International Conference on“Structural Engineering &Construction Management” SECM-2016

Organized byDepartment of Civil Engineering MarAthanasius College of Engineering, Kothamangalam, Ernakulam, Kerala

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Int. J. Engg. Res. & Sci. & Tech. 2016 Athira Rajan et al., 2016

RESPONSE OF RCC SLAB SUBJECTED TO AIRBLAST LOADING

Behaviour of Reinforced Cement Concrete (RCC) members subjected to blast loading is atopic of crucial concern as they find application in the field of military engineering and industrialstructures. Blast loading on reinforced concrete structural elements lead to rapid ruination andcan result in catastrophe. This paper investigates the dynamic response of steel reinforcedconcrete slab subjected to blast loading, by employing the commercial hydrocode - AUTODYN.A three-dimensional (3D) numerical model is developed incorporating relevant concrete andsteel damage models, duly considering the strain rate effects. The developed numerical modelis calibrated with experimental results available in the literature. The obtained results can serveas a reference for blast resistance design of concrete slab elements.

Keywords: RCC, Blast loading, Hydrocode, Strain rate effect, Numerical model, Blast resistantdesign

INTRODUCTIONBlast analysis of structures is gaining attention inacademia and industry for the past few yearsowing to the recent terrorist attacks and industrialaccidents. Steel reinforced concrete is theprincipal construction material in nuclear powerplants as well as protective structures in militaryand space engineering. The risk of explosiveloads on reinforced concrete structures hasincreased the need to study the response ofconcrete structural components against blastloading so as to develop reliable design guidelines.1 Department of Civil Engineering, SCMS School of Engineering and Technology, Ernakulam 683582, India.2 Department of Civil Engineering, Mangalam College of Engineering, Ettumanoor 686631, India.3 Department of Civil Engineering, Indian Institute of Technology Madras, Chennai 600036, India.

Int. J. Engg. Res. & Sci. & Tech. 2016

ISSN 2319-5991 www.ijerst.comSpecial Issue, Vol. 3, No. 1, April 2016

International Conference on “Structural Engineering &Construction Management” SECM-2016

Organized by: Department of Civil Engineering Mar AthanasiusCollege of Engineering, Kothamangalam, Ernakulam, Kerala

© 2016 IJERST. All Rights Reserved

Research Paper

A few experimental studies on reinforcedconcrete slabs subjected to blast loads have beenreported, such as tests on singly reinforcedsquare concrete slabs with both ends fixedcondition conducted by Zhao and Chen (2013),explosive test on reinforced concrete one-waypanel done by Sun (2009) and blast loading trialson doubly reinforced concrete slab with two shortedges supported condition carried out byThiagarajan et al. (2015). In addition, blast loadtests were also attempted on singly reinforcedpavement panel by Luccioni and Luege (2006).

Jinju Jose C1, Athira Rajan2* and Bennet Kuriakose3

*Corresponding Author: Athira Rajan 11athiraa@gmail.com

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Int. J. Engg. Res. & Sci. & Tech. 2016 Athira Rajan et al., 2016

As full scale blast experimental tests aregenerally costly and time consuming, resortingto numerical simulation studies is advantageous.The high magnitude explosive loads acting in shortduration exhibit strong spatial as well as temporalvariations, thereby, leading to varying strain ratein the structural materials (Hao and Hao, 2014).To incur an accurate prediction of the nonlinearresponse of structures subjected to blast loading,sophisticated tools incorporating the explicitdynamics of solids, fluids and their interactionneed to be used. These software tools are oftenidentif ied as ‘hydrocodes’, among whichAUTODYN (2007) and LS-DYNA are mostpopular. So far, several researchers haveattempted numerical analysis of concretestructures subjected to blast loading employingthese hydrocodes. Zhao and Chen (2013) studiedthe damage mechanism of the reinforcedconcrete square slab subjected to air blast loadsusing LS-DYNA. Nyström and Gylltoft (2001)employed AUTODYN to simulate the responseof reinforced concrete wall strip subjected to bothblast and fragment loading. Zhou et al. (2008)contemplated a dynamic plastic damage modelfor idealising concrete in AUTODYN, so as toanalyse the response of an ordinary steelreinforced concrete slab and a high strength steelfibre reinforced slab. Exercising LS-DYNA, anumerical model for the blast analysis ofreinforced concrete slabs was developed by Linet al. (2014) accounting the strain rate effects onconcrete in tension and compression separately.Thiagarajan et al. (2015) performed a numericalstudy on the behaviour of both high strengthconcrete and normal strength concrete slabs,doubly reinforced with conventional and highstrength steel bars subjected to explosive loadsusing LS-DYNA. After conducting a numericalsimulation study on a reinforced concrete slab

