface, the nodes are constrained for translational movements along the X and Yeaxis, but they are free to move along the Zeaxis and rotate about all

three DOFs, shown in Fig. 14. The axial force of the RC column is loaded after the transient heat transfer, and the failure modes of the column under different fire exposures are plotted in Fig. 14 compared with the test results in reference (Wu et al., 2007). As showed in Fig. 14, the axial or lateral displacement was obviously after applying the axial loads because the RC columns were unevenly damaged after the transient heat transfer. The simulated failure mode of each column is consistent with the test

Fig. 9. Comparison between numerical simulation and test for the specimen. (a) T ¼ 200 C and 3_ ¼ 77 s1, (b) T ¼ 350 C and 3_ ¼ 69 s1.


17

Fig. 12. Temperature fields of RC columns under different fire exposures at 250 min time. (a) case A: four fire exposures, (b) case B: three fire exposures, (c) case C: two opposite fire exposures (d) case D: two adjacent fire exposures.

result (Wu et al., 2007). All of RC columns can basically be categorized into two failure modes. One mode is the material damage, which is due to symmetrical fire exposures under axial displacement as shown in case A and case C; the other mode is the nonesymmetrical structural damage, as shown in case B and case D, induced by the nonesymmetrical fire exposures. The legends of the numerical results in case A and C are illustrated in equivalent

Table 4 Simulation thermal parameters of concrete. Temp/ C

Density

20 100 300 500 700

2400 2400 2400 2400 2400

kg/m3 kg/m3 kg/m3 kg/m3 kg/m3

Heat conduction coefficient/W/(m$K)

Specific heat/J/(kg$ C)

1.96 1.8 1.47 1.2 1

913 965 1080 1172 1242

Table 3 Simulation parameters of reinforcement for heat transient analysis. Temp/ C Density kg/m3

Heat conduction Expansion coefficient/W/(m$K) coefficient/ m/(m$ C)

Heat capacity/J/(kg$ C)

0 7800 48.0 20 7800 47.6 650 7800 33.7 725 7800 32.1 800 7800 30.4 900 7800 28.2 1000 7800 26 Temperature characteristics in elastic and

1.19 E-005 1.20E-005 1.46 E-005 1.49 E-005 1.52 E-005 1.56 E-005 1.60E-005 plastic state

Temp/ C Young's Poisson's ratio modulus/Pa

Yield stress/Pa Plastic strain

20 200 400 600 800

3.5Eþ08 3.43Eþ08 2.38Eþ08 77319000 10842100

2Eþ11 1.67Eþ11 1.51Eþ11 8.09Eþ10 2.86Eþ10

0.3 0.3 0.3 0.3 0.3

420.4 439.8 751.6 1401.3 579.6 650.4 650

0 0 0 0 0 Fig. 13. Contrast between simulation and test of the measured temperatures.

18


Fig. 14. Failure modes of the columns under different fire exposures. (a) case A, (b) case B, (c) case C, (d) case D.

plasticity strain. The performance evaluation criterion of damage in materials is tagged as PEEQ in ABAQUS. In order to distinguish the influence of non-symmetrical fire loads on the column failure modes, the legends of the numerical results in case B and D are illustrated in field node temperature (NT11), but not PEEQ. Wu (Wu et al., 2007) et al. conducted an experimental study on the extreme fire performance of RC columns. The axial displacement time histories of RC columns under different fire exposures

are shown in Fig. 15. It is clear that the numerical results basically consistent with those of the tests on fire performance time. Hence, material parameters and element size in this finite element model have been validated, which provides a foundation for the residual strength analysis of RC columns under the same fire time. Numerical analyses of the residual strength of RC columns under different fire exposures are carried out in accordance with the same test in reference (Wu et al., 2007). The analytical results are shown


19

Fig. 17. Typical gas indoor blast overpressure loading with orifice. Fig. 15. Axial displacement time histories of RC columns under different fire exposures.

columns subjected to blast loading. The problem of resolving nonelinear equations in the numerical analysis of structural responses to blasts makes explicit analysis necessary, the reason of which is that its short integration time step to impart the blast energy into the structure in numerical simulations. However, it results in long computation hours in the quasiestatic process of heat transfer in RC columns. Additionally, the high cost prevents application of explicit analysis in the heat transfer process. A reasonable three-step numerical technique for the responses of RC columns subjected to the coupling effect of fire and blast is proposed in this manuscript. The procedure is divided into three steps:

Fig. 16. Curves of axial presseaxial displacement for RC columns under different fire exposures.

