The behaviour Analysis of RC Frame Structure under Explosion Loading

Transcription

1 The behaviour Analysis of RC Frame Structure under Explosion Loading Marin LUPOAE Assoc. Prof. PhD Civil Eng. Military Technical Academy Bucharest, Romania Marin Lupoae, born 1970, received his mechanical degree from the Military Technical Academy, Bucharest, Romania Carmen BUCUR Professor. Phd. Civil Eng. Technical Univ. of Civil Eng. Bucharest, Romania Carmen Bucur, born 1951, received her civil engineering degree from the Technical Univ. of Civil Eng. Bucharest Romania Cătălin BACIU Lecturer PhD student Civil Eng. Military Technical Academy Bucharest, Romania Cătălin Baciu, born 1978, received his civil engineering degree from the Military Technical Academy. Summary Terrorist attacks with explosives are, after earthquakes, the most encountered extreme loadings that can produce the collapse of a structure. More over, it was observed that in terrorist attacks most deaths were caused due to the collapse of structures and not due to the shock waves or fragments projection. The latest of this paper in the study of reinforced concrete frame building behaviour under terrorist attack are: (i) the study of phenomena, as a whole, for terrorist attack (the detonation, the shock waves propagation, the plastic hinge occurrence, the failure of strong loaded elements, the initiation and the eventual propagation of collapse) and (ii) the approach of this item using a new numerical method applied element method. Keywords: explosion, collapse, progressive collapse, modeling, simulation, applied element method 1. Introduction During their lifetime, civil engineering structures could be subjected to natural hazards (earthquakes, hurricanes, tornadoes, floods and fires) or manmade hazards (blast and impact). Structures are not usually designed for extreme loadings and when such events occur can lead to catastrophic failure. In recent times, events such as earthquakes (Northridge , Kobe , and recent earthquakes of Haiti and Chile 2010) or terrorist attacks (1995 Murrah Federal building bombing and 2001 attack on the World Trade Center) have led to structural failures and collapse resulting in related loss of life and staggering economic loss. The particular local failure of Ronan Point building (London 1968) was called progressive collapse or disproportionate collapse regarding the initial cause. Therefore, extreme events such as blast and impact which were considered improbable in the past are now considered to be credible events, with a finite probability of occurrence. During last years structural design professionals have concerned about the description, definition schedule terms realisation, but they have especially tried to include in calculus this phenomenon with the many characteristics it can be. In order to mitigate the potential of progressive collapse the structures design mode demands another treatment as the conventional one. This has to focus on these events with low probability of occurrence, like what can be wrong/unanticipated/unhappened and after that to imagine scenarios able to perform an appropriate design process. The goals of this paper are represented by the study of the potential progressive collapse of a structure under blast loadings, using the applied element method. The object of study is a reinforced concrete structure with 4 bays, 2 spans and 6 floors.

2 2. The Applied Method short Element presentation In order to simulate the behavior of the structure under blast loadings the Applied Element Method was used, which combines features from finite element and discrete element methods. The main advantage of this method is that it can track the structural collapse behavior passing through all stages of the application of loads, elastic stage, crack initiation and propagation in tension-weak materials, reinforcement yielding, element separation, element collision (contact), and collision with the ground and with adjacent structures, [1, 2]. The structure is modeled as an assembly of small elements, of special shape and determined dimensions. These types of elements do not deform, the change of their position is as a rigid medium. AEM elements are connected using the elements entire surface, through a series of connecting springs that adopt all material type and properties. There is a single type of element. There are used cuboids to model the structure to be analyzed, fig. 1. Two elements are connected through a series of contact points. In every point three springs are attached: a normal spring and two shear springs. Each group of springs completely represents stresses and deformations of a certain volume and each element has six degree of freedom. There is no need for transition elements, it is allowed the partial element connectivity and the springs are generated at interface of elements. The global stiffness matrix [K], is determined as sum of contributions of all springs used to model the structure. The using of this modeling method allowed that the initiation and propagation of cracks and the failure of the structure can be studied using only one initial model. The location of failure is determined during the cycling process. d d 2 2 Normal and Shear springs d d a a a Volume represented by a pair of normal and shearing springs Separation strain a) The connectivity b) The separation Fig. 1: The connectivity and separation of the elements in AEM [3]. The Extreme Loadings of Structures (ELS) software use Applied Element Method to simulate progressive collapse of structures. Maekawa compression model is used to model the concrete under compression [3]. In this model, the initial Young's modulus, the fracture parameter, representing the extent of the internal damage of concrete and the compressive plastic strain are introduced to define the envelope for compressive stresses and compressive strains. Therefore unloading and reloading can be conveniently described. The tangent modulus is calculated according to the strain at the spring location. The model presented by Ristic et al is used for reinforcement springs [3]. The tangent stiffness of reinforcement is calculated based on the reinforcement spring strain, loading status (either loading or unloading) and the previous history of steel spring controlling the Bauschinger's effect. ELS software can perform the following types of analyses: (i) Linear Static Analysis; (ii) Non- Linear Static Analysis; (iii) Linear Dynamic Analysis and (iv) Non-Linear Dynamic Analysis. The software has two special options in order to simulate collapse events: (i) sudden removing of an element and (ii) demolition of an element by blasting.

