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Collision capacity evaluation of RC columns by impact simulation and probablisticHYDOXDWLRQ Na-Hyun Yi , Ji-Hun Choi , Sung-Jae Kim , Jang-Jay Kim

Journal of Advanced Concrete Technology, volume 13 ( 2015 ), pp. 67-81

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Journal of Advanced Concrete Technology Vol. 13, 67-81, February 2015 / Copyright © 2015 Japan Concrete Institute

Scientific paper

Collision Capacity Evaluation of RC Columns by Impact Simulation and Probabilistic Evaluation Na-Hyun Yi1, Ji-Hun Choi2, Sung-Jae Kim2, and Jang-Ho Jay Kim3* Received 14 June 2014, accepted 26 January 2015

doi:10.3151/jact.13.67

Abstract Recently, increasing traffic in urban areas has led to a dramatic increase in collisions between speeding vehicles and structural columns. An impact applies a greater force to a column than its regular static or dynamic load because of the mass acceleration effect of the vehicle. Vehicle impact can cause catastrophic damage to structural columns and ultimately cause them to collapse; therefore, an in-depth study of their structural resistance to vehicle impact is needed. This paper reports the behavior of a reinforced concrete (RC) compression member or column under a lateral impact load. The study quantitatively assessed the columns’ resistance capacity and developed an impact-resistance capacity evaluation procedure. Because it is extremely difficult and costly to experimentally perform a parametric study for column impact scenarios, this analytical study was carried out using LS-DYNA, a commercial explicit finite element (FE) analysis program that simulates the effects of a high strain rate from impact or blast loading on structural and material behavior. The parameters used for this case study were cross-section shape variation, impact load angle, axial load magnitude ratio, concrete compressive strength, longitudinal and lateral reinforcement ratios, and slenderness ratio. Using the analysis results, an impact resistance capacity evaluation procedure using a probabilistic approach is proposed.

1. Introduction Recently, due to increasing construction of roads and other transportation-related infrastructures as well as increasing traffic in urban areas, collisions between speeding vehicles and structural columns and walls have increased dramatically (Ferrer et al. 2010; Nam et al. 2009a; Nam et al. 2010; Tian et al. 2011). Also, the 9/11 terror attack on the World Trade Center, which caused a total collapse, led to intense public concern about structural collapse from sudden impact or blast loading (Nam et al. 2009b; Englekirk 2005). Due to heightened anxiety about accidents and terrorism, structural engineers and designers have been greatly interested in design procedures to protect structures from such threats. The most important part of a structure is the column or compression member, because it supports the superstructure. As shown in Fig. 1, if columns fail, structural collapse occurs from the progressive failure mechanism. Because columns are important to the overall safety of a

structural system, it is critical to protect them from accident scenarios. An impact load arising from a vehicle accident can cause localized damage to columns, which leads to a

(a)

1

Research Fellow, School of Civil and Environmental Engineering, Yonsei University, 134 Shinchon-dong, Seodaemun-gu, Seoul, South Korea, and School of Civil & Environmental Engineering, Nanyang Technological University, Singapore. 2 Doctoral student, Concrete Structural Engineering Laboratory, School of Civil and Environmental Engineering, Yonsei University, Seoul, South Korea. 3 Associate Professor, Concrete Structural Engineering Laboratory School of Civil and Environmental Engineering, Yonsei University, Seoul, South Korea. *Corresponding author, E-mail: [email protected]

(b) Fig. 1 Collapsed bridge due to vehicular collision (ElTawil et al. 2005).

N-H. Yi, J-H. Choi, S-J. Kim, and J-H. J. Kim / Journal of Advanced Concrete Technology Vol. 13, 67-81, 2015

plastic hinge type of behavior (Consolazio and Cowan 2005). This localized damage is similar to that caused by an earthquake or other dynamic-load related event in which damage is concentrated in a small area of the structural component. However, a collision from a speeding vehicle causes more serious damage than an earthquake or other dynamic-loading event because of the additional load applied to the structure by the mass acceleration effect (Kernal and Fahri 2011). Transient impact loading is especially detrimental to a column, because the impact loading is extremely fast and the structure does not have time to absorb or transfer the applied load energy through thermal release or stress transfer; thus the structure can sustain severe damage (Kim et al. 2011). Therefore, it is critical to systematically evaluate the impact resistance capacity of the column at the design stage. The current design methods for structural columns regarding vehicle or ship collisions transform impact loads into additional static loads by adding an impact load factor less than or equal to 0.3 (Nam et al. 2010). However, such load factor multiplication can result in over- and under-design of the structures (El-Tawil et al. 2005; Konishi et al. 1990). Therefore, the transient impact characteristic or high strain rate effect must be properly considered in the design using precise impact simulation results. However, the degree of damage caused to a column by an impact load is rarely calculated precisely, because few designers carry out a suitable impact analysis using explicit finite element analysis (FEA) (Nam et al 2009a; Sastranegara et al. 2005; Kim et al. 2012) To more accurately predict the effect of an impact on columns, impact resistance capacity must be determined using high strain rate and explicit FEA programs such as LS-DYNA to simulate structural behavior under impact loading. Also, because of the difficulty of capturing the instantaneous column behavior from an impact experiment, analytical data obtained from precise FEA simulations are needed for impact damage characterization and resistance capacity evaluation from a probabilistic point of view (Harries and McNeice 2006; Jain et al. 2001). Using a probabilistic impact resistance capacity evaluation procedure, the most realistic behavioral trends and failure mechanisms of the structure under impact loading can be represented with a probabilistic curve as a function of various structural parameters. This probabilistic approach to determine behavioral trends from complicated and unclear data with multiple parameters has been previously implemented by Shinozuka et al. (2000b) and Kim et al. (2011) to set up fragility curves and satisfaction curves, respectively, for structural seismic failure evaluation and performance-based concrete mixture design, respectively (Kwon et al. 2011). By using the most critical probabilistic behavioral trend curves from impact loading, designers can easily predict the impact resistance capacity of the components exposed to impact collisions. Because the precise evalua-

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tion of structures’ impact resistance capacity will minimize human casualties and serious damage from impact loading, this research performed precise impact analyses of RC columns using LS-DYNA for various column parameters. This study also proposes a procedure for drawing probabilistic curves for impact behavioral trends using the impact analysis results. Finally, it suggests specific considerations for impact loaded RC columns based on the outcomes of the trend curves.