in Fig. 16 in details. It can be found in Fig. 16 that there is a rapid increase in axial displacement in the post fire stage of axial direction compaction, which reveals the residual strength of RC columns, as shown in Table 5. 5. Responses of RC columns subjected to coupling effects of fire and blast 5.1. Analytical approach The inertia effect and strain rate effect for material properties must be taken into consideration in the analytical process of RC

Table 5 Residual strength of RC columns under different fire exposures. Fire exposures

Residual strength/MPa

Residual strength ratio

No fire (case E) Case A Case B Case C Case D

92 9.78 12.98 37.8 15

100% 10.63% 14.11% 41.08% 16.3%

Step 1 (temperature loading stage): fire load is applied to the RC columns in four different fire exposures. The transient heat transfer implicit method is applied in this step; Step 2 (static loading stage): data transmission approach is used in this step. The temperature of the RC columns calculated in the first step can be used as the initial conditions for the second step. RC columns are axially loaded based on step 1. The implicit static analysis method is applied in this step; Step 3 (blast loading stage): a blast load is applied to the surface of RC columns after heat transfer analysis. The data transmission approach is also utilized, and the explicit dynamic analysis method is implemented in this step.

5.2. Analytical results and discussions The overpressureetime curve of internal structure blast is quite different from that in completely airtight containers. Maximum peak overpressure and duration will be lower for venting pressure induced by doors and windows of the structures. The propagating speed of thermal radiation caused by indoor explosion is faster than that of a shock wave. Hence, the thermosphere is formed before the arrival of the shock wave, which causes an additional shock wave in the curve of timeepress for the typical gas indoor blast overpressure loading with orifice. Thus, the typical gas shock wave has two pressure peaks, in which the first one is lower than the other one (Li). The standard overpressureetime curve for the characteristics of blast wave under the condition of constrained by gas diffusion was proposed by Smith and Hetherington (Smith and Hetherington, 1994), which was idealized by Izzuddin (Song et al., 2000; Izzuddin et al., 2000). And the blast load model for the simulation in this section was illustrated in Fig. 17. Numerical simulation models of RC columns were shown in Fig. 11. Both the top surface and the bottom surface of the columns

20


Fig. 18. Damage on RC column under different fire exposures. (a) case A, (b) case B, (c) case C, (d)case D, (e) case E.

were fixed by being constrained against horizontal motions (i.e., in the xe and ye direction), while the bottom surface was also constrained against vertical motion (i.e., in zedirection). The blast load shown in Fig. 17 was uniformly applied to the front faces (shown in Fig. 12) of RC columns with a peak of 3 MPa, and the axial pressure of 1350 KN was preeloaded on both sides of the RC columns. The element size of the model also remained the same as that of the heat transfer analysis for the purpose of data transmission approach. The element C3D8R for concrete was substituted with C3D8RT, which is an 8enode coupled temperatureedisplacement element using trilinear reduction integration approach with hourglass control. Each node in C3D8RT element has three translation DOFs and one temperature field DOF. The truss element, T3D2, is also utilized for reinforcement in the coupling analysis of fire and blast. All the RC columns in this simulation are exposed to different fire exposures, and heated for 250 min according to the curve of ISO834. The same blast loads were uniformly loaded onto the same surfaces of the RC columns. The damage and the mid-span displacement time histories for RC columns with the same blast load under different fire exposures are shown in Figs. 18e20.

Fig. 19. Midespan displacement time histories for RC columns under different fire exposures.

Damage to RC columns caused by the blast loads was mainly concentrated at both ends of the column for the fixed constrained boundary. Additionally, some kinds of damage occurred in the middle of the columns. The damage to the middle of the column was the most severe in case A, while the damage to the middle of the column was least severe in case E. The damages for the rest of the RC columns under different fire exposures from the top to bottom are case B, case D and case C which are consistent with the tests qualitatively (Li). Besides the damage discussed above, the damage at the end of the column in case E was slightly worse than the damage incurred in case B, C and D. The failure mode is mostly shearing in case E, for there was no softening effect caused by fire load, which is completely different in comparison to the other cases. 6. Conclusions A new SHPB test apparatus for concrete under elevated temperature was designed and discussed to study the dynamic mechanical properties of concrete under each elevated temperature. A new constitutive model considering coupling effects of high temperature and high strain rate for concrete is proposed based on the experimental results, and the constitutive model was firstly studied

Fig. 20. Damage time histories on RC columns under different fire exposures.


