On the Influence of Charge Shape, Orientation and Point of Detonation on Air-blast Loadings Pushkaraj Sherkar1, Andrew Whittaker2, Amjad Aref3 1
Structural Engineer, Thornton Tomasetti, Los Angeles, CA 90045; formerly Graduate Student, Department of Civil, Structural and Environmental Engineering, University at Buffalo, Buffalo, NY 14260. 2 Professor and Chair, Department of Civil, Structural and Environmental Engineering, University at Buffalo; Director, MCEER; 212 Ketter Hall, Buffalo, NY 14260;
[email protected] 3 Professor, Department of Civil, Structural and Environmental Engineering, University at Buffalo, 235 Ketter Hall, Buffalo, NY 14260;
[email protected] Abstract Charts in the UFC-3-340-2 design manual are used to compute peak incident overpressures and impulse generated by a detonation of an explosive as a function of scaled distance and angle of incidence. These charts assume either a spherical or hemi-spherical charge and do not account for the variation in charge shape, charge orientation and the point of detonation within the charge. A numerical study was performed using AUTODYN to study the influence of charge shape, charge orientation and point of detonation within the charge on the free-field overpressure distributions and the response of an A992 Grade 50 W14 × 257 column. A set of analyses was performed with cylindrical charges with different aspect ratios. Results were compared with those involving a baseline analysis of a spherical charge. The resulting peak incident overpressure and impulses, and the pressure contours were compared in the near-, mid- and far- fields. In the near-field, the overpressure distributions are influenced significantly by charge shape and the point of detonation in the charge. The influence of these variables diminishes with distance. The loading and subsequent response of the W14 × 257 column to a near-field detonation showed significant dependence on the charge shape and charge orientation and clearly demonstrated that SDOF assumptions are inappropriate for blast-resistant design against detonations of improvised explosive devices at small standoff distances. Introduction Design manuals, guidelines and standards such as UFC-3-340-02 (DoD, 2008) and ASCE/SEI 59-11 (ASCE, 2011) compute incident and reflected overpressure histories in the mid-field and far-field as a function of scaled distance and the angle of incidence. Charts are provided for spherical free-air bursts and hemispherical surface bursts. The assumption of spherical or hemispherical charge shape is consistent with a point source detonation and was the basis of early calculations of pressure histories from detonations of nuclear weapons and high explosives. The empirical data
available in the UFC do account for the influence of charge shape, charge orientation and the point of detonation within the charge on the overpressure distributions in part because these effects were expected to be insignificant at larger scaled distances. A numerical study was performed using AUTODYN (ANSYS, 2009) to study the influence of charge shape, charge orientation and point of detonation within the charge on the free-field overpressure distributions and the response of an A992 Grade 50 W14 × 257 column. A set of analyses was performed with cylindrical charges with different aspect ratios. Results were compared with those involving a baseline analysis of a spherical charge. The resulting peak incident overpressure and impulses, and the pressure contours are compared in the near, mid and far fields. This paper summarizes the study. Sherkar et al. (2010, 2014) describe the study and its conclusions in detail. Influence of Charge Shape on Overpressure Distributions To investigate the effect of charge shape on distributions of overpressure, a free-air burst of 10 kg of TNT-equivalent explosive was analyzed. A baseline analysis was performed with a spherical charge. The incident overpressures and impulses were monitored at every charge diameter in the range of 5 (Z = 0.53 m/kg0.33) to 40 (Z = 4.22 m/kg0.33) from the point of detonation. A set of analyses was then performed with cylindrical charges of the same mass but with varying ratios of length, L, to diameter, D (L/D = 1 to 5). Similar to the analysis of the spherical charge, the incident overpressures and impulses were monitored at distances up to 40 charge diameters but in both the radial and axial directions. A central detonation was assumed for these analyses. Only 1D and 2D analyses were performed. All analyses were performed in two stages: 1) initial expansion of the explosive until the blast wave reached 3 charge diameters, and 2) subsequent propagation of the blast-wave through to the analysis termination time. This approach was adopted to allow the use of finer meshes in the initial stages of the blast-wave expansion. For the spherical charge analysis, the first stage consisted of a 1D wedge analysis using radial symmetry. The TNT was modeled with the JWL EOS per Dobratz and Crawford (1985). Air was modeled as an ideal gas. The radius of the 10 kg TNT spherical charge was 0.227 m. An element size of 0.5 mm was used for both the explosive and the air. A 1D wedge analysis was performed and the analysis was run until the blast wave reached a distance of 3 charge diameters (0.681 m). The output of the 1D analysis was then mapped into an axially symmetric 2D air domain with dimensions of 10m × 10m . The 2D domain consisted of air modeled as an ideal gas and initialized at atmospheric pressure. The air was modeled with 800 × 800 elements, resulting in an element size of 12.5 mm. The single material Euler-FCT solver was used for the air. The termination time for the analysis was set such that it was sufficient to capture the overpressure history at the last monitoring gauge.