2. Background theory Research on concrete structural behavior under impact loading is being actively pursued worldwide (Ferrer et al. 2010; Nam et al. 2009a, 2009b, 2010). However, due to the inherent time-dependent characteristics of impact loading, it is difficult to properly obtain precise data regarding structural behavior from impact tests (Nam et al. 2009a). In particular, the multiple experiments required for parametric studies to obtain sufficient data for structural design purposes are too costly and difficult; therefore, the only feasible means to obtain a wide variety of data are precise impact simulation analyses. Precise simulations need to be performed using proven commercial explicit finite element programs such as LS-DYNA, which has been repeatedly validated by researchers and engineers (Nam et al. 2009a, 2009b; Consolazio and Cowan 2005; El-Tawil et al. 2005; He et al. 2013). 2.1 Failure criterion for a concrete component under an impact load The behavioral trends and failure mechanisms of RC columns from impact loading depend on loading magnitude and angle as well as column strength and stiffness (ASCE 1997, 1999). Instantaneous and severe loading cases, such as impact and blast loads, normally cause columns to displace in excess of their elastic range and usually reach their ultimate displacement and rotational capacities independent of their strength (Kernal and Fahri 2011). Therefore, columns under impact loading have to be evaluated based on the concept of ductility rather than strength, which is why the American Society of Civil Engineers (ASCE) selected ductility and boundary rotation limit values as the impact damage criteria (Table 1). Therefore, this study obtained analysis results for displacement and rotation following impact loading for comparison with ASCE damage criteria. 2.2 Probabilistic impact resistant capacity evaluation In any probabilistic impact resistance capacity evaluation procedure, the target performance criteria for the impact-loaded structures need to be selected (Harries and McNeice 2006). Given the probabilistic approach, the performance degree and satisfaction criteria have to be expressed as probabilistic values. In other words, depending on structures’ original intended uses, they are

69


Table 1 Typical failure criteria of ASCE (ASCE, 1997; 1999). Type ASCE, 1999

ASCE, 1997

Criteria

Element type

ΔL / l Support Rotation, θ

Column

Beam-Columns

Failure type Compression

Light 1%

Damage Moderate 2%

Severe 4%

Low

Medium

High

1

2

4

Flexure: Compression (C) Tension (T) Between C&T Shear

* ΔL / l : Ratios of shortening to height Table 2 Steps for performance-based evaluation using Bayesian probability Step 1 2 3 4 5 6 7

Description Setup of the criteria for the parameters using 0 and 1 for fail and safe, respectively Selection of the parameter for the x-axis of the satisfaction curve Virtual data generation using lognormal, normal, etc., for the number of current data Classification of damage level as Critical, Major, Normal, or Minimal Determination of the fail/safe status of each data point and development of the satisfaction curve Summation of various combinations of satisfaction curves into a single satisfaction curve for observation of overall trends: Total satisfaction curve = Σ(Single-parameter satisfaction curves) Verification of the accuracy of the developed satisfaction curve using chi-square distribution

assigned different levels of required performance throughout their service life. The levels of required performance are expressed in probabilistic terms as satisfaction percentages. Failure-resistant envelope curves, such as the fragility curve developed by Shinozuka et al. (Kim et al. 2011; Shinozuka et al. 2000a, 2000b), are used to express structural performance in a probabilistic manner. Using fragility curves, one can determine whether a structure is safe or not as a function of probability ranging from 0 to 100%. The evaluation of the performance satisfaction probability of an impacted RC column can thus be calculated for various magnitudes of impact force and angle as well as for various structural and material properties. Because the principle of a structural component’s possibility of failure under applied loading (fragility curve) is opposite to the structural component’s possibility of satisfying performance criteria, the new terminology of a satisfaction curve better represents the failure envelope curve used for this evaluation. Both satisfaction curves and fragility curves are probabilistic evaluation curves used to determine an RC column’s impact resistance and characteristics in a probabilistic manner. Table 2 shows the seven-step procedure for using PBD in this study’s data evaluation approach (Kim et al. 2011, 2012).

3. Analysis details of RC columns under impact loading With respect to impact analysis, much research about the impact loading of vehicles, missiles, and airplanes as well as the impact behavior of various materials and components has been conducted (Kim et al. 2011; Krauthammer et al. 1994; Zaouk et al. 1996). However, There has been limited research with respect to probabilistic impact resistance capacity evaluation for a con-

Table 3 Analysis geometry and material properties of impacted column section. Classification

Circular section Square section

D = 1200 1200 × 1200 Height (mm) 3300 3300 Main rebar dia. (mm) D25(25.4) @36 D25(25.4) @36 Main rebar ratio 0.0161 0.0127 Main rebar spacing (mm) 86.47 111.11 Lateral tie dia. (mm) D13(12.7) D13(12.7) Lateral tie spacing (mm) 300 300 fck (MPa) 24 24 fy (MPa) 300 300 Section size (mm)

crete structural component under impact loading. Therefore, this study carried out a simulation of RC columns under truck impact loading using LS-DYNA, which can perform structural analysis using high strain-ratedependent constitutive models and high-speed impact loading (Nam et al. 2009a, 2010). 3.1 Selection of column cross-sections and vehicle models The RC column selected for this study is an actual overpass highway column supporting a continuous span slab-bridge in Korea. The column has a circular crosssection with height and diameter dimensions of 3,300 mm and 1,200 mm, respectively. In the simulation, the circular cross section was converted to a square cross section with a width equal to the circular diameter. This conversion was chosen to make the effective impact area for both the square and circular columns equal for analysis. The column dimensions and material properties used for analysis are tabulated in Table 3. The generated mesh and boundary conditions for the analysis are shown in Fig. 2(a). To implement the most severe damage-inducing boundary conditions, the analysis used


(a) FEM models and boundary conditions of column

70

(b) FEM model of truck

Fig. 2 Finite element analysis model.