3 3. Case study 3.1 The description of the structure A six storey reinforced concrete frame as show in the figure 2 was used as case study. This structure has 2 spans of 6 m and 4 bays (2 bays of 7 m at the extremity and 2 bays of 5 m in the middle). The first storey height is 4 m and all the other levels are 3 m high. Dimensions of the columns are 60x60 cm, the reinforcement is 4Ø25 mm on a side (represented a total reinforcement ratio of 1,9%). Dimensions of the perimeter beams are 25x55 cm and 30x70 cm for the central beams; the reinforcement ratio is nearly 2%. Thickness of the slab is 15 cm, with 0,5% reinforcement ratio. The elements dimensions and the amount of reinforcement correspond to the Bucharest seismic demand. The concrete compressive strength at 28 days is 30 MPa with elastic modulus E b = 32,5 GPa. The yield strength of reinforcement is 300 MPa with elastic modulus E a = 210 GPa. Fig. 2: The ELS model of the RC building The structure is subjected to a various types of loads: dead load (D) 1,5 kpa on every floor, live load (L) 2,50 kpa on every story except the top floor and snow load (S) 1,50 kpa on the top floor. The combination for the column removing cases: D 0,4( L S) (1) 3.2 The demolition scenario The instantaneous remove of the exterior columns of the structure was performed in accordance with GSA guidelines [4], figure 3: a column located at the corner of the building, a column located at the middle of the short side of the building and a column located at the middle of the long side of the building. Exterior Interior Fig. 3: Loss scenarios for columns complying with GSA 2003 In all three cases the loss of the columns happened instantaneous at time t = 0,025 s and this type of analysis combined with the constitutive material models for concrete and reinforced bars lead to a non linear dynamic analysis.

4 3.2.1 The instantaneous loss of the column located at the corner of the building The maximum vertical displacement of the joint located above the removed column was of about 1,62 cm, figure The instantaneous loss of the column located in the middle of the long side The maximum vertical displacement of the joint above the removed column is about 0,63 cm, figure 5. Vertical displacement (Oz axis), in cm Fig. 4: Displacements of joints above the removed column. Vertical displacement (Oz axis), in cm Fig. 5: Displacements of joints above the removed column The instantaneous loss of the column located in the middle of the short side The maximum vertical displacement of the joint above the removed column is about 1,35 cm, figure 6. The variation of vertical displacements curves of joints in second floor, above removed columns are shown in figure 7. After the variation curves of vertical displacements of the joints above removed columns were analyzed one can see that the oscillations of the structure are higher for the corner and for the short side columns than those for the column located on the long side of the structure. The maximum vertical displacements are comparable as order of magnitude to those measured by Sasani after removing two adjacent columns of the San Diego Hotel, which finally was demolished by controlled blasting [5]. Vertical displacement (Oz axis), in cm Fig. 6: The displacements of joints above column removed.

5 Z displacement,[cm] Corner column Long side column Short side column Blast scenario The modeling of blast action on structure using Extreme Loading for Structures software has some advantages: (i) calculation of the pressure resulting from the blast wave; (ii) the loading of the each element with the corresponding pressure, if there is a direct ray extending from the element face to the bombe source. At the same time it has minuses: (i) the free-field pressure wave models used by ELS does not take into consideration the reflection and refraction of pressure wave at the ground surface and surrounding elements and buildings; (ii) for small stand-off distance the implemented model does not take into account the explosion products effect. For small stand-off distance, the blast pressure is concentrated at the expected failed column. As a consequence, the effect of this pressure on the adjacent element is relatively small and is analogous with demolition scenario. For large stand-off distances the effect of blast pressure on the adjacent elements can be very significant. The energy of the blast load is weighted by the scaled distance: R Z (2) 3 w Time, [s] Fig. 7: Variation of the vertical displacements curves for joints in second floor, above removed columns. where: Z is the scaled distance, R is the stand-off distance and w is the charge weight. According to this relation is assumed that the energy transferred to certain targets of the same scale distance is identical. The energy delivered by 1000 kg TNT to a target at stand-off distance of 10 m is the same with the energy delivered by 8 kg TNT at a stand-off distance of 2 m, both having the same scaled 1/ 3 distance of1m /1kg. Using of an explosive charge of 2700 kg TNT, placed at 1,5 m high above the ground and at 10 m stand-off distance from the face of the corner column, will conduct to the separation and propulsion of a part of the column. The amount of explosive charge corresponds to a vehicle bomb attack and the 10 m stand-off distance was chosen in accordance with minimum defended stand-off distances in order to respect the medium ISC level of protection for reinforced concrete construction [6, 7]. The blast wave propagation from explosive charge is performed as a concentric wave, with center in explosive charge place, figure 8. As a result, almost all elements of the structure are loaded by the blast wave, each of them in a different proportion, depending on the position and the distance from the explosion source.