Two-dimensional analyses were performed in both stages for the cylindrical charge. The modeling procedure was similar to that was used for the spherical charges. The first stage analyses were run until the blast-wave had expanded to a distance of 3 charge diameters. The output was then remapped to a larger 2D domain. The size of the air domain, element sizes and the termination time were the same as those used for the analysis of the spherical charge. Table 1 lists the notation used for the 5 geometries of cylindrical charge. The dimensions of the charges are also listed.
Table 1: Notation used for cylindrical charges Charge aspect ratio
Notation
1
Charge dimensions L (mm)
D (mm)
Cyl_I
198.4
198.4
2
Cyl_II
315.0
157.5
3
Cyl_III
412.8
137.6
4
Cyl_IV
500.1
125.0
5
Cyl_V
580.3
116.1
Influence of Detonation Point on Overpressure Histories To study the effect of point of detonation within the charge, three charges with aspect ratios 1, 3 and 5 were used. An axially symmetric 2D model was generated. The cylindrical charges Cyl_I, Cyl_III and Cyl_V were used. However, the point of detonation was moved to the left-hand end of the charge axis. A termination time of 25 msec, used for the analyses with centrally detonated charges, was adopted. Influence of Charge Shape on Structural Response To study the effect of charge shape on structural response, numerical simulations on a sample structural steel column were performed using AUTODYN. Although not conclusive, these analyses can inform decisions on modeling, analysis and design of structural components to resist air-blast loadings. A baseline analysis was performed first using a spherical charge. The blast loading was generated by a detonation of 1000 kg of TNT in front of an A992 Grade 50 (350 MPa) W 14 × 257 steel column at a standoff distance of 3 m to the column flange ( Z ≤ 0.3 m/kg0.33). The numerical analysis was performed in two steps: 1) 1D analysis that involved detonation of the explosive and the consequent wave propagation until the blast wave reached the column; and 2) 3D analysis after the results of the 1D analysis were remapped into a 3D numerical model that consisted of the air and the W 14 × 257 steel column.
The 1D analysis of the sample problem was described earlier in the paper. The results of this analysis were remapped into a 3D numerical model. The 3D model in AUTODYN consisted of an air domain with dimensions of 4m × 3m × 6m . The air was modeled with 750,000 elements with an element size of 40 mm and an aspect ratio 1. The steel column was modeled with 30,000 elements such that there were two elements through the thickness of the flanges and across width of the web. The column was 5 m long and was loaded about its strong axis. A fixed boundary condition was applied at both ends of the column by restraining the translational and rotational velocities of all boundary nodes. Air was modeled as an ideal gas with a constant specific heat ratio equal to 1.4, and was initialized at an atmospheric pressure of 101.3 kPa (1 atm). The yield stress of steel increases with strain rate. One of the most widely used constitutive material models for metals is the Johnson-Cook (1983) model and that was adopted here. The values of the parameters for the Johnson-Cook (J-C) model are not available for ASTM A992 (Grade 50) structural steel that is used for rolled steel shapes in the United States. Instead, the values of the parameters for AISI 1006 carbon steel were used (Meyers, 1994). The reaction histories at only one boundary were monitored because the loading on the column was symmetric. Gauges were placed at the mid-height, the quarter height and near the top boundary to monitor the reflected overpressures and temperatures a few millimeters from the surface of the column. Five gauges were placed through the depth of the column at its mid-height to monitor the change in temperature of the steel column. To quantify the effects of strain-rate on the response of the column, a companion analysis was performed in which the strain-rate effects were ignored. Temperature effects were also ignored for the reasons given previously. The values of the parameters of Johnson-Cook model were revised accordingly to consider only the effect of strain hardening. Strain-rate effects played no significant role in the response of the column. To study the effect of charge shape on the response of the column, the analysis was repeated with cylindrical charges Cyl_I and Cyl_V. The analyses were performed in two stages: 1) a 2D axially symmetric analysis until the detonation products expanded to 3m, and 2) a 3D analysis with the output of the 2D analysis mapped into a 3D domain that contained the air (initialized at atmospheric pressure) and the column. Four analyses were performed; two for each charge with the charges oriented horizontally and vertically. Summary and Conclusions Blast loads on structures and components thereof are determined using empirical design curves provided in technical manuals and standards such as UFC-3-340 and ASCE/SEI 59-11 assume a spherical or hemispherical charge and do not account for variations in charge shape, orientation and point of detonation within the charge. Numerical studies were conducted using AUTODYN to determine the influence of these variations on the blast loads and the response of a sample structural component.