to improve the concrete damage plasticity model in ABAQUS. The different kinds of mechanical characteristics of concrete resulting from the aforementioned coupling effects were well deduced by the improved model, which was validated by the perfect coincidence in peak stress between tests and simulations. The transient heat transfer analysis of RC columns exposed to ISO834 in different fire scenarios and following fire resistances of RC columns with constant axial forces were numerically investigated on the basis of the improved concrete model, which was validated by the corresponding test data, and the residual axial loading capacity of RC columns was quantitatively calculated. According to the different merits of the implicit algorithm applied to the heat transfer analyses and the explicit algorithm used in the blast analyses, a numerical approach to analyze the responses of RC columns subjected to the coupled loadings of fire and blast was finally developed. Midespan displacements and damages to RC columns subjected to fire and explosions were quantitatively calculated and discussed. The proposed approach was proved to be effective in predicting the responses of RC structures subjected to coupling loadings of fire and blast. Acknowledgments This paper was sponsored by the National Natural Science Foundation of China (No. 51210012, No. 51178462, No. 51378016, and No. 51321064), the National Basic Research Program of China (No. 2012CB026204, No. 2015CB058003). The experiments mentioned in this manuscript received selfless help from Xiquan Jiang. References Bazant, Z.P., Kaplan, M.F., 1996. Concrete at High Temperatures: Material Properties and Mathematical Models. Longman Group Limited, London. Bischoff, P.H., Perry, S.H., 1991. Compression behavior of concrete at high strainerates. Mater. Struct. 24, 425e450. CEBeFIP Model Code, 1990. Comite EuroeInternational Du Beton. Chen, H., Richard Liew, J.Y., 2005. Explosion and fire analysis of steel frames using mixed element approach. J. Eng. Mech. 131 (6), 606e616. Chiddister, J.L., Malvern, L.E., 1963. Compressioneimpact testing of aluminum at elevated temperature. Exp. Mech. 3, 81e90. European Committee for Standardization, 1994. ENV 1994e1e2, Eurocode 4, Design of Composite and Concrete Structures, Part 1.2: Structural Fire Design. Fang, Qin, Zhao, Jiankui, Chen, Li, 2010. Numerical simulation of fire resistance of steel beams subjected blast and fire. China Civ. Eng. J. 43, 62e68 (in Chinese). Fang, Qin, Ruan, Zheng, Zhai, Chaochen, Jiang, Xiquan, Chen, Li, Fang, Wenmin, 2012. Split hopkinson pressure bar test and numerical analysis of salt rock under confining pressure and temperature. Chin. J. Rock Mech. Eng. 31 (9), 1756e1765 (in Chinese). Fang, Qin, Zhao, Jiankui, Chen, Li, Li, Dapeng, 2013. Numerical simulation of deformation and failure of steel columns subjected to blast and fire. J. PLA Univ. Sci. Technol. (Natural Science Edition) 14 (4), 398e403 (in Chinese). Fang, Qin, Zhao, Jiankui, Chen, Li, Li, Dapeng, 2015. Numerical prediction of fire resistance of RC beam subjected to blast and fire. J. Tianjin Univ. (Science and Technology) 21, 1e7 (in Chinese). Guo, Zhengehai, Li, Wei, 1991. Test Study for Heat Resistant Mechanical Properties of Concrete. Department of Civil Engineering, Tsing Hua University, pp. 9e20 (in Chinese). He, Yuaneming, Huo, Jingesi, Chen, Baiesheng, Xiao, Yan, 2010. Tests on dynamic behavior of concrete at elevated temperatures. J. Railw. Sci. Eng. 8 (Suppl. 7), 27e30 (in Chinese). Heinfling, G., Reynouard, J.M., Merabet, O., Duval, C.A., 1997. Thermoeelastic model