subjugated to explosive loads, Tai et al. (2011)found that the damage pattern of the slab dependson the percentage of reinforcement.Investigations on long carbon fibre reinforcedconcrete panels subjected to air blast loading wasperformed by Tabatabaei et al. (2013), employingLS-DYNA. Using AUTODYN, research on steelfibre reinforced cementitious composite panelswith high velocity impact loading was exercisedby Prakash et al. (2015).

Although the aforementioned studies provideplentiful results and insights on the behaviour ofreinforced concrete slabs subjected to explosiveloading, more perceptiveness into the problem isrequired as a result of its complexity. In this paper,the popular package AUTODYN is employed forthe finite element modelling and nonlinear explicitdynamic analysis of RCC slab panel. Advancedplasticity models for steel and concrete areincorporated in the numerical model, consideringthe dynamic strain rate effects due to shortduration impulsive loads. The developed modelis validated by comparing with the test dataavailable in the literature. The results can furtherbe employed to develop guidelines for designingreinforced concrete slabs with adequateresistance against explosive loadings.

MATERIAL PROPERTIESAND FORMULATIONThe present numerical formulation employs theRHT concrete constitutive model developed byRiedel et al. (1999), which is an advancedplasticity model for brittle materials. The RHTmodel is a combined plasticity and shear damagemodel and in this, the deviatoric stress is limitedby a generalised failure surface, which is afunction of pressure, equivalent stress, lode angleand equivalent strain rate as (Zhou et al., 2008):

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Int. J. Engg. Res. & Sci. & Tech. 2016 Athira Rajan et al., 2016

3( , , , ) ( ) ( ) ( ) ( )eq eqP P P R

...(1)

where, eq is the equivalent stress, ( )P is thepressure dependent curved meridian of triaxialcompression, ( )P is the dimensionless capfunction, 3R is the third invariant dependence termand ( ) is a rate dependant enhancement factor..This failure surface can be used to representpressure hardening, strain hardening, strain ratehardening in tension and compression, thirdinvariant dependence for compressive and tensilemeridians, strain softening (shear induceddamage) and coupling of damage due to porouscollapse of the materials.

The steel in the present numerical formulationcomplies with JC steel model, developed byJohnson and Cook (1983). The JC modelrepresents the strength behaviour of materialssubjected to large strains, high strain rates andhigh temperatures. In the JC model, the yieldstress varies according to strain, strain rate aswell as temperature. The model defines the yieldstress y as,

( ) (1 ln ) (1 )n my p p HA B C T ...(2)

where, p is the effective plastic strain, p is thenormalised effective plastic strain rate, whereas,A, B, C, n and m are material constants. HT isthe homologous temperature depending on theroom temperature ( roomT ) and meltingtemperature ( meltT ) and is given by

( ) / ( )H room melt roomT T T T T ...(3)

An equation of state (EOS) is the relationbetween the state variables in the problemdomain. In the present study, concrete is assumedto be a homogenous porous material and ismodelled according to P- EOS Hao et al. (2014).The compaction parameter is defined as the ratio

of specific volume of the porous material to thespecific volume of the material in the solid state atthe same pressure and temperature. Thisvariablerepresents the volumetric stiffness of theporous material between the initial compactionpressure and the fully compacted pressure, andis given as Zhou et al. (2008).

1 ( 1)n

sp

s e

p p

p p

...(4)

where, p is the value of at the initial plasticyielding, p is the current pressure and n is thecompaction exponent. The reader may refer tothe following references for detailed descriptionon the material models and EOS: Zhou et al.(2008), Hao and Hao (2014), and Lin et al. (2014).