(a) Failure surfaces of concrete model

(b) Constitutive behavior

Fig. 3 Concrete damage material model based on Malvar’s model (Malvar et al. 1997).

(a) Strength enhancement of concrete due to high strain-rates

(b) Effective plastic strain versus yield stress of steel

Fig. 4 Strain rate effect of concrete and steel (Nam et al. 2009a).

a fixed bottom and freed top (i.e., a cantilever). To simulate the non-linear FEA of a concrete structure under impact loading, the concrete damage model rel3, based on Malvar’s model (Malvar et al. 1997; Nam

et al. 2010) and implemented in LS-DYNA, was used to consider the strain rate effect, as shown in Figs. 3 and 4(a), respectively. Malvar’s model modifies the William-Warnke failure surface to represent blast dynamic

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hardening-softening nonlinear behavior based on accumulated effective plastic strain (Malvar et al. 1997; Nam et al. 2009a). It is a plasticity-based formulation with three independent failure surfaces, as shown in Fig. 3, which change shape depending on the pressure. Meanwhile, rf is the strength enhancement factor with strain rate effect. The enhanced strength of concrete is multiplied by enhancement factor of static concrete strength as shown in Fig. 3(a). The relationship between the strain rate and the concrete strength enhancement factor shown in Fig. 4(a) was linearly extended from the CEB model. The piecewise linear plasticity model was used for the reinforcing steel, based on the von Mises criterion. The strain rate effect used for the reinforcing steel was implemented by defining the relationship between effective plastic strain and yield strength based on Table 4 Truck FEM model characteristics. Classification Shell Solid Beam

Number of elements

Weight of car (ton) Yield stress (MPa) Elastic modulus (MPa) Impact velocity of car (km/h) Car geometry (B×H×L, mm)

Ford truck 19,479 1,248 124 8 270 205,000 100 2400×3200×8500

Table 5 Case titles and parameter variations used for impact analysis. Case title AVC ARS-R

Parameter variation Vehicle collision angle to column Square section angle to column center line (only used for square column) UAL(R)-CS Uniform axial load (ratio) to compressive strength VLS-US Longitudinal reinforcement area to uniform stirrup spacing VCS-US Lateral reinforcement area to uniform stirrup spacing L-SR-C Slenderness ratio and aspect ratio to column height (only used for circular column) CEL-SR Slenderness ratio to effective length coefficient

Structure θ , Impact Angle v, Impact Velocity

the experimental data shown in Fig. 4(b). The effects from girders, slabs, the single standing foundation, and soil type were not considered in the analysis; only the impact behavior of the RC column was studied. For analysis, the impact loading was applied using an 8-ton truck model as shown in Fig. 2(b). This model, provided by the National Crash Analysis Center (NCAC) of the USA for vehicle impact research (NCAC; EL-Tawil et al. 2005; Zaouk et al. 1996), is the most realistic and severe impact loading scenario currently available. As shown in Table 4, the body of the truck has 19,479 shell elements, and its internal parts were modeled using 1,240 solid elements. The modeled truck is similar to the actual vehicle; the engine and transmission parts use an elastic material model, the connecting parts use a rigid material model, and the body parts use a piecewise linear plasticity material model considering the strain rate, as shown in Fig. 4(b). The elements used for the vehicle model (i.e., shell, solid, and beam) were connected using various constraints similar to those in actual vehicles. This study did not use the eliminating element technique in the vehicle or column models. The speed of the truck was chosen based on the regulations of the Ministry of Land, Transport, and Maritime Affairs of Korea, which limits highway traffic speed to between 120 km/h and 80km/h, with an average speed of 100 km/h (MLTM 2008). From published impact analysis reports (Zaouk et al. 1996; MLTM 2008; ElTawil et al. 2005), the authors realized that proper modeling of the interface between the column and the vehicle is important to simulate a vehicle crash impact with large deformation within the transient time duration. A realistic vehicle impact load is best generated using a contact algorithm. This study used the Automatic Contact Surface to Surface algorithm for the interface between the solid and shell elements of the vehicle and the column surface, respectively (MLTM 2008; Nam et al. 2010). 3.2 Analysis parameters To develop a realistic impact resistance satisfaction curve for RC columns, a full set of structural and material parametric studies must be performed. Case titles and parameter variations for the impact analysis are tabulated in Table 5. Detailed descriptions of the parameters are provided in the following sections. 3.2.1 Index of severity by impact angle Damage or impact resistance is represented by an index of severity (IS) calculated as the energy transfer for impact angle, collision speed, and vehicle type as shown in Fig. 5 (Jung et al. 2001). The IS equation is expressed as a function of vehicle mass, collision velocity, and impact angle.

IS = Fig. 5 Index of severity based on vehicle impact angle.

1 ⎛ V ⎞ m⎜ sin θ ⎟ 2 ⎝ 3.6 ⎠

2

(1)

72


60°

75°

proposed that the axial force ratio of a column must be ≤0.1−0.05 when a 1,868 kN axial force is divided by its gross cross-sectional area and the designed concrete compressive strength is as shown in Eq. (2) and Table 6 (UAL-CS). Axial load

45°

30°

(a) Impact angle of vehicle 30°

45°

60°

90°

(b) Impact structure angle to vehicle Fig. 6 Impact angle of vehicle and structure.

