Failure of masonry under explosion effect

Transcription

1 Failure of masonry under explosion effect D. Makovička 1 & D. Makovička Jr. 2 1 Czech Technical University in Prague, Klokner Institute, Czech Republic 2 Static and Dynamic Consulting, Czech Republic Abstract The purpose of the paper is a comparison of the character and differences of the dynamic response of partition structures of different thicknesses to the explosion of methane/air mix beyond their rear face. The paper is based on comparison of the results of theoretical analyses with those of experiments in a testing mine. The duration of the effect of the explosion was longer than the basic natural period of the partition structures. The paper compares the influence of the variability of mechanical partition wall characteristics, their boundary conditions and the way of failure. It defines the failure characteristics and compares the failure prediction with experimental results. Keywords: masonry wall, explosion load, dynamic response, failure. 1 Introduction In the course of several research programme phases, the dynamic behaviour of single brick partitions (alternatively 65 mm, 140 mm and 290 mm thick) was verified by theoretical and experimental methods. A testing mine has made it possible to test partition masonry wall structures sized mm, fitted into a steel frame built in a R.C. supporting structure across the test mine. Mechanical characteristics of the brick partition were described in detail in previous publications such as Makovička [2] and [3]. In this paper, therefore, we give only those characteristics, which are required for the discussion of results. The strength characteristics of partition masonry are based on the provisions of Czech Standard ČSN [1]. The wall was built of mm solid building bricks (CP). Their strength classification was P10, density 1800 kg/m 3, compressive strength 10 MPa, tensile strength in flexure 1.7 MPa.

2 476 Structures Under Shock and Impact VIII The compressive strength of cement-and-lime mortar after 28 days was 4~5 MPa. The damping used for the response prediction was 1.9 % of critical damping in relation to experimental results of measured response. Of particular importance for the analysis of partition response is the determination of the real magnitude of the modulus of elasticity of the brickwork as a dominant part of the bending stiffness of masonry structure. In this respect the analysis of the structure has considered the following possible limits of the modulus of elasticity (according to Standard requirements [1]): E = (1 0.5) 536 = MPa Figure 1: FEM model of barrier structure (mine outline, R.C. supporting wall structure with vending openings and steel frame with built-in testing masonry wall). 2 Load effect The load-time history applied to the structure was measured in the testing gallery during the explosion of a methane/air mix (parameters of explosion, see [7]). The history of this loading is shown in the response diagram in fig. 2. To enable a comparison of the response of structures having different thicknesses the same load (fig. 2) was used for the theoretical analysis for all the different thicknesses.

3 Structures Under Shock and Impact VIII 477 Figure 2: Calculated displacements x 1 in midspan and x 2 and x 3 in upper and bottom quarters of wall span (for wall thickness 65 mm) versus explosion overpressure history p(t). Figure 3: Measured displacements x(t) in midspan and pressure histories p(t) for wall thickness 65 mm and three tests in the vicinity of wall limit bending capacity.

4 478 Structures Under Shock and Impact VIII The explosion pressure generates a regularly distributed continuous load. This load is applied to both the tested partition and the supporting structure in which the partition was fitted. To ascertain the influence of the supporting structure on the partition response, the theoretical analyses modelled the tested masonry partition and the R.C. supporting structure. The model of the whole structure and its finite elements mesh is shown in fig. 1. Figure 4: Calculated versus measured displacement histories x(t) of masonry wall (65 mm thick). 3 Dynamic response Under dynamic load applied perpendicularly to the middle plane of the wall plate partition structure and the transverse R.C. wall this structure behaves as a plate subjected to flexure. The tuning of the structure depends on the structural stiffness and its mass has a decisive role for the magnitude of dynamic response, apart from the load characteristics. A comparison of the lowest natural modes of both partition structures is given in table 1 and shown in fig. 5. The tuning of the structure is also manifested in the character of the response. If the duration of the overpressure phase generated by the explosion is significantly longer than the lowest natural vibration period of the test structure, the mode of partition response corresponds with the mode of the history of dynamic load generated by the gas overpressure. Superposed on this quasi-static deformation are the frequency components of the natural vibrations of relatively low amplitude. Fig.2 shows a comparison of theoretical displacement histories with the load history.