21

for concrete at elevated temperatures including cracking and thermoemechanical interaction strains. In: Comp. Plasticity, Fundamentals and Applications. CIMNE, Barcelona, Espana, pp. 1493e1498. Izzuddin, B.A., Song, L., Elnashai, A.S., 2000. An integrated adaptive environment for fire and explosion analysis of steel framesePart II: verification and application. J. Constr. Steel Res. 53 (1), 87e111. Jia, Bin, Tao, Junlin, Li, Zhengliang, Wang, Ruheng, Zhang, Yu, 2008. Effects of temperature and strain rate on dynamic properties of concrete. Trans. Tianjin Univ. 14, 511e513. Jia, Bin, Tao, Jun-lin, Li, Zhengeliang, Wang, Rueheng, 2009. SHPB test for dynamic mechanical performances of concrete at high temperatures. Acta Armament. 30 (Suppl. 2), 208e212 (in Chinese). Jia, Bin, Li, Zhengeliang, Tao, Junelin, Fan, Chao, 2010. SHPB test on high temperature dynamical mechanical behavior of concrete. J. Wuhan Univ. Technol. 32 (21), 34e37 (in Chinese). Kodur, V.K.R., Sultan, M.A., March/April 2003. Effect of temperature on thermal properties of highestrength concrete. J. Mater. Civ. Eng. 15 (2), 101e107. Li Guoehao, Dynamic Mechanics of Blast Resistance for Engineering Structure. Shanghai, Shanghai Science and Technology Press, (in Chinese). Li, Huaedong, 1994. Test Study for Bending Component Characteristic of Reinforcement Concrete at Elevated Temperature. Tsing Hua University, Beijing. Master's Thesis. (in Chinese). Li, Zhiwu, Xu, Jinyu, Bai, Erlei, 2012. Static and dynamic mechanical properties of concrete after high temperature exposure. Mater. Sci. Eng. A 544, 27e32. Lie, T.T. and Denham, E.M.A. Factors affecting the fire resistance of circular hollow steel columns filled with barereinforced concrete. NRCeCNRC Internal Report, No.651. Liu, Chuanxiong, Li, Yulong, Wu, Ziyan, Guo, Weiguo, Ge, Yuzhuo, 2011. Dynamic compression behavior of heated concrete. China Civ. Eng. J. 4 (44), 78e83 (in Chinese). Ma, Chenjie, 2006. The Research of the Fire Resistance of Steel Frames After Subjecting to Impact Loads. Harbin Institute of Technology (in Chinese). Ministry of Housing and UrbaneRural Construction (MHUC), 2010. Code for Design of Concrete Structures (GB50010e2010). Architecture & Building Press, Beijing, China. Nemat-Nasser, S., Isaacs, J.B., 1997. Direct measurement of isothermal flow stress of metals at elevated temperatures and high strain rates with application to Ta and TaeW alloys. Acta Mater. 45, 907e919. Richard Liew, J.Y., Chen, H., 2004. Explosion and fire analysis of steel frames using fiber element approach. J. Struct. Eng. 130 (7), 991e1000. Smith, P.D., Hetherington, J.G., 1994. Blast and Ballistic Loading of Structures. ButterwortheHeinemann, Oxford, U. K., p. 80 Song, L., Izzuddin, B.A., Elnashai, A.S., 2000. An integrated adaptive environment for fire and explosion analysis of steel framesePart I: analytical models. J. Constr. Steel Res. 53 (1), 63e85. Sun, Qiang, Nuo, Liechun, 2009. Steel column dynamic analysis under heatecoupled force. J. Univ. Sci. Technol. China 39 (6), 644e648 (in Chinese). Tao, Junelin, Qin, Liebo, Li, Kui, Liu, Dan, Jia, Bin, Chen, Xiaoewei, Chen, Gang, 2011. Experimental investigation on dynamic compression mechanical performance of concrete at high temperature. Explos. Shock Waves 31 (1), 101e106 (in Chinese). ABAQUS, User's Manual V. 6.10e1, 2010. Dassault Systemes Simulia Corp., Providence, RI. Wang, Zheneqing, Han, Yuelai, Wang, Yongejun, Su, Juan, 2007. Dynamic response of a steel beam simply supported under shock wave in fire field. J. Vib. Shock 26 (4), 69e72 (in Chinese). Wu, Bo, Tang, Guihe, Wang, Chao, 2007. Experimental study on fire resistance of RC columns with different faces exposed to fire. China Civ. Eng. J. 40 (4), 27e31 (in Chinese). Xu, Wenejing, Duan, Lieping, Zhao, Jinecheng, 2013. Research on response of restricted steel beam under elevated temperature and blast loading. J. Disaster Prev. Mitig. Eng. 33 (3), 342e347 (in Chinese). Yan, Shi, Qi, Baoxin, Xin, Zhiqiang, Liu, Lei, Li, Peng, Li, Xiaojie, 2010. Numerical analysis on dynamic response and failure mode of light steel column under elevated temperature and blast loading, 43, 484e489 (in Chinese). Yaozhuang, Li, Yu, Tang, Zhichang, Zeng, 2008. Development and trend of the research on fireeresistance of reinforced concrete structures. J. Catastrophol. 23 (1), 102e107 (in Chinese). Zhuang, Zhuo, Zhang, Fan, Cen, Song, et al., 2005. ABAQUS Nonlinear Finite Element Analysis and Examples. Science Press, Beijing, pp. 214e217 (in Chinese).