where IS is the impact severity (KJ), m is the vehicle (tons), V is the impact velocity (km/h), and θ is the impact angle (°). Most actual vehicle-column collisions occur at an impact angle rather than head-on. Different impact angles cause different types of damage, because they apply different impact forces to a structure. As a control specimen for the square column, an orthogonal impact angle or head-on-collision equivalent to 90 degrees to the column face was selected. This study considered two types of impact angles varied by changing the vehicle (AVC) or structural impact angle (ARS-R). Various vehicle and structural impact angles were analyzed to obtain the IS for structures, as shown in Figs. 6(a) and 6(b), respectively. 3.2.2 Axial load magnitude and axial load ratio Both axial force and flexural moment occur in a slender column when an axial load is applied. Because the behavior of a laterally impacted column is greatly influenced by axial load magnitude, axial load magnitude and ratio were chosen as parameters. A constant axial force of P = 1,868 kN was chosen from previous reports for the parameter study of concrete compressive strength for RC columns (Jung et al. 2001). The study

ratio =

P ≥ 0.1 ∼ 0.05 Ag f ck

(2)

The axial load was varied by changing the concrete compressive strength to maintain a constant axial load ratio. Therefore, the axial force and axial force ratio selected as parameters are an axial force of 1,868 kN (UAL-CS) resulting in an axial force ratio of 0.0686 and 0.0539 (UAL-CS) for circular and square columns, respectively, from Eq. (2). 3.2.3 Confinement stress parameters Column buckling failure can be eliminated by increasing RC column ductility by applying abundant confinement stresses using additional ties and stirrups. Lateral column reinforcements such as ties and stirrups also control buckling by resisting shear stress and applying confinement to the concrete core section. The stirrup type, longitudinal to lateral reinforcement ratio, and core concrete strength are the main parameters that dictate the magnitude of the confinement stress generated in RC columns (Fradis 2004; KCI 2007). Equations (3) and (4) show that the confinement stress generated in a confined section of RC column depends on core concrete compressive strength, stirrup spacing, and reinforcement size.

f c* − 0.85 f cu = 4.0 f 2′ f 2′ =

2 Asp f y dc s

(3) (4)

where f c* is the compressive strength of the core section of the column, f cu is the unconfined concrete compressive strength, f 2′ is the confinement stress applied to the core concrete section, Asp is the cross sectional area of the stirrup or lateral reinforcement, d c is the diameter of the confined section, and s is the spacing of the stirrups. The uniaxial compressive strength of the core concrete was varied for the impact simulation: 18 MPa, 24 MPa, 28 MPa, and 32 MPa. The longitudinal to lateral reinforcement ratio was varied by changing the rebar size and stirrup spacing. The rebar size and stirrup spacing used for the analyses were longitudinal reinforcements of D44.4, D31.2, D25.0, D22.0, and D19.6 (VLS-US), lateral reinforcements of D16.3, D14.6, D13.0, D10.4, and D7.37 (VCSUS), and spacing of 100 mm, 200 mm, 300 mm, 400 mm, and 500 mm. 3.2.4 Height and boundary conditions for buckling behavior If the slenderness ratio of a column is less than 22, it is

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Table 6 Input analysis parameter for the circular and square sections. Case1) Control. AVC30 AVC45 AVC60 AVC75 AVC90 ARS30-R ARS45-R ARS60-R ARS90-R

D L AR2 fck Impact (MPa) angle (mm) (mm) (°) 1200 3300 2.75

24

1200 3300 2.75

24

1200 3300 2.75

24

UAL18-CS18

18

UAL18-CS24

24

1200 3300 2.75

UAL18-CS28

28

UAL18-CS32

32

UALR68-CS18

18

UALR68-CS24

24

1200 3300 2.75

UALR68-CS28

28

UALR68-CS32

32

VLS44-US VLS31-US VLS25-US VLS22-US VLS19-US

18 24 28 32

1200 3300 2.75

VCS07-US

Axial force (kN)

90

3086

30 45 60 75 90 30 45 60 90

771.6 1543.2 2314.8 2879.7 3086 771.6 1543.2 2314.8 3086

90

90

90

Axial force ratio

Longitudinal steel

22 (18.3)

0.534 0.178 0.107

100 300 500

2

18.3

D13

0.534 0.267 0.178 0.133 0.107

100 3.03(2.378) 200 6.04(4.756) 300 9.06(7.135) 400 12.13(9.549) 500 15.07(11.87)

2

22 (18.3)

D13

0.534 0.267 0.178 0.133 0.107

100 3.03(2.378) 200 6.04(4.756) 300 9.06(7.135) 400 12.13(9.549) 500 15.07(11.87)

2

22 (18.3)

D13

0.545 0.2685 0.178 0.1329 0.106

100 200 300 400 500

9.06 (7.135)

2

22 (18.3)

0.178

100 200 300 400 500

9.06 (7.135)

2

22 (18.3)

300

9.06 (7.135)

1.613

D13

0.534 0.178 0.107

36-D25

1.27

D13

3086

1868

0.0915 (0.0719) 0.0686 (0.0539) 36-D25 0.0588 (0.0462) 0.0515 (0.0404)

1.613 (1.27)

3086

1397 (1778) 1863 (2371) 0.0686 36-D25 2172 (0.0539) (2766) 2483 (3161)

1.613 (1.27)

3086

0.0686 36-D25 1868 (0.0539) 4

1.613 (1.27)

1868

0.0686

36-D25

1868

0.0539

1868

36-D44.4 36-D31.2 0.0686 36-D25.0 36-D22.0 36-D19.6

(%)

4.937 2.433 1.613 1.204 0.961

D10.4 90

3086

1868

0.0686 36-D25 (0.0539)

1.613 (1.27)

D13 D14.6

32

18 24 28 32

1200 3300 2.75

18 24 28 32

2.378 7.135 11.87

D7.37

D16.3

90

3086

1868

0.0915 0.0686 0.0588 0.0515

1868

0.0915 (0.0719) 0.0686 (0.0539) 36-D25 0.0588 (0.0462) 0.0515 (0.0404)

90

3086

36-D25

1.613

D13

0.534 0.178 0.107

100 300 500

3.03 9.06 15.07

2

0.5 1.613 (1.27)

D13

0.534 0.178 0.107

100 3.03(2.378) 0.7 300 9.06(7.135) 500 15.07(11.87) 1.0 2.0

11 18 22 25 30 40 5.5 (4.58) 7.7 (6.42) 11 (9.17) 22 (18.3)

