Behavior of an impacted reinforced concrete slab: percussion and punching analysis

Transcription

1 Behavior of an impacted reinforced concrete slab: percussion and punching analysis P. Perrotin 1, F. Delhomme 1,2, M. Mommessin 1 & J.-P. Mougin 1 1 Laboratory Design Optimisation and Environmental Engineering (LOCIE-ESIGEC), RNVO, University of Savoy, France 2 Tonello I.C. Office, France Abstract This paper concerns the behavior of a reinforced concrete slab impacted by a block (velocity of about 25 m/s). Experimental campaigns have been led on a one third scale model of an actual structure. It appears that two damaging modes have to be considered: punching of the slab and bending. In this article, we focus on the punching effects. In order to propose a design method of a new concept of rock-shed (Structurally Dissipating Rock-shed), we determine the experimental value of contact time and percussion load. This strength is compared with the punching load of the slab calculated by an analytical model (Menétrey) and a standard code (Eurocode 2). Keywords: rock fall, rock-shed, reinforced concrete, impact load, punching. 1 Introduction The usual passive protection achieved in mountainous area to protect roads against rock falls consists of a slab covered with an embankment of ground (fig. 1). In this technique, the slab is calculated under static loading, the embankment playing the role of shock absorber. The new concept of rock-shed structure called Structurally Dissipating Rock-shed (SDR) designed by Tonello I.C. office [1] consists of a RC slab, without ground embankment, supported by specific supports (fig. 2). The advantages of SDR are the significant reduction of the deadweight, which leads to important saving in concrete and foundations. Due to the impact energy dissipated in the slab and supports, this kind of structure has to be calculated under dynamic loading.

2 420 Structures Under Shock and Impact VIII This paper presents the experiments led on a model of SDR and the theoretical approach to design such a structure. We focus in the percussion analysis and the determination of the impact load. 1 m 4.70 m 0.70 m 6 φ 25 / m 12 φ 32 / m m m E = 1800 kj E = 3360 kj Figure 1: Classical solution. Figure 2: SDR. 2 Experiments of a SDR model 2.1 Presentation of the model The tested structure is a 1/3 scale model of the rock-shed of Essariaux (Savoy - France). It consists of a horizontal slab of 4.8 m out of 12 m with 0.28 m thickness. It is built with a concrete of compressive strength of 35 MPa and is reinforced by a strong density of steel reinforcements (4300 kg of steel for 16 m 3 of concrete). The slab is supported by metal fuses which consist of a steel tube welded into two square plates; these fuses have an elasto-plastic behavior and a buckling load of about 260 kn. 2.2 Tests carried out In order to simulate rock impact, the model is impacted by a cubic reinforced concrete block. A block of about 450 kg is dropped at 15 m height to simulate a common impact loading (68 kj) and at 30 m height to replicate an exceptional impact loading (135 kj). We test also the structure with a block of 810 kg released at 37 m height (294 kj: destructive test of the slab). A total number of six tests have been achieved (3 on the unused slab and 3 after repairing). For the following analysis, we use the results of the last four tests: Test T3: an impact of 135 kj is realized on the unused slab in the central area; Test T4: an impact of 138 kj is carried out on the area which has been repaired after the test T3;

3 Structures Under Shock and Impact VIII 421 Test T5: an impact with an energy of 134 kj is realized on the area already shocked by a 68 kj test; Test T6: the area previously impacted by test T4 is subjected to an ultimate shock of 294 kj. 2.3 Instrumentation of the slab The slab has been tooled up with a set of sensors connected to a data acquisition station whose sampling rate is 7000 Hz (strain gauges on the lower and higher longitudinal reinforcements; strain gauges on the shear reinforcements; 9 LVDT displacement sensors under the slab; 7 accelerometers under the slab; 1 accelerometer on the impacting block; 5 load sensors regularly positioned under a line of supports). A high-speed camera (1000 fps) has been used to record the impact. 3 Dissipation of impact energy in a SDR The energy of a block impacting the slab is transferred by different effects: heat generation, cracking of the block and of the surface of the slab and actuation of the slab. The slab can be damaged by: the punching of the slab: a cone of concrete tends to be ejected [2], which creates tension stresses in the shear reinforcements. To determine if the reinforcements can resist to punching, it is necessary to know the evolution of the loading during the percussion and particularly the maximum impact load to which the slab is subjected; the plastic strain of the slab during its oscillation. An energetic approach is required to determine the maximum bending stresses in concrete and in reinforcements in order to check the correct design of the structure [3]. 4 Percussion analysis 4.1 Theoretical considerations The product of a force by an elementary contact time dt is called elementary impulse d τ. If the application time of the force ( F ) becomes small, the impulse (τ ) becomes a shock or a percussion [4]: t1 τ = F.dt with [t 0, t 1 ] very small. (1) t0 For a body of mass m going up from velocity v 1 to v 2, without external force, this percussion is equal to the variation of the momentum which it generates: τ = m.(v 2-v 1) τ in N.s (2) For an impact between a sphere and a plane, an elastoplastic model can be constructed assuming a constant contact pressure at the interface (fig. 3): an initial elastic compression (governed by Hertz law); an additional plastic

