Jan 28, 2015 - of Large-Scale Explosions ... explosions, in which the pressure data in the data set were not ...... M.Sc. thesis, Dalhousie Univ., Halifax, NS.
Quantification of the Blast-Loading Parameters of Large-Scale Explosions
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Tuan Ngo 1; Raymond Lumantarna 2; Andrew Whittaker 3; and Priyan Mendis 4
Abstract: A field trial involving the surface detonation of the equivalent of 5,000 kg of trinitrotoluene (TNT) was carried out in Woomera, South Australia. The overpressures, impulses, and related information obtained from this trial were analyzed and compared against available predictive procedures and previously published data sets. A predictive procedure that is adopted in the widely used Unified Facilities Criteria (UFC) 3-340-02 is based on equations that are established through a small data set, in which issues such as afterburning, increased pressure as a result of the chemical reaction zone, and blast wave asymmetricality were not addressed. The data set contains data from mid and far-field explosions, in which the pressure data in the data set were not directly measured, but were inferred through the arrival-time data. This leads to a significant level of uncertainty in the UFC 3-340-02 procedure, especially for closed-in explosions. Differences between the field measurements and the predictions made when using the blast-parameter charts in UFC 3-340-02 and a computational fluid dynamics code are identified and analyzed in this paper. The findings of the analysis imply that the current predictive approach will neither capture the variabilities of blast parameters in an actual event, as it does not account for the shape of the charge, nor capture the uncertain behavior of the blast wave at a close standoff distance. This may lead to an overly conservative prediction of the impulse or an underestimation of the peak overpressure. The findings of the analysis show that in an uncontrolled blast event, the reliability of the empirical charts provided in the UFC 3-340-02 is questionable. DOI: 10.1061/(ASCE)ST.1943-541X.0001230. © 2015 American Society of Civil Engineers. Author keywords: Blast loading; High explosive; Field blast trial; Hemispherical surface burst; Blast resistant design; Shock and vibratory effects.
Introduction A single field test involving a very large high explosive was executed in Woomera, South Australia. The trial was designed to collect pressure histories (as a function of the standoff distance) and data on the performance of glazing systems, ballistic-resilient systems, industrial framing systems, and retrofitted reinforced concrete panels. The overpressure histories are the focus of this paper. Field measurements are compared with results that were acquired from predictive charts in the Unified Facilities Criteria (UFC) 3-340-2 and available data sets, and calculations were performed with a computational fluid dynamics (CFD) code. The utility of the design charts in the UFC 3-340-2 is important because they are used widely in the United States, Canada, the United Kingdom, Australia, and many other countries around the world for blast resistant design. The Woomera blast trial data are contrasted with two published data sets: (1) the trials documented by Kingery et al. (Kingery and Pannill 1964; Kingery 1966; Kingery and Coulter 1983), and 1 Director, Advanced Protective Technologies for Engineering Structures (APTES), Dept. of Infrastructure Engineering, Univ. of Melbourne, Parkville 3010, Australia (corresponding author). E-mail: dtngo@unimelb .edu.au 2 Research Fellow, Dept. of Infrastructure Engineering, Univ. of Melbourne, Parkville 3010, Australia. 3 Professor and Chair, Dept. of Civil, Structural and Environmental Engineering, State Univ. of New York at Buffalo, New York 14260. 4 Professor, Dept. of Infrastructure Engineering, Univ. of Melbourne, Parkville 3010, Australia. Note. This manuscript was submitted on March 20, 2014; approved on November 18, 2014; published online on January 28, 2015. Discussion period open until June 28, 2015; separate discussions must be submitted for individual papers. This paper is part of the Journal of Structural Engineering, © ASCE, ISSN 0733-9445/04015009(11)/$25.00.
© ASCE
(2) the trials documented by Bogosian et al. (2002). The Kingery et al. data set was the first comprehensive collection of data from hemispherical blast trials and forms the basis of the design charts presented in the UFC 3-340-02 (UFC 2008). The limitation of the Kingery et al. data set is that the pressure data are inferred from the arrival time data rather than by direct measurement. The Bogosian, Ferrito, and Shi data set consists of data that were collected from field trials of weapons of various types, shapes, and internal points of detonation. The pressure data in this data set were measured directly. The Bogosian data introduced variability in the pressure and impulse data that does not exist in the Kingery and Pannill (1964) and Kingery (1966) data sets, which addressed the surface detonation of trinitrotoluene (TNT) charges. This source of variability should be considered in design because terrorist weapons generally do not consist of idealized shapes that are detonated at specific locations within the charge. The discrepancies between the predictions (UFC 3-340-02 and CFD analysis) and the blast data sets are used to determine potential variabilities in blast-parameter prediction, which occur as a result of uncertainties in the UFC 3-340-02 charts and variabilities in an actual blast event. The implications of these errors on the application of the UFC 3-340-02 charts are established in this paper.