3) IS: Index of severity 4) ( ): In case of square section

considered to be a stocky column, as shown in Eq. (5) (KCI, 2007). < 22

2

0.178

1) Case: Refer to Table 4. 2) AR: Aspect ratio, L/D

r

100 3.03(2.378) 300 9.06(7.135) 500 15.07(11.87)

D13

CEL20-SR22

kl

22 (18.3)

ρs

CEL05-SR55

CEL10-SR11

2

(%)

Space (mm)

Size

VCS14-US

CEL07-SR77

kl r

ρs

28 VCS16-US L1650-SR11-C 1650 1.38 L2700-SR18-C 2700 2.25 L3300-SR22-C 3300 2.75 1200 L3750-SR25-C 3750 3.125 3.75 L4500-SR30-C 4500 5 L6000-SR40-C 6000

ρl

k

Size

24 1200 3300 2.75

Lateral steel

ρl

18

VCS10-US VCS13-US

IS3 (kJ)

(5)

where k is the effective buckling length coefficient, l is the actual height of the column, and r is the radius of gyration equal to I / A where I is the second moment

of inertia, and A is the cross sectional area of the column. Therefore, to consider the buckling and effective height effect of a slender column, the height of the column has been varied to 1650 mm, 2700 mm, 3750 mm, 4500 mm, and 6000 mm (L-SR-C). The effective buckling length coefficient k also has been varied to 0.5, 0.7, 1.0 and 2.0 by changing the boundary conditions of the column (CEL-SR).

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4. Impact resistance capacity evaluation results and discussion

4.1.1 Cross sectional shape variation To investigate the cross sectional shape effect, the impact analysis of circular and square columns was performed with the same material and geometrical properties: height of 3300 mm, diameter of 1200 mm, lateral stirrup spacing of 300 mm, concrete compressive strength of 24 MPa, impact angle of 90 degrees to column face, and lateral steel ratio of 0.178. The lateral views of a truck crashing into an RC column simulation

4.1 Analytical results for the various parameters The various analytical parameters used to perform the study of RC columns under impact loading are tabulated in Table 7.

Table 7 Summary of analysis results. Circular section

Case1) 100mm mm degree

200mm mm

0.534

AVC

mm

-

degree

Square section 400mm mm

0.178

500mm

degree

mm

-

degree

100mm mm

0.107

degree

200mm mm

0.534

300mm

degree

mm

-

degree

400mm mm

0.178

degree

500mm mm

-

degree

0.107

30°

1.066 0.02

-

-

1.549

0.03

-

-

1.191

0.02

14.81

0.26

-

-

6.135

0.11

-

-

19.64

0.34

45°

1.822 0.03

-

-

2.212

0.04

-

-

1.424

0.02

22.59

0.39

-

-

32.89

0.57

-

-

39.96

0.69

60°

3.409 0.06

-

-

6.112

0.11

-

-

3.913

0.07

72.21

1.25

-

-

89.94

1.56

-

-

95.89

1.66

75°

102.2 1.77

-

-

118

2.05

-

-

135.5

2.35

57.3

0.99

-

-

76.35

1.33

-

-

87.79

1.52

90°

95.27 1.65

-

-

133.2

2.31

-

-

184.7

3.20

48.78

0.85

-

-

71.71

1.24

-

-

95.12

1.65

CA2) ARS -R

degree

300mm

-

-

-

-

-

0.534

-

0.178

-

0.107

30°

-

-

-

-

-

-

-

-

-

-

98.43

1.71

-

-

136.4

2.37

-

-

163.5

45°

-

-

-

-

-

-

-

-

-

-

87.5

1.52

-

-

126.5

2.20

-

-

160.4

2.78

60°

-

-

-

-

-

-

-

-

-

-

80.34

1.39

-

-

105.0

1.82

-

-

126.6

2.20

90°

-

-

-

-

-

-

-

-

-

-

48.78

0.85

-

-

71.71

1.24

-

-

95.12

1.65

fck

2.84

Axial Force = 1,868 kN

UAL 18MPa 91.18 1.58 18 24MPa 95.27 1.65 -CS 28MPa 99.96 1.74

120.3

2.09

133.5

2.32

163.3

2.83

182.6

3.17

51

0.89

59.28

1.03

68.33

1.19 72.37 1.26 80.63

1.40

115.9

2.01

133.2

2.31

157.1

2.73

184.7

3.20

48.78

0.85

64.12

1.11

71.71

1.24 71.74 1.25 95.12

1.65

121.4

2.11

137.5

2.39

163.4

2.83

174

3.02

48.15

0.84

56.69

0.98

71.74

1.25

1.36 105.3

1.83

32MPa 93.82 1.63

135.7

2.35

144.4

2.51

156

2.71

168.4

2.92

45.89

0.80

60.09

1.04

64.51

1.12 80.24 1.39 107.4

1.86

126.2

2.19

118.6

2.06

154.4

2.68

193.3

3.35

37.02

0.64

56.69

0.98 65.83

1.14

72.9

1.27 86.08

1.49

115.9

2.01

133.2

2.31

157.1

2.73

184.7

3.20

49.5

0.86

59.28

1.03 70.46

1.22

79.6

1.38 87.11

1.51

125.4

2.18

171

2.97

169.8

2.95

203.2

3.52

45.92

0.80

53.94

0.94 73.53

1.28 83.01 1.44 97.11

1.69

121.7

2.11

163.2

2.83

165.3

2.87

230.5

4.00

40.19

0.70

50.39

0.87 61.85

1.07 77.91 1.35 99.04

1.72

78.1

Axial Force Ratio = 0.0686 (0.0539)4)