4 422 Structures Under Shock and Impact VIII deformation in a central region occurring at the constant pressure σ 0, surrounded by an elastic annulus; and a restitution process involving elastic recovery of the plastic zone [5]. Impact load F max experimental schematisation t c Time Figure 3: Theoretical signal shape. An elastic regime is not present in the case of the penetration of a plane surface by a conical or pyramidal indenter, as plastic flow is generated instantaneously [6]. By neglecting the initial elastic mode and the restitution, the impact load can be regarded as constant: F =S.σ (3) max 0 where σ 0 3.σ y (σ y = uniaxial compressive strength) and S = contact surface. On the basis of the eqn. (2) and supposing a constant mass of the block and the slab is motionless : m. i ( vi,2 vi,1) Fmax = (4) tc where v i,1 = impactor velocity before impact; v i,2 = impactor velocity after impact; m i = impactor mass; t c = contact time; F max = maximal impact load. The calculation of the maximum impact load can be summed up in the determination of impactor velocity and contact time. 4.2 Experimental analysis The determination of the impact load is carried out on tests T4, T5 and T6. The recordings of the following sensors are analysed: A high-speed camera records the block impacting the slab. The frames analysis allows to determine the velocity of the center of gravity (c.o.g.) of the block. For test T4 and T5, a LVDT displacement transducer is positioned under the slab at the vertical of the impact point. It records the vertical displacements of the slab. With this sensor, it is possible to know the slab velocity, by derivation of the displacements; For the test T4 and T6, an accelerometer is fixed on the impactor, to measure the vertical deceleration of the block during the shock. Due to the

5 Structures Under Shock and Impact VIII 423 break of the connection, we cannot measure the acceleration during the rebound. The analysis of the three tests [7] shows that the shock breaks down into the following steps (the contact is never plane to plane): 1. Time t 1 : the block touches the slab on a corner and it strongly decelerates. The slab begins to move. 2. Time t 2 : the block turns around the first impact point, its vertical deceleration becomes almost nil and the slab velocity decrease. After this time, we can suppose that the contact load between the block and the slab is near zero. The interval [t 1,t 2 ] corresponds to the first contact time. 3. Time t 3 : the whole face of the block touches the slab. The block decelerates and the slab velocity increases. A second percussion load is applied. 4. Time t 4 : the block begins to separate from the slab which has reached its maximum vertical displacement. The interval [t 3,t 4 ] corresponds to the second contact time. Block displacements c. o. g. (mm) ms v0 = m.s ms v1 = 4.3 m.s Block deceleration (g)600 Broken connection 0 0 t 1 t 2 10 t Figure 4: Diagrams of test T6. The figure 4 is an example of diagrams for the test T6. We can see the block deceleration during the first contact time and the variation of the velocity of the c.o.g. of the block during the shock. In using eqn. (4), the experimental impact loads of table 1 are obtained. The results of the test T4 are given for the second

6 424 Structures Under Shock and Impact VIII contact time. The block impact with a important angle and the second percussion load is most significant than the first one. The impact load of the test T3 is supposed to be equal to the one of the test T5 because the impact angles of the block and the impact energies are the same. Table 1: Impact loads. Tests Impact energy (kj) Velocity before impact (m.s -1 ) Velocity after impact (m.s -1 ) Contact time (ms) Impact load (MN) T ± ± ± ± 0.2 T5-T ± ± ± ± 0.2 T ± ± ± ± Punching of the slab 5.1 Bibliography It is very important to know the level of punching load, among other things, to design a slab under impact. The percussion analysis allows to estimate the value of this phenomenon. In the bibliography [8] [9], we can find the description of the kinematic of punching mechanism for a static loading: formation of a roughly circular crack around loading area on the tension surface of the slab and its subsequent propagation into the compression zone of concrete; formation of new flexural cracks; initiation of an inclined crack. With increasing loads the inclined crack develops towards the concrete and reaches the tension and compression reinforcements. At the final stage, the punching strength is expressed like the summation of each resisting vertical forces in concrete and in steel (shear and flexural). In this paper, only two approaches are used: an analytical model by Menétrey [10]: it is the main model [8] with takes in account the influence of the shear reinforcement; the EC2 [11] because it is the official European Code. 5.2 Analytical model by Menétrey This model is based on the summation of each resisting vertical forces: F pun = F ct + F dow + F sw (5) Where F ct is the vertical component of the concrete tensile force, F dow is the dowel contribution of flexural reinforcement, F sw is the shear reinforcement contribution [10].