5 Structures Under Shock and Impact VIII 479 Table 1: Natural frequencies (Hz) for various wall thicknesses, modulus of elasticity of masonry and boundary conditions. Wall model D B E A E2 A2 F C Wall thickness (mm) Modulus E (MPa) Boundary conditions Fixed Fixed Hinged Fixed Natural frequencies * 131.5* * 141.2* * 173.4* Note: * different shape f (i) Table 2: Wall response analysis for identical load overpressure and failure prediction of first cracks origin and total destruction. Wall model D B E A F C Wall thickness (mm) Modulus of elasticity E (MPa) Boundary conditions Fixed Fixed Fixed Response quantities for identical load overpressure 39.1 kpa Principal stress - upper face (MPa) Principal stress - lower face (MPa) Displacement x in midspan (mm) Max. rotation (deg) Prediction of first cracks origin for principal stress > 0.1 MPa Overpressure - cracks in midspan (kpa) Overpressure - cracks along boundaries (kpa) Displacement x in midspan (mm) Destruction prediction for limit angle > 1~2º Overpressure - for rotation 1 (kpa) Overpressure - for rotation 2 (kpa) Midspan displacement x - for rotation 1 (mm) Midspan displacement x - for rotation 2 (mm)

6 480 Structures Under Shock and Impact VIII The response computations with the results shown in fig. 4 and table 2 were made for the linear stress/strain relation, so that the magnitude of the displacement x under quasi-static load is compliance with this load. This assumption is justified for masonry and has been proved experimentally in previous works. Figure 5: First six natural modes of tested walls. Consequently, if we convert, e.g., the response in midspan of the partition for a 65 mm wall, we obtain for the pressure of 6.7 kpa and the modulus of elasticity within the limits of 268 and 536 MPa the computed

7 Structures Under Shock and Impact VIII 481 deflection amounting to 41.7~22.1 mm. Actually the deflection measured during the experiment varied between 22.5 and 24 mm. The mode of computed response at the upper limit of the modulus of elasticity E corresponds with measured values (fig. 3 and fig. 4). 4 Failure of masonry Under a real dynamic load the wall structure is loaded, apart from the dynamic load component, also by the weight of its own masonry. This partition pretensioning makes the joints between the bricks themselves close even in the case of crack origin, if enabled by the weight of superposed masonry. Also, the movement along crack surfaces is restrained owing to the friction along these surfaces, especially in the initial phase, when the crack surface has not yet been smoothed by repeated displacements. Under this load type the ultimate tensile stress, which is decisive for masonry failure, is significantly lower than the compressive strength of the masonry. That is why a structure is broken by cracks even under relatively small tensile forces see fig.6 [4, 5, 6]. The basic principles of masonry failure under a load generated by the effect of explosion can be summed up as follows: 1) In case of a very long effect of the overpressure phase of the load as compared with the tuning of the loaded structure (quasi-static load effect the time of load effect of which is longer than 1.5 multiple of the lowest natural vibration period) the vibrations at the lowest natural frequency represent the dominant vibration mode, as a rule. 2) Superposed on dynamic tensile, compressive and shear stresses in the joints between bricks, generated by explosion effects, are the stresses due to the weight of the masonry (the masonry is pretensioned by its own weight and that of superposed structures and their loads). Thanks to the effect of pretensioning at the time of the first crack appearance, the masonry is so stable, as a rule, that it does not collapse immediately. This rule, however, applies only if the load effect, or the stress state of the masonry generated by this load, is in the proximity of the ultimate strength of masonry material. If the dynamic effects exceed significantly this ultimate strength of masonry material, the load produces the destruction of the structure. 3) Due to the static pretensioning of masonry by its own weight, the cracks in the joints may remain closed in the case of a low number of explosion cycles. The movement along these cracks is influenced by the friction along their surfaces. In the case of repeated explosion loads applied to one structure further cracks originate in masonry which first cause, apart from the cracks in the joints between bricks, also the breaking of small parts of bricks (edges, corners, etc.). After several such pressure loads, the edges of the bricks are already hacked by the break-off of individual pieces so that after numerous loading cycles the system behaves as kinematically unstable and particularly thin partitions (such as the tested 65 mm partition), which may buckle under the effect of transverse pressure, may collapse.