fck 18MPa 101.3 1.76

UALR 68-CS 24MPa 95.27 1.65 28MPa 90.55 1.57 32MPa 96.71 1.68 fck

As

44.4 mm2

31.2 mm2

25.0 mm2

22.0 mm2

19.6 mm2

44.4 mm2

31.2 mm2

25.0 mm2

22.0 mm2

19.6 mm2

18MPa 75.44 1.31 VLS -US3) 24MPa 81.6 1.42 28MPa 74.33 1.29

116.4

2.02

133.5

2.32

172.7

3.00

220.8

3.83

37.06

0.64

56.81

0.99 68.33

1.19 75.59 1.31 93.01

136.3

2.37

133.2

2.31

193.9

3.36

212.8

3.69

37.43

0.65

77.24

1.34 71.71

1.24 90.14 1.56 99.11

1.72

111.9

1.94

137.5

2.39

160

2.78

168.9

2.93

32.59

0.57

66.5

1.15 71.74

1.25 76.15 1.32 98.32

1.71

32MPa 84.83 1.47

112.1

1.94

144.4

2.51

152.6

2.65

225.8

3.91

31.58

0.55

54.15

0.94 64.51

1.12 90.21 1.57 106.1

1.84

fck

As

7.37 mm2

10.4 mm2

13 mm2

14.6 mm2

16.3 mm2

7.37 mm2

10.4 mm2

13 mm2

14.6 mm2

1.61

16.3 mm2

18MPa 150.3 2.61 VCS -US3) 24MPa 160.2 2.78 28MPa 142.9 2.48

136.7

2.37

133.5

2.32

138.2

2.40

139.3

2.42

62.02

1.08

72.58

1.26 68.33

1.19 63.35 1.10 67.23

1.17

142.6

2.47

133.2

2.31

146.8

2.55

151.4

2.63

68.08

1.18

71.8

1.25 71.71

1.24 71.39 1.24 74.82

1.30

145.7

2.53

137.5

2.39

140.2

2.43

154.5

2.68

66.02

1.15

72.61

1.26 71.74

1.25 74.55 1.29

77

1.34

32MPa 132.8 2.30

136.5

2.37

144.4

2.51

137.5

2.39

158.5

2.75

65.21

1.13

67.75

1.18 64.51

1.12

74.4

1.29

78.4

1.36

H(mm)

L-SRC

CEL -SR

1600

113.9 4.07

-

-

174.3

6.22

-

-

259.6

9.22

-

-

-

-

-

-

-

-

-

-

2700

97.27 2.06

-

-

155.4

3.29

-

-

192.9

4.09

-

-

-

-

-

-

-

-

-

-

3300

95.27 1.65

-

-

133.2

2.31

-

-

184.7

3.20

-

-

-

-

-

-

-

-

-

-

3800

82.92 1.25

-

-

117.2

1.77

-

-

176.4

2.66

-

-

-

-

-

-

-

-

-

-

4500

83.94 1.07

-

-

113.7

1.45

-

-

146.6

1.87

-

-

-

-

-

-

-

-

-

-

6000

72.52 0.69

-

-

109.4

1.04

-

-

159.3

1.52

-

-

-

-

-

-

-

-

-

-

0.5

55.02 0.96

-

-

95.27

1.65

-

-

102.0

1.77

26.72

0.46

-

-

41.71

0.72

-

-

53.28

0.92

0.7

58.42 1.01

-

-

78.37

1.36

-

-

97.62

1.69

28.23

0.49

-

-

43.45

0.75

-

-

51.7

0.90

1.0

83.76 1.45

-

-

152.7

2.65

-

-

193.4

3.35

48.5

0.84

-

-

66.11

1.15

-

-

98.38

1.71

2.0

95.27 1.65

-

-

133.2

2.31

-

-

184.7

3.20

48.78

0.85

-

-

71.71

1.24

-

-

95.12

1.65

1) Case : Refer to Table 4. 2) CA : Just for square section column 3) US : Uniform steel ratio (longitudinal / confining steel ratio) = 9.06(Circular), 7.135(Square) 4) ( ) : In case of square section


are shown in Fig. 7 from the start to the end of the impact. The continuous lateral displacement versus the time curves for both the circular and square columns at the center of the impact are shown in Fig. 8. The lateral displacement curves from the impact load were larger for the circular column than for the square column (Fig. 8). The results show that the impact resistant total crosssectional area of the square column (1.44 × 106 mm2) is

75

1.27-fold larger than that of the circular column (1.13 × 106 mm2). Also, the displacements occurred at the time of collision contact, and residual displacements increased continuously as the impact loading continued. The maximum displacement with respect to the height of the square and circular columns occurred at the point of impact approximately 1500 mm from the column base (Fig. 9). For the circular column, the maximum

(a) 17.998 msec

(b) 44.996 msec

(c) 65.998 msec

(d) 89.996 msec

(e) 159 msec Fig. 7 Behaviors of concrete column at incremental simulation time.

76


Rectangular

Circular

Fig. 10 Impact resistant effective area comparison (unit: 2 mm, mm ).

Fig. 8 Sectional displacement-time history.

Fig. 9 Maximal displacement distribution of column height.

lateral displacement was approximately 138 mm, which is equivalent to moderate damage in the ASCE classifications. Generally, for earthquake-loaded columns, circular columns perform better than square columns due to the confining effect of the core concrete. However, for the impact-loaded column in this study, the square column performed better than the circular column due to its cross sectional characteristics. Because the impact behavior of RC columns is a very complicated problem due to the coupling effect of impact load and structural response, there are several possible reasons for this phenomenon. (Wilbeck 1978). One is shape induced effective impact resistant cross-section area of the impacted column. Another is variation in contact condition at vehicle-structure interfaces. In order to simplify the complex impact behavior of RC columns, an effective impact surface area was calculated for the square and cir-