7 Structures Under Shock and Impact VIII Eurocode 2 (EC2) Like Menétrey s model, the punching load [11], is obtained as a summation of a part of the punching shear capacity without shear reinforcement (concrete tensile force and dowel effect) and the contribution of the shear reinforcements. V Rd,cs = 0.75 V Rd,c + V s (6) Where V Rdc = v Rdc u.d u = length of the critical perimeter, d = mean effective slab depth, V s is the contribution of the shear reinforcements, v Rdc is the punching shear stress, 0.75 is a coefficient to take account that the yielding of the shear reinforcements is not reached. 5.4 Comparison of impact and punching loads In order to compare EC2 and Menétrey model, we don t take partial safety factor. The angle of punching crack is 45 (our experimental observation) for Menétrey s model and 26.6 for EC2 (imposed by this method). The table 2 present the impact loads obtained with the experimental approach and the values calculated with Menétrey s model and EC2. Table 2: Comparison experimentation models. Tests SR Experimental approach Punching load (MN) φ Impact load (MN) Observation Menétrey EC2 T3 8 mm 3.0 ± T4 10 mm 2.1 ± T6 10 mm 5.3 ± SR : shear reinforcement, (1) breaking SR, (2) without breaking SR Photograph 1: Breaking of SR. Photograph 2: The dowel effect. The punching loads obtain with Menétrey s model and EC2 are closed. Every time, we have noticed breaking of shear reinforcements (T3 and T6), the impact loads are systematically upper than the values of the two models. For the test T4, the maximal impact load are lower than the values of punching load and we see

8 426 Structures Under Shock and Impact VIII no punching phenomenon. We can say that models are a good estimation of the reality. The breaking of the shear reinforcement is observed after demolition of the concrete (photograph 1). The experiments show the importance of the dowel effect of the flexural reinforcement (photograph 2), which cannot be neglected. 6 Conclusion In this study, the percussion load of a block impacting a RC slab, assuming a perfectly plastic shock, is determined experimentally from the variation of the linear momentum of the block and contact time. The punching load of the slab is also computed with two methods: Menétrey s model and EC 2. The combination of different sensors (accelerometers, LVDT, gauges, highspeed camera, ) and visual observations has permitted to obtain a detailed analysis of punching and percussion phenomena. To develop simplified design methods based on energetic approach, it remains to analysis the concrete compaction in the contact area and to model the bending behaviour of the slab taking dynamic effects into account. Acknowledgment The writers wish to thank TONELLO I.C. office, designer of Structurally Dissipating Rock-sheds, and Léon GROSSE company for its support in the realization of the slab. References [1] Mougin, J-P., Perrotin, P., Mommessin, M., Tonello, J., Agbossou, A. (2003). Rock fall impact on reinforced concrete slab: An experimental approach. Proposed in International Journal of Impact Engineering. [2] Dinic, G., Perry, S. H. (1990). Shear plug formation in concrete slabs subjected to hard impact. Engineering Fracture Mechanics, Vol. 35, N 1/2/3, p [3] Delhomme, F., Agbossou, A., Mommessin, M., Mougin, J-P., Perrotin, P. (2003). Behavior study of a rock-shed slab. Proc. of the 1st Int. Conf. on Response of Structure under Extreme Loading, Toronto, Canada. [4] Larralde, J. P. (1986). Dynamique. Edition Masson, p [5] van Mier, J. G. M., Pruijssers, A. F., Reinhardt, H. W., Monnier, T. (1991). Load-Time Response of Colliding Concrete Bodies. Journal of Structure Engineering, Vol. 117, N 2, February, p [6] Golsmith, W. (1960). Impact. Arnold, London. [7] Delhomme, F., Perrotin, P., Mommessin, M., Mougin, J-P. (2003). Impact on a RC rock-shed slab: percussion analysis. Proc. of the 5th Int. Conf. on Shock & Impact Loads on Structures, Changsha, China.

9 Structures Under Shock and Impact VIII 427 [8] CEB-FIP. (2001). Punching of structural concrete slabs. Technical report, Bulletin 12, Avril [9] Theodorakopoulos, D.D., Swamy, R.N. (2002). Ultimate punching shear strength analysis of slab-column connections. Cement & Concrete Composites, Vol. 24, p [10] Menétrey, P. (2002). Synthesis of punching failure in reinforced concrete. Cement & Concrete Composites, Vol. 24, p [11] Eurocode 2. (2003). Design of concrete structures-part 1.1: General rules and rules for buildings. European Standard, April 2003.