In the present finite element model, 8-nodedbrick elements are used to discretise theconcrete, air and explosive parts of the problemdomain. A 2-noded beam element were utilisedto model the steel rebars. A Lagrangianformulation in which the elements are free todeform without any material transportationbetween them is considered to be associatedwith concrete and steel. The air and explosiveare enforced with Eulerian formulation that allowsfor multi-material flow (Fairlie, 1998). An interactionbetween the Euler and Lagrange elements areallowed for the transfer of energy at the interfaces.

NUMERICAL EXAMPLEThe developed numerical procedure is employedfor computer simulation of an experimental studyconducted by Sun (2009). The problem concernswith a reinforced concrete slab of dimensions1300 mm × 1000 mm × 120 mm, simplysupported on two short edges, as schematisedin Figure 1. The slab is reinforced at both top andbottom, with 10 mm steel bars at spacings

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Int. J. Engg. Res. & Sci. & Tech. 2016 Athira Rajan et al., 2016

The predicted reflected overpressure historyat the midspan of the slab is compared with theresult reported in the literature as shown in Figure3, and is found to be in good agreement. Themaximum deflection at the midspan of the slabis observed to be 51.12 mm which is alsocompared with the results of experimental andnumerical studies available and is presented inTable 2, which is in turn found to be in excellentconcordance. The deflection time history of theRCC slab at the midspan is depicted in Figure 4.

Figure 1: Geometry of the Reinforced Concrete Slab

100 mm and 200 mm centre to centre inlongitudinal and transverse directions,respectively. The compressive strength andYoung’s modulus of concrete are 48 MPa and 48GPa, respectively. The yield strength of steelreinforcement is considered to be 560 MPa,whereas, the Young’s modulus is 230 GPa. Anequivalent spherical charge weight of 2.09 kg ofTNT is used as explosive at a stand-off distanceof 600 mm from the surface of the slab.

In the present numerical model, the slab isdiscretised using 10 mm elements whereas theair is meshed with 5 mm elements. The materialproperties and EOS parameters considered aregiven in Table 1. Taking advantage of thesymmetry, quarter portion of the domain alone isconsidered in the numerical model.

The dynamic solution of the numerical modelupto 25 ms is performed using explicit timeintegration scheme available in AUTODYN. As theexplicit methodology is conditionally stable, timestep was calculated using the Courant-Friedrich-Levy criterion with a safety factor of 0.6667. Figure2 presents the status of explosion at 0.16 ms inthe computer simulation.

Figure 2: Numerical Simulation of Air BlastProcess

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Int. J. Engg. Res. & Sci. & Tech. 2016 Athira Rajan et al., 2016

EOS P -a

Reference densit y 2 .4 g/cm 3

Bulk m odulus 3 .527e7 kP a

St rengt h RHT concret e

Shear m odulus 1 .9e7 kP a

Com pressive st rengt h 4 .8e4 kP a

Failure RHT concret e

Dam age const an t , D1 0.04

Dam age const an t , D2 1

T ensile failure P rincipal st ress

P rincipal t ensile failure st ress 4 .8e3 kP a

Fract ure energy 100 J/m 2

Erosion Geom et ric st rain

Erosion St rain 0 .0035

EOS Linear

Reference densit y 7 .85 g/cm 3

Bulk m odulus 1 .59e8 kP a

St rengt h JC St eel

Shear m odulus 8e7 kP a

Yield st ress 5 .6e5 kP a

Failure P rincipal st ress

P rincipal t ensile failure st ress 5 .6e5 kP a

Reference densit y of air 0 .001225 g/cm 3

EOS for air Ideal gas

Gam m a 1.4

Reference densit y of T NT 1.63 g/cm 3

EOS for T NT JW L

C on cre te Param e te rs

S te e l Param e te rs

Ai r an d TNT Param e te rs

Table 1: Material Parameters

The numerically simulated damage profile of theconcrete slab, 25 ms after the detonation of theexplosive is shown in Figure 5.