cular column under a head-on impact condition. This simple calculation clearly showed that the vehicle impact contact surface of a square column with flat side was much larger than the curved surface of a circular column as shown in Fig. 10. Assuming that a quarter of the column depth is impacted, the effective areas of the square and circular columns are 3.6 × 105 mm2 and 2.21 × 105 mm2, respectively, showing that the effective impact-resisting area of the square column is 1.63-fold larger than that of the circular column. Also, if the maximum displacements obtained from the head-on collisions with the columns are normalized with respect to the total cross-sectional areas and the second moment of inertia, the normalized maximum displacements of the circular column were still 1.46- and 1.42-fold larger than those of the square column, respectively, validating the hypothesis and impact displacement behavioral trend. However, the actual coupling mechanism will have to be studied in future research to precisely understand the phenomenon. The von Mises stress profile results for the front, right, and rear faces of the circular column at the initial impact loaded time of t=36 msec and the maximum displacement time of t=93 msec are shown in Fig. 11. The maximum von Mises stresses occurred at the lower back corner of the column (Fig. 11). This type of displacement can be considered as plastic hinge behavior with the maximal rotation occurring at this location, which is a logical failure behavior for an impacted column. 4.1.2 Impact angle The varied impact angle analysis for the circular and square columns was conducted on AVC and ARS-R specimens, respectively. The vehicle collision angles to the column considered with the square column were 30°, 45°, 60°, 75°, and 90°, with 90° representing a head-on collision of the front face as shown in Figs. 6(a) and 6(b), respectively. The impact angle was varied to estimate the impact area and damage level of the cross section. The results from the varied impact angle simulation of the AVC specimens indicated that when the impact angle increased, the maximum lateral displacement and the column base rotation increased along with the stirrup spacing. The ARS-R results indicated that when the impact angle increased, the maximum lateral displacement and column base rotation decreased. The

77


Maximum stress

(a) Front, t=36 msec

(b) Rear, t=36 msec

(c) Right, t=93.0 msec

(d) Rear t=93.0 msec

Fig. 11 Distribution of von Mises stress on circular column.

largest impact load and surface area occurred when the impact angle for ARS-R decreased rather than when the impact angle for AVC or IS level increased. Therefore, when calculating the IS level, one should consider both the angle and impact surface area. 4.1.3 Axial load ratio The axial load ratio analysis was carried out on RC columns with different concrete compressive strengths while applying a constant axial load and while varying lateral reinforcement spacing. As shown in the UAL18CS analytical results in Table 7, when the lateral reinforcement ratio decreased or spacing increased, the column experienced greater damage. However, as the axial load ratio decreased or the compressive strength increased, the impact behavior of the column became random and no clear trend was found. These random results could be explained in two ways: 1) as the axial load ratio decreased, an optimal lateral reinforcement ratio and spacing gave the best or largest confinement effect to the column, which resulted in less damage to the column, as also observed in UALR 68-CS specimens; 2) the flexure tendency from impact loading is much larger than the resisting flexure moment from the axial load, even though the axial load ratio decreased with increasing compressive strength. Therefore, in designing an RC column for impact loading, the relationship between the axial load ratio and stirrup spacing or lateral reinforcement ratio has to be considered to obtain the optimal design. 4.1.4 Longitudinal to lateral reinforcement ratios For both VLS-US and VCS-US specimens, the ratio of longitudinal to lateral reinforcement was kept constant while the longitudinal reinforcement area or lateral reinforcement ratio was varied. When the longitudinal reinforcement’s cross-sectional area decreased or the lateral reinforcement ratio decreased, the damage to the column increased as shown in the VLS-US simulation results. When the lateral reinforcement ratio was kept

constant by changing the lateral reinforcement’s cross sectional area and compressive strength, no clear trend was found, as shown in the VCS-US simulation results. 4.1.5 Column slenderness The column slenderness was varied by changing the total height of the column and its boundary conditions, which changed the effective buckling length coefficient k. In the L-SR-C analysis, the impact load was applied at a constant height from the base of the column. Even though the slenderness ratio or the column height increased, the maximum lateral displacement decreased due to its heavier self-weight where the self-weight load of a taller column was larger than its buckling load. To consider the effect of buckling length coefficient k on structural behavior, the boundary conditions of the analytical model were varied as shown in the CEL-SR results. When k or the slenderness ratio increased, the damage to the structure also increased. In particular, when the slenderness ratio equaled 11 (e.g., k=1.0), a larger lateral displacement occurred due to rotation constraint at the base of the column. 4.2 Accuracy of analysis results The accuracy of the numerical analysis results was confirmed by conservation of energy: the total kinetic en-

Fig. 12 Energy results from the analysis model.


ergy produced by a vehicle has to be equivalently transformed into the residual kinetic energy, friction energy loss, internal energy of the deforming vehicle and column components, and hourglass energy consumed by the hourglass algorithm for finite elements with reduced integration formulations. Energy has to be conserved during numerical analysis to indicate that numerical problems are not rampant. In some initial simulations, hourglass energy can be used as an indicator for accuracy of a numerical analysis using the hourglass energy ratio to total energy (El-Tawil et al. 2005). In an impact simulation, the kinetic, internal, and hourglass energy relationship is the most important. If kinetic energy is transformed into excessive hourglass energy, the simulation result is inaccurate. Therefore, a sufficiently small hourglass energy value is a necessary condition to con-

(a) Crash angle (circular)

(c) Stirrup spacing to axial force ratio (circular)

(e) Stirrup spacing to main steel bar area (circular)

78

sider when examining the accuracy of simulation results. In this study, the accuracy of the collision simulation results was determined based on the concrete column behavior with the given hourglass energy value. As shown in Fig. 12, at the peak impact loading point of 80 msec, the hourglass energy ratio is 3.37%, which is low based on an hourglass energy ratio of 15.2% at impact time. Based on the reports of El-Tawil et al. (2005) and Zaouk et al. (1996), an hourglass energy ratio of 17% is acceptable in a valid simulation of a head-on collision exercise. Therefore, the results of this analysis can be considered reasonable given that the hourglass energy ratio at the peak impact loading point is extremely small, and that the maximum hourglass energy value at the end of the simulation is not excessively large.