Background Beshara (1994) extensively studied the blast-loading effects on aboveground structures as a result of different explosive sources. The findings concluded that accurate prediction of blast loading on a structure is difficult to obtain, because many uncertainties will arise from the interaction between blast wave and structure, and the assumptions to derive those relationships. The magnitude of blast loading, duration, and general shape governs the response of a structure, which is very sensitive to small changes in those
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characteristics. Blast resistant design typically involves two uncoupled, sequential steps: (1) calculation of the incident blast overpressure and impulse, and (2) design of the element. This paper focuses on the first step, which was published in the U.S. Army Corps of Engineers’ TM5-1300 (USACE 1990) and was more recently published in the UFC 3-340-02 (UFC 2008). This step has traditionally applied charts that were prepared by the U.S. Department of Defense. These charts present values of blast-wave parameters as a function of the scaled distance, Z, calculated as the distance R divided by the charge weight W to the power of 1=3, namely, R=W 1=3 . Charts are presented for spherical free-air bursts and hemispherical surface bursts. Available blast parameters include the peak incident and reflected overpressures and impulse, arrival time, and positive-phase duration. Negative-phase data sets are also provided but are rarely used in the design of structures. The information provided in the charts can be used to construct the Friedlander blast-pressure history (UFC 2008) on a loaded component, in which the overpressure decays exponentially from a peak value to ambient pressure. However, the reflected overpressure and specific impulse, i.e., the impulse resulting from the positive blast pressure phase, are typically used to derive a simple triangular loading function on the loaded element, in which all parts of the element receive the same loading at the same time, thus implying far-field loading (common arrival time and small angle of incidence). A typical blast pressure history can be divided into two phases: positive and negative. The first phase is the positive phase, which is a result of the rapid expansion of the explosive. Because of the rapid expansion of the core of the explosive, a shell of pressurized air is formed on the outermost layer of the expanding gas: the blast wavefront. This phase consists of a dynamic transient load with a near-instantaneous increase of pressure to a peak value, followed by a rapid decay to ambient pressure. Depending on the explosive energy and the distance between the explosive and the target, the magnitude of the peak overpressure can be many orders of magnitude above atmospheric pressure, and the decay time to ambient pressure may be a few milliseconds. The second phase consists of a suction or negative pressure, which occurs as a result of the momentum of the expanding gas. The amplitude of the negative phase is generally much less than that of the positive phase (and is capped at 101 kPa), but the duration of the negative phase is generally much longer than that of the positive phase. UFC 3-340-02 and TM5-1300 provide background information on blast-wave propagation in the far field (USACE 1990; UFC 2008). The design charts in the UFC 3-340-02 are based on trial data that were collected from several reports (Kingery and Pannill 1964; Kingery 1966; Kingery and Coulter 1983; Kingery and Bulmash 1984). The semi-empirical blast model is also known as the Kingery and Bulmash (K-B) model. The blast-parameter model for hemispherical blast pressures was developed based on the data published in Kingery and Pannill (1964) and Kingery (1966), whereas Kingery and Coulter (1983) focused on blast-load reflections on finite structures. Kingery and Bulmash (1984) presented design charts for spherical free air burst explosions based multiple data sets involving detonations of spherical and hemispherical (after adjustment for weight) explosives. The uncertainties in the K-B model are quantified in terms of model error relative to the experimental data (Kingery 1966). (The data set used in the development of the K-B model is denoted as the K-B data set in this paper). The K-B data set includes empirical measurements of field tests performed by defense research agencies in Canada, the United Kingdom, and the United States. The trials consisted of 5,000 kg, 20,000 kg, 200,000 kg, and 500,000 kg of TNT charges that were stacked hemispherically, © ASCE
and detonated to simulate a hemispherical surface burst. The K-B data set contains information for scaled distances between 0.19 and 170 m=kg1=3 . Uncertainties in the K-B data set partly result from limitations in the measurement technology available at the time of the trials. For example, the peak overpressure and specific impulse were inferred from the shock front velocity using the Rankine-Hugoniot relationship, which conserves mass, momentum, and energy across a shock front (Glasstone and Dolan 1977; Needham 2010). The shock front velocity was not measured in the trials but was also inferred from the arrival time data. Although pressure transducers were used in the trials, they functioned as blast switches, and were used to identify the arrival and duration of the blast wave (Kingery 1966). Furthermore, blast wave features resulting from the chemical reactions (Davis 1981, 1998) and afterburning (Donahue 2009) could not have been inferred, although the effect of both are likely to be limited for the minimum scaled range of 0.19 m=kg1=3 . In brief, the K-B data set contains not only blast-parameter variation as a result of the hemispherically stacked charge shape, but also significant uncertainties that may occur in the arrival-time measurement and factors assumed in the Rankine-Hugoniot equations. The second data set that was analyzed in this paper contains experimental data collected by Bogosian et al. (2002) from multiple sources. This data set contains varying charge shapes, explosive materials, and heights of burst, and is denoted as the Bogosian, Ferrito and Shi (BFS) data set in this paper. The BFS data set consists of trials with approximately hemispherical blast wave propagations; however, unlike the trials in the K-B data set, the charges were not hemispherically stacked. The BFS data set actually represents a more realistic representation of an actual event as a result of the variation in charge shape, source, and height of burst. The charge shape, explosive material, and height of a detonation will not be known ahead of time by the designer but it is very unlikely that the weapon would be TNT stacked hemispherically. The BFS data set contains information from a number of trials conducted after the K-B data set was compiled, in which direct measurements of pressure histories were made. The uncertainty introduced by indirect measurements of pressure is eliminated in the BFS data set. However, uncertainties and variabilities remain because of a lack of metadata and calibration data for the instruments, lack of redundancy in the instrumentation systems used, transformation of charge compositions to a TNT equivalent, charge