The results of numerical studies on the influence of charge shape, charge orientation and point of detonation on overpressure distributions were summarized. Details are provided in Sherkar et al. (2010, 2014). The overpressure histories in the axial and radial direction, resulting from the detonation of 10 kg cylindrical charges and a 10 kg spherical charge were compared. The influence of point of detonation was investigated by comparing contour plots of pressure for the end detonated and centrally detonated charges. The effect of charge shape and orientation on the response of a column in the near field subjected to a detonation of 1000 kg of TNT was studied. The key conclusions are: 1. Charge shape influences substantially the overpressure distributions in the nearand mid-field regions. The incident overpressures and impulses generated by a cylindrical charge are significantly greater than those generated by a spherical charge. Ignoring charge shape in the analysis and design of structural components and framing systems subjected to near-field detonations may result in underestimates of response and inappropriate conclusions regarding the level of performance. 2. For cylindrical charges and a given scaled distance, a) the incident impulse increases (decreases) in the radial (axial) directions with increasing aspect ratio; b) the peak overpressures are greater in the axial direction than the radial direction; c) significant secondary shocks are present in the overpressure histories at large scaled distances (Z > 3.15 m/kg0.33) in the axial direction; d) multiple shocks, which are less significant than the primary shocks, are seen at all scaled ranges (Z = 0.53 to 4.2 m/kg0.33) and increase substantially the total impulse. If the impulse due to secondary and tertiary shocks is ignored, the effect of cylindrical charge shape on the incident overpressures, impulses, and the overall shape of the blast wave, becomes negligible beyond a scaled distance of 2.64 m/kg0.33; that is a spherical charge can be used for analysis. 3. The effects of charge shape are substantially independent of the mass of the explosive. 4. The choice of point of detonation (center, end) in a cylindrical charge on the overpressure distributions and the overall shape of the blast wave is important for small values of scaled distances but can be ignored for scaled distances greater than 3 m/kg0.33. 5. Charge shape (spherical or cylindrical) and orientation (axis vertical, axis horizontal) affect the response of a column subjected to a near-field detonation. Horizontally detonated charges (axial direction of the charge perpendicular to the front face of the structure) produced localized damage in the subject column, whereas the damage due to the vertically detonated charges is widespread. The response of the column is more sensitive to the change in aspect ratio of the horizontally detonated charges than that in the vertically detonated charges. 6. For the sample problem, which may be representative of many blast-resistant analyses/designs of building structures in North America in terms of threat (weapon size and standoff), the increase in temperature of the component under consideration was negligible, and inclusion of thermal effects in the constitutive model is unnecessary. For the sample problem that involved a heavy W 14 × 257 rolled column of Grade A992 steel, the effect of strain-rate on yield stress was
minimal and the inclusion of strain-rate effects in the Johnson-Cook model did not significantly alter either the local or global responses of the column. Acknowledgements The financial support for the studies described herein was provided by MCEER (www.mceer.buffalo.edu) under Thrust Area 3, Innovative Technologies, through a grant from the State of New York. This support is gratefully acknowledged. Any opinions, findings, conclusions or recommendations expressed in this paper are the authors and do not necessarily reflect those of either MCEER or the State of New York. References American Society of Civil Engineers (ASCE). (2011). Blast Protection of Buildings, ASCE/SEI Standard 59-11, Reston, VA. ANSYS. (2009). AUTODYN User Manual (Version 12.1), ANSYS, Inc. Canonsburg, PA. Dobratz, B., & Crawford, P. (1985). "LLNL explosives handbook." Report No. UCRL-52997, Lawrence Livermore National Laboratory, Livermore, CA. DoD. (2008). "Design of structures to resist the effects of accidental explosions." Report No. UFC-3-340-02, Washington D.C. Johnson, G., and Cook, W. (1983). "A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures." Proceedings of the Seventh International Symposium on Ballistics, The Hague, Netherlands. Meyers, M. (1994). Dynamic Behavior of Materials, Wiley-Interscience, New York. Sherkar, P., Whittaker, A. S., and Aref, A. J. (2010). "Modeling the effects of detonations of high explosives to inform blast-resistant design." Report No. MCEER10-0009, MCEER, Buffalo, NY. Sherkar, P., Whittaker, A. S., and Aref, A. J. (2014). "On the influence of charge shape, orientation and point of detonation on blast-resistant design." Paper submitted to Engineering Structures for review and possible publication.