(b) Crash angle (square)

(d) Stirrup spacing to same axial force ratio (square)

(f) Stirrup spacing to main steel bar area (square)


(g) Stirrup spacing to slenderness ratio due to height of column (circular)

(i) Stirrup spacing to confining steel ration due to effective length factor of buckling (circular)

(k) Effective length factor of buckling (circular)

79

(h) Height of column (circular)

(j) Stirrup spacing to confining steel ration due to effective length factor of buckling (square)

(l) Effective length factor of buckling (square)

Fig. 13 Damage satisfaction curves.

4.3 Resistance capacity evaluation based on performance satisfaction Using the analytical results obtained from the column impact analysis, performance satisfaction was evaluated. Based on the performance evaluation proposal in this study, initial design and maintenance of structural hazard mitigation or prevention can be effectively performed. To quantify the impact performance evaluation, satisfaction curves (SCs) are based on ASCE-defined damage criteria (Table 1) (ASCE 1997, 1999). The support rotation angle in the numerical simulation was measured from the bottom point, maximum displacement point, and top point of the column opposite to the impact. Using the SCs, impact damage levels can be determined based on the calculated base rotation results

(ASCE 1997, 1999). The distribution of the probability of resistance ranging from 0 to 1 (0 = perfect failure, 1 = perfect safety) is shown in Fig. 13. Impact damage characterizing SCs was developed for the various parametric study results obtained from the column impact analyses. Depending on the damage criterion, the curves had different shapes with data ranging between 0 and 1. However, if a curve for a damage criterion was calculated to be 0 or 1 throughout the parameter range (x-axis), it was not included in Fig. 13. The SCs developed for the impact angle using the ASCE’s base rotation criterion for moderate damage are shown in Figs. 13(a) and 13(b). The probability of resistance decreased as the impact angle increased. These


SCs showed that the criteria used for the curve development dictated a damage trend, which engineers and designers can define as an RC column’s impact resistance capacity. The SCs for the square column with a 45° impact angle for low, light, and moderate damage criteria (Fig. 13(b)) show very different trends because the impact area increased as the impact angle of the vehicle increased, causing greater damage to the column. The SCs for the lateral reinforcement ratio using the ASCE base rotation criterion for moderate damage are shown in Figs. 13(c) and 13(d). Different stirrup spacing caused different types of damage to the column. Also, the behavior trend changed with the damage criterion selected for evaluation. However, in general, the circular column sustained more damage than the square column. The SCs for a constant longitudinal to lateral reinforcement ratio while changing the longitudinal cross sectional area are shown in Figs. 13(e) and 13(f). When the longitudinal reinforcement area is reduced to decrease the longitudinal reinforcement ratio, the square column had less deformation than the circular column. These results show that the longitudinal reinforcement’s cross sectional area has a stronger effect on the damage level of the circular column than of the square column. When the height of the column increased, more damage was observed, as shown in Figs. 13(g) and 13(h). Also, more damage was observed in the column using the severe damage criterion than the medium damage criterion due to the buckling effect. The SCs for slenderness ratio with varying boundary conditions, which changed the effective buckling length coefficient k, are shown in Figs. 13(i), 13(j), 13(k), and 13(l). As k increased and exceeded 1.0, more damage was observed in the column using the medium damage criterion than the light damage criterion. Therefore, column design using various k and heights should be considered with respect to slenderness ratio and the buckling effect.

5. Conclusions This study proposes a new performance-based damage assessment method for RC columns under vehicle impact loading. The conclusions from the study are as follows. (1) RC columns’ structural behavior under a truck impact load can be simulated using an explicit FEA program such as LS-DYNA. The parameters used for the evaluation were cross-sectional shape, impact load angle, axial load magnitude and ratio, concrete compressive strength, longitudinal and lateral reinforcement ratios, and slenderness ratio. (2) The calculated maximum displacements of the circular and square RC columns are 133 mm and 71 mm, respectively, from impact with an 8-ton truck traveling at 100 km/h. The circular and square columns thus sustained severe and moderate damage levels, respectively, based on the ASCE-defined

80

classification. (3) The analysis results were converted into structural resistance capacity probabilities using a probabilistic approach and the ASCE (1997, 1999) design criteria. Using the newly proposed performance-based damage assessment and resistance capacity evaluation procedure for RC columns that sustained a vehicle impact, Satisfaction Curves describing the columns’ impact failure probability for defined failure criteria were developed. (4) Using satisfaction curves from the parametric study, damage assessment of the RC columns evaluated their probabilistic impact resistance capacity and that information can be incorporated into RC column design schemes. (5) The accuracy of the numerical analysis results was confirmed by the principle of conservation of energy using the hourglass energy ratio to total energy. Generally, the accuracy check of the analytical results using this approach is considered reasonable. However, in order to better confirm the accuracy of the simulation results, the results must be verified using compatible test results. Acknowledgements This study was supported in part by a National Research Foundation of Korea (NRF) grant by the Ministry of Education, Science, and Technology (No. 20110014752). This work was also supported in part by an NRF grant from the Korean government (MSIP) (No. 2011-0030040). References ASCE, (1997). “Design of blast resistant buildings in petrochemical facilities.” Task committee report on blast resistant design of the Petrochemical Committee of ASCE.” New York: American Society of Civil Engineers. ASCE, (1999). “ASCE structural design for physical security: state of the practice report.” Task Committee on Physical Security, New York: American Society of Civil Engineers. Consolazio, G. R. and Cowan, D. R., (2005). “Numerically efficient dynamic analysis of barge collisions with bridge piers.” Journal of Structural Engineering, 131(8), 1256-1266. El-Tawil, S., Severino, E. and Fonseca, P., (2005). “Vehicle collision with bridge piers.” Journal of Bridge Engineering, 10(3), 345-353. Englekirk, R. E., (2005). “The impact of prescriptive provisions on the design of high-rise buildings.” Structural Design Tall Special Buildings, 14(5), 455464. Ferrer, B., Ivorra, S., Segovia, E. and Irles, R., (2010). “Tridimensional modelization of the impact of a vehicle against a metallic parking column at a low speed.” Engineering Structure, 32(8), 1986-1992. Fradis, M. N., (2004). “Current development and future


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