8 482 Structures Under Shock and Impact VIII 4) Decisive for masonry failure origin of the first cracks in the joints between bricks are the principal tensile stresses in the mortar of the joints. Until the origin of the first cracks, the stress/strain relation is practically linear (the linearity was confirmed experimentally). 5) Before the origin of the first cracks, the structure is described with sufficient accuracy by physical characteristics corresponding with elastic deformations of the respective dominant natural modes (their superposition). The first cracks originating in the joints, or in marginal parts of the bricks, cause a change particularly of natural frequencies as the consequence of the change of global mechanical masonry characteristics, which influence also the drop of natural frequencies. 6) The change of stiffness at the time of origination of the first cracks is influenced, primarily, by a significant change of the modulus of elasticity of the masonry, which drops approximately by 20 % of its initial value for the intact structure. 7) The process of the change of characteristics is repeated at the moment of origin of another group of micro-cracks until the moment of the collapse of structure. 8) Under a dynamic load, the structure vibrates in one or in a superposition of several natural vibration modes. Very dangerous for the failure of the structure is the origin of resonance with one of the dominant natural modes the period of load application is comparable with one of the natural periods. Under such load, the beading capacity stability of the structure is on the minimum. 9) The masonry structure collapses at the moment when the angle of the change of gradient of the bending line (angle of failure) near midspan area or above supports attains or exceeds its limit value of ψ > 1 to 2. The angle value 2 is valid for the new structures without dominant cracks, while for the older structures the angle of 1 is valid more likely. Figure 6: Failure of masonry wall (65 mm thick, hinged boundaries).

9 Structures Under Shock and Impact VIII 483 According to this theory, based on the comparison of experimental and theoretical results, the factors decisive for the failure of the masonry include both the main tensile stress in the mortar and masonry elements (bricks) and the magnitude of the maximum deflection of the bent masonry member which depends on the actual stiffness of the structure. If we compare the maximum deformation (deflection) of the partition and the maximum surface tensile stress, e.g., for the 65 mm partition hinged on the periphery, we obtains the limits see table 2 and fig. 6 at the achievement of which the masonry fails by the compliance of the one (stresses) or the other (deflections) condition. 5 Conclusion This paper is concerned with the analysis of the response of a partition of brick masonry to the load represented by an overpressure generated by an explosion of a gas mix behind the partition, the period of whose overpressure phase is longer than, or comparable with, the lowest period of the natural vibrations of the structure. The paper compares the partition response of three different thicknesses of 65 mm, 140 m and 290 mm, ascertained theoretically and experimentally by tests in a testing mine. The mutual comparison of measured and computed values reveals the progress of failure of this type of structure with the possibility of a theoretical prediction of the explosion resistance of partition structures primarily thanks to the determination of the influence of individual parameters on the character of the failure process: a) The influence of the accuracy of determination of the stiffness characteristics for masonry (in particular the modulus of elasticity E) on the magnitude of the structural response and on the individual phases of its failure. b) The influence of boundary conditions supports of the wall structure on the tuning and response of the whole structure. c) The influence of the history of the impact load (duration of overpressure phase) on the character of the response. d) The origin of the first cracks versus the collapse of the whole structure in dependence of tensile stresses and limit value of the deformation angle of failure of the masonry wall structure. Acknowledgement This research was supported as a part of research projects of the GAČR No 103/03/0082 Nonlinear response of structures under extraordinary loads and man induced actions, GAČR No 103/01/0039 Pressure fields effects modelling during emergency and crash explosions of gases in closed buildings on engineering structures and CEZ: J04/98: Risk assessment and reliability of engineering systems for which the authors would like to thank the Agencies for the support of the research of this problem.

10 484 Structures Under Shock and Impact VIII References [1] Czech Standard ČSN : Design of Masonry Structures (in czech), Czech Standard Institute: Prague, [2] Makovička, D., Failures of masonry structures by explosion effects, CTU Reports, Theoretical and Experimental Research in Structural Engineering, CTU Publishing House 2: Prague, Vol. 4, pp , [3] Makovička, D. & Makovička, D., Jr., Dynamic response of thin masonry wall under explosion effect, Structures Under Shock and Impact VII, eds. Jones, N., Brebbia, C.A. & Rajedran, A.M., WIT Press: Southampton, pp , [4] Makovička, D., Král, J., Makovička, D., Jr. & Šelešovský, P., Brick masonry structure analysis to gas explosion on partition back side, Fire Prevention 2002, 1 st Part, VŠB-TU: Ostrava, pp , [5] Makovička, D. & Makovička, D.: Failure of masonry partition structure under explosion effect, CTU Reports, eds P. Konvalinka & J. Máca, CTU in Prague, Fac. of Civ. Engn.: Prague, Vol. 7, 2003/1, pp , [6] Makovička, D. & Makovička, D., Jr., Explosive failuring of masonry structure, Transactions of 17 th International Conference on SMiRT, ed. S. Vejvoda, University of Technology: Brno, p pp. on CD, [7] Janovský, B., Podstawka, T., Makovička, D., Horkel, J. & Vejs, L.: Pressure wave generated in vented confined gas explosions: Experiment and Simulation, Transactions of 17 th International Conference on SMiRT, ed. S. Vejvoda, University of Technology: Brno, p pp. on CD, 2003.