Abstract submission guidelines for the Conference on ...

Transactions, SMiRT-23 Manchester, United Kingdom - August 10-14, 2015 Division VII

Missile Impact on Reinforced Concrete Barrier Slab Using Various Failures Models Mrigendra Nath Ray1 ,Thiru Venkata Babuji2 1 2

Consultant (Nuclear) ,Larsen&Toubro Technology Services ,Vadodara, India Executive Engineer, Larsen&Toubro Technology Services ,Vadodara, India.

ABSTRACT This paper aims at examining the effect of Impact of a Steel semi rigid Missile on Concrete Barrier which resembles the Safety cover on important safety systems in a Nuclear Plant. In general, rigid missiles are ejecting out of various rotating machinery, high pressure valves installed in plant working area. Though these missiles eject on an angular path but for simplicity we will consider that these will hit the barrier at perpendicular to the plane of the barrier. Reinforced Concrete had been used as barrier considering its structural stiffness and ductility for absorbing Impact Energy. Two different concrete barriers will be modelled in Finite Element Programme ABAQUS vers6.12 in explicit domain with reinforcement and without reinforcement and critical depth of barrier will be assessed based on the computer stress output on the impact zone based on two failure models ,Brittle cracking Model and Concrete Damaged Plasticity Model. In addition, Empirical formulae will be used to verify Finite Element Results. INTRODUCTION Reinforced concrete had become an excellent material for barrier against missile hit..The Missile in this paper is limited to missile made of carbon steel element cylindrical in shape and Hitting the target with a very high velocity. This paper examines the material behaviour of plain and reinforced concrete barrier with and without reinforcement. Computer programme ABAQUS vers6.12 is used to model the problem in explicit domain for two different failure model of concrete Namely Brittle Cracking model and Concrete Damage Plasticity model. Physics of Stress Strain Behaviour of Reinforced Concrete Two main failure mechanisms of concrete are Crushing of Concrete due to Compression and Cracking under Tension. Here in this paper we presume only Uniaxial State of Stress for Concrete as it matches the main theme of study that is Impact of Missile on Concrete.

Fig-1 :Compressive Stress-Strain Relationship for ABAQUS

23rd Conference on Structural Mechanics in Reactor Technology Manchester, United Kingdom - August 10-14, 2015 Division VII

Fig-2: Tensile Stress-Strain Diagram for Concrete The Compressive Stress Strain Diagram in Fig-1 has two zones namely Elastic zone which is assumed to

σ

be in the range of 0 to 0.5σcu in the ascending curve and Inelastic Zone from 0.5 cu in the ascending curve to 0.3σcu in the descending curve where σcu is the characteristic strength (maximum cube strength) of concrete in a compression test. Fig-1 is developed by Hsu and Hsu in 1994 [1] after carrying out laboratory tests and verified with numerical results. To define Stress Strain relationship in Compression zone we have to input Compressive stress σc and corresponding inelastic strain εin by deducting elastic strain εel from the total strain εc marked in Fig-1 .In addition, a parameter dc which is designated as damage parameter in compression and is calculated as equal to the ratio of inelastic strain /total strain. Here the total strain is obtained from the graph and elastic strain is calculated by the ratio of Compressive stress σc and Initial tangent Modulus of Concrete EO. Similar exercise is done for processing the Tensile Stress Strain Data plotted in fig-2 in which fct is max tensile stress obtained in a tensile test of concrete and corresponding strain is designated as total strain εt. Now input for Tensile stress behaviour and Tensile damage is similarly to be derived from the Test data and a parameter Tensile Cracking Strain εck is calculated as the difference between total tensile strain εt. Minus elastic tensile strain εet for the undamaged concrete. Similarly tensile damage parameter is calculated as ratio of cracking strain by total tensile strain. For all the cases of parametric study, we have used Concrete Grade M50 as per Indian Standard for Plain & Reinforced Concrete IS 456-2000 [3]. As regards Stress Strain profile of Steel used in this paper, we have used only one type of Carbon Steel Material of Grade ASTM Grade A36. Stress strain data used in the analysis.

The Best option would be to generate lab test data for Concrete as well as Steel but as our principal aim in this paper is to analyze Impact of Missile on Concrete Barrier, therefore data for both Concrete and Steel was taken from literature [2] mostly from Research paper. Effort was made to generate Stress Strain data for Concrete in Uniaxial Compression and Tension using approach by Hsu and Hsu(1994) [1].