6 Fig. 8: The propagation and the action of the shock wave on structure. Fig. 9: The vertical displacement variation with time of the joint above the column removed. The analyze of the time-variation of the vertical displacement of the joint of the second floor above the removed column, figure 9 shows that in the first stage the structure is moving in the shock wave direction, because of the value of overpressure, and only after that the structure is moving down to the ground as the column is damaged and thrown, figure 10. The maximum value of the vertical displacement of the joint above column removed by the blast scenario is 22 times greater than in case when the column is removed using demolition scenario. The vertical displacement (Oz axis), in cm Fig. 10: The damage of the column under blast action. In case a 3000 kg explosive charge is detonated at 12 m stand-off distance from the face of the corner column and 1,5 m high above the ground, the structure is collapses due to the failure of certain vertical (columns) and horizontal (slabs and girders) bearing elements. The shock wave and the evolution of the damages are presented in figure 11.

7 Fig. 11: The shoch wave propagation, the damages and collpase evolution in case of the explosive charge increasing. 4. Conclusion The main goal of this paper is to study the starting and the development of a frame structure collapse, when the building is under blast loadings. The model was analyzed using Extreme Loading for Structures software, based on the Applied Element Method. Two scenarios were set up: (i) the demolition scenario to simply remove the columns, (ii) blast scenario to destroy the vertical elements. Using the option of column removal in demolition scenario, vertical displacements of the joints above removed column were obtained with values comparable to those in other papers in the domain literature. The geometrical configuration of the model and the reinforcement position allow the efforts redistribution of the appeared efforts so that to avoid the collapse. The most unfavorable case is the removal of the corner column, because of the small number of alternative ways to redistribute the efforts, in contrast with the other cases (removal of the column located in the middle of the short side of the building or of the column located in the middle of the long side of the building). The option of blast destruction for the vertical elements is closer to reality in case of the large stand-off distance (larger than the range of explosion products action), because the greater number of structural elements are affected and because of the free-field pressure wave models used by ELS. The analyze of vertical displacements of the joints above removed or blast destroyed columns showed that the maximum value of the displacement in case of blasted column is 22 times greater than if the column is removed using demolition scenario. There was also found that, for small stand-off distances, the pressure wave model does not take into consideration the action of the

8 explosion gases and also the reflection and refractions of pressure wave at the ground surface and surrounding elements and buildings. ACKNOWLEDGEMENT: The authors acknowledge the financial support of the PN II - CDI project code CNCSIS program IDEI, ID_8/ Progressive Collapse and the free use (Academic Licence) of the Extreme Loading for Structures software from Applied Science International LLC References [1] MEGURO K., TAGEL-DIN H. S., Applied Element Method Used for Large Displacement Structural Analysis, Journal of Natural Disaster Science, vol. 24, No 1, 2002, pp [2] TAGEL-DIN H., RAHMAN N. A., The Applied Element Method: The Ultimate Analysis of Progressive Collapse, Structure Magazine, No 4, April 2006, pp [3] *** ASI Extreme Loading for Structures - Technical Manual [4] *** U.S. General Service Administration (GSA 2003), Progressive collapse analysis and design guidelines for new federal office buildings and major modernization projects, Washington, D.C. [5] SASANI M., SAGIROGLU S., Progressive Collapse Resistance of Hotel San Diego, Journal of Structural Engineering march 2008, pp [6] *** Interagency Security Committee (ISC) (2004). ISC Security Design Criteria for New Federal Office Buildings and Major Modernization Projects, Washington, DC. [7] *** Office of the Deputy Prime Minister, The building regulations 2000, Part A, Schedule 1: A3, Disproportionate collapse, London (UK), 2004 [8] BALDRIGE S.M., HUMAY F.K., Preventing Progressive Collapse in Concrete Buildings, Concrete International, vol 25, no 11, nov 2005, pp [9] BUCUR. C,. BUCUR V., LUPOAE M., Simularea numerică a prăbuşirii progresive, a IXa Sesiuni de comunicări ştiinţifice SIMEC [10] ELVILA, MENDIS P., LAM N., NGO T., Progressive collapse analysis of RC frame subjected to blast loading, Australian Journal of Structural Engineering, Vol.7, No [11] IOANI A., CUCU L., MIRCEA C., Assessment of the potential for Progressive Collapse in RC frame, Ovidius University Annals Series, vol 1, no 9, may 2007 [12] IZZUDDIN B.A., VLASSIS A.G., ELGHAZOULI A.Y., NETHERCOT D.A., Progressive collapse of multi-storey due to suden column loss, Part I, Simplified assessment framework, Engineering Structures, vol 30, 2008, pp [13] LUPOAE M., BUCUR C., Building demolation Positive Aspect of Progressive Collapse MTA-Review Military Technical Academy Publishing House Vol XIX No. 4 December 2009 pp ISSN [14] *** ASCE Standard 7-05, Minimum Design Loads for Buildings and Other Structures (ASCE 7-05/ANSI A58) (2005), American Society of Civil Engineers, Reston, VA. [15] *** Unified Facilities Criteria (UFC 2005), Design of buildings to resist progressive collapse, Department of Defense, Washington, D.C.