Table 2: Maximum Deflection at Midspanof the Slab

StudyMaximum

Deflection (mm)%

Variation

Experimental study(Sun, 2009)

50 2.2

LS-DYNA model(Lin et al ., 2014)

53.9 5.44

AUTODYN model(present)

51.12 -

Figure 4: Deflection History at the Midspanof the Slab

Figure 5: Damage Profile of the Slab

Figure 3: Reflected Overpressure Historyat the Midspan of the Slab

Lin et al. (2014)

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Int. J. Engg. Res. & Sci. & Tech. 2016 Athira Rajan et al., 2016

CONCLUSIONA numerical model is developed in AUTODYN tocharacterise the effect of high explosivedetonation on reinforced concrete slab in thisarticle. Nonlinear material models incorporatingthe dynamic strain rate effects were consideredseparately for the concrete and the steel. Theproposed finite element model is demonstratedto be effective for blast analysis of RCC slabsand has been validated. The numerical model canbe further modified by incorporating thedebonding and slip of the reinforcement so as tobetter accord the reality. The proposedmethodology can effectively be utilised fordeveloping design criteria for reinforced concreteelements subjected to air blast loads.

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Version 11.0, Concord (CA, USA) CenturyDynamics, p. 528.

2. Fairlie G E (1998), “The NumericalSimulation of High Explosives UsingAUTODYN-2D&3D”, Explo’98, Institute ofExplosive Engineers 4 th BiannualSymposium, pp. 1-13.

3. Hao Y and Hao H (2014), “Influence of theConcrete DIF Model on the NumericalPredictions of RC Wall Responses to BlastLoadings”, J. Struct. Eng., Vol. 73, pp. 24-38.

4. Johnson G R and Cook W H (1983), “AConstitutive Model and Data for MetalsSubjected to Large Strains, High StrainRates and High Temperatures”, Proceedingsof the 7th International Symposium onBallistics, pp. 541-548.

5. Lin X, Zhang Y X and Hazell P J (2014),“Modelling the Response of Reinforced

Concrete Panels Under Blast Loading”,Mater. and Design, Vol. 56, pp. 620-628.

6. LS-DYNA Livermore Software TechnologyCorporation, LS-DYNA Keyword User’sManual, Version 960, Livermore (CA).

7. Luccioni B M and Luege M (2006), “ConcretePavement Slab Under Blast Loads”, Int. J.Impact Eng., Vol. 32, pp. 1248-1266.

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9. Prakash A, Srinivasan S M and Rao A R M(2015), “Numerical Investigation on SteelFibre Reinforced Cementitious CompositePanels Subjected to High Velocity ImpactLoading”, Int. J. Mater. and Design, Vol. 83,pp. 164-175.

10. Riedel W, Thoma K, Hiermaier S andSchmolinske E (1999), “Penetrating ofReinforced Concrete by BETA-B-500Numerical Analysis Using a NewMacroscopic Concrete Model forHydrocodes”, Proceedings of NinthInternat ional Symposium of IEMS ,pp. 315-322, Berlin.

11. Sun W (2009), “Experimental Studies onReinforced Concrete (RC) Slabs Subjectedto Blast Loads”, J. Liaoning Tech. Univ. (NatSci), Vol. 28, pp. 217-220.

12. Tabatabaei Z S, Volz J S, Baird J, Gliha B Pand Keener D I (2013), “Experimental andNumerical Analyses of Long Carbon FiberReinforced Concrete Panels Exposed toBlast Loading”, Int. J. Impact Eng., Vol. 57,pp. 70-80.

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Int. J. Engg. Res. & Sci. & Tech. 2016 Athira Rajan et al., 2016

13. Tai Y S, Chu T L, Hu H T and Wu J Y (2011),“Dynamic Response of a ReinforcedConcrete Slab Subjected to Air Blast Load”,Theor. Appl. Fract. Mec., Vol. 56, pp.140-147.

14. Thiagarajan G, Kadambi A V, Robert S andJohnson C F (2015), “Experimental andFinite Element Analysis of Doubly ReinforcedConcrete Slabs Subjected to Blast Loads”,Int. J. Impact Eng., Vol. 75, pp. 162-173.

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