Brittle Cracking Model For Concrete. B.C Model is considered for applications in which the behaviour of concrete is dominated by Tensile cracking. It is most accurate in applications where brittle behaviour dominates such that the assumptions, that the material is linear elastic in compression, is adequate. It is generally accepted that Concrete exhibits two primary modes of behaviour, A brittle mode in which micro cracks gradually transforms to macro crack with highly localised deformation And A ductile mode where micro cracks develops uniformly through the specimen leading to Non localised deformation. This model allows removal of material based on brittle failure criteria. Concrete Damaged Plasticity Model

The concrete damaged plasticity model is primarily intended to provide a general capability for the analysis of concrete structures under cyclic and/or dynamic loading. The model is also suitable for the analysis of other quasi-brittle materials, such as rock, mortar and ceramics; but it is the behavior of concrete that is used in this model to motivate different aspects of the constitutive theory. Under low confining pressures, concrete behaves in a brittle manner; the main failure mechanisms are cracking in tension and crushing in compression. The brittle behavior of concrete disappears when the confining pressure is sufficiently large to prevent crack propagation. In these circumstances failure is driven by the consolidation and collapse of the concrete micro porous microstructure, leading to a macroscopic response that resembles that of a ductile material with work hardening. Modeling the behavior of concrete under large hydrostatic pressures is out of the scope of the plastic-damage model considered here. The constitutive theory in this section aims to capture the effects of irreversible damage associated with the failure mechanisms that occur in concrete and other quasi-brittle materials under fairly low confining pressures (less than four or five times the ultimate compressive stress in uniaxial compression loading). These effects manifest themselves in the following macroscopic properties: Different yield strengths in tension and compression, with the initial yield stress in compression being a factor of 10 or higher than the initial yield stress in tension; Softening behavior in tension as opposed to initial hardening followed by softening in compression; Different degradation of the elastic stiffness in tension and compression; Stiffness recovery effects during cyclic loading. DESCRIPTION OF THE PROBLEM DISCUSSED IN THIS PAPER.

Case-1: Brittle Shear Crack failure Mode. Case-1(a) Plain Concrete Plate Impacted By Steel Cylinder shaped Missile. To understand the effect of Impact on Concrete Barrier, we have taken a simple square plate of size 5 meter made of Plain concrete of thickness 20 cm and a Carbon steel solid cylinder of length 0.5 meter and diameter 0.4 meter as shown in fig-3.The Concrete Plate was fixed at the 4 edges. Now this steel cylinder is made of Carbon steel with Modulus of Elasticity as 206Gpa and Poisons Ratio 0.3 , Grade of Concrete was M50 implying Max Characteristic Strength under compression as 50 Mpa. Both the parts were modeled in ABAQUS 6.12 in explicit domain In this model, Concrete Plate was having 400 Linear Hex elements C3D8R type and Steel Cylinder Having 135 Linear Hex element C3D8R.This plate was impacted by the steel cylinder having an Impact velocity 150m/sec considering damage model as Brittle Shear Crack Model . Though total time of Impact was input as 0.2 sec but we could see penetration of the plate in the first time step itself which was 0.02sec.Penetration was a clear Punching Shear Type as the Von Misses Stress on Concrete elements


away from the boundary of the impact zone was within allowable tensile stress of concrete of grade M50 which is 0.7√fck where fck =Characteristics strength on Concrete which is 50Mpa in this case. Case-1(b) Reinforeced Concrete Plate Impacted by Steel Cylinder shaped missile. In this case, all material parameter and the Geometry of the RC Plate excepting the thickness which is increased to 30cm and Steel Cylinder remains as same and the Impact velocity also is unchanged. But the number of Hex elements for Concrete M50 is increased to 59225 and the same for Rebar ASTM A36 is counted as 18250 whereas total number of element for Steel Missile ASTM A-36 is increased to 47300.These differences are caused due to placement of Rebar of diameter 20mm at mid depth at regular interval of 40mm center to center. While defining contact of Steel Missile with Concrete and Steel Rebar Surface to surface contact was considered between missile and concrete and between rebar and concrete. Fig-3 ,4 and 5 shows the screenshots of Von Misses Stress contours of Brittle Shear Crack Model on Reinforced Concrete Plate. Total time of impact was considered as 5 millisecond.

Fig-3. Brittle Shear Crack Model on UnReinforced Concrete Plate

Fig-4 Brittle Shear Crack Model on Reinforced Concrete Plate.


Fig-5 Von Mises Stress Mapping on Rebar for Brittle Cracking Model.

Fig-6 Concrete Damaged Plasticity Model on Reinforced Concrete Plate.


Fig-7 Von Mises Stress mapping on Rebar and Cylinder for Concrete Damaged Plasticity Model.

Fig-8 Von Mises Stress Mapping on elements just around depression for CDP Model without Rebar.


Case-2 .Concrete Damaged Plasticity(CDP) Model. Case-2(a) Plain Concrete Plate Impacted By Steel Cylinder shaped Missile. Here the plate geometry, Projectile are unchanged with some increase in total plate element from the Unreinforced Brittle Shear Model in case 1(a) .Total concrete element is now 867 and the same for Steel Missile is 170. Fig-8 shows the feature of the model taken as screen shot of the CDP Model without Rebar. Case 2(b) Reinforeced Concrete Plate Impacted by Steel Cylinder shaped missile. Here the plate geometry, Projectile are not changed so as to observe any changes in results in respect of total deformation and stresses in both Rebar and Concrete element and compare with that of Reinforced case of Brittle Crack Model in Case 1(b). Material data for Concrete and Steel remained same as M50 for concrete and ASTM A-36 for steel for both Rebar as well as Missile. Fig-6&7 shows the screenshots of Von Mises Stress Mapping for Concrete Plate and Steel Rebar.Total elements considered in this model compared to the model in case-1(b) is unchanged and is 59225 for concrete plate element ,18225 for rebar and 47300 for steel cylinder. ANALYSIS OF RESULTS BETWEEN CASES. It is principally justified if comparison is made between similar cases. In this paper authors have tried to compare results of Plain Concrete Target being hit by Steel missile for both the cases of Brittle Crack Model(BC) and Concrete Damaged Platicity Model(CDP).These are designated as Case 1(a) and Case2(a).Similarly Case1(b) and Case 2(b) are compared for B.C Model as well as CDP Model wherein Reinforced Concrete Plate is hit by Steel Missile. Case 1(a) and 2(a) Unreinforced BC model (case 1a) shows that under the effect of Impact, degradation of material starts in the impact zone and in close vicinity of contact area when strain in the concrete elements reaches beyond yield strain or precisely in ABAQUS terms cracking strain. But all elements outside these impact zone does not fail which is practically an indication of shear failure and so is name of this model designated in ABAQUS as Brittle Shear Crack Model. Degradation of Concrete Starts at 5 millisecond on case 1(a),Whereas as CDP Model (case 2a) does not show any material degradation but the plate deforms beyond elastic limit in the Impact zone and its vicinity. The Condition of front end of the Missile which remained in contact with Concrete is found to be gone to a state of yield at 5 millisecond. Case 1(b) and 2(b) Reinforced BC model ( case 2a) shows clear degradation of concrete and few Steel rebar in the impact zone completely bent down and stress mapping in these rebar show it had already accumulated Tensile stresses beyond yield. Time of Impact was limited to 5 millisecond .Here the entire Steel Missile has gone a state of yield. Concrete in the Impact zone and at support in some places have failed completely within this time of 5milisec. Whereas the Reinforced CDP Model in case 2(b) shows similar state of stresses only in the Impact zone and its vicinity where concrete and Rebar have failed completely and Steel rebar has bent down considerably but in different shape that of reinforced B.C Model. Lower part of the steel missile also gone into yield. EMPERICAL METHODS TO DESIGN CONCRETE BARRIER. We have taken the Empirical formulae for missile protection from General Design Criterion 4 of Appendix A to 10 CFR 50 which requires that structures systems and components important to safety be protected from the effects of missiles. Missile barriers and protective structures are designed to withstand and absorb missile impact loads to prevent damage to safety-related components. Formulae used for missile penetration calculations into steel or concrete barriers are from the National Defense Research Committee (NDRC) modified formula for concrete and for steel.


Concrete (Modified NDRC Formula) 𝑉 1.8 0.5 4KNWd X = --------------- (1a) for x/d 2.0 1000𝑑

(

[

(

) ]

)

Where X= Penetration Depth (in), K= Experimentally obtained material coefficient =180/√𝑓𝑐 fc =Concrete Compressive Strength in kips/sqinch N =Missile Shape factor =0.72 (min value) W = Missile Weight in lbs d = diameter of missile in inch V= Missile velocity in feet/sec. If we put all the values of our example cases in equation 1(a) considering x/d =8/16=0.5 , V= 150m/sec =150X3.28 ft/sec = 492ft/sec d =40cm =40/2.54 = 16 in fc =50 N/mm2 /0.006894 =7353psi ρ =7850kg/m3 =7850x2.28lbs/m3 K = 180/85.75= 2.1 W =( π/4)*(d)2 * L* ρ =(3.14*0.16*0.5*7850*2.28)/4 =1124 lbs X is Calculated as 14.16 Inch where as Our Plate Thickness in the example case is 8inch For Unreinforced Concrete And For Reinforced Plate Plate Thickness Assumed As 12 Inch.

From Empirical formula, calculated penetration depth with above missile data works out to be 14.16 inch. Scabbing Thickness ts and perforation thickness tp is given by the following equations

ts =d*[2.12+1.36(x/d)]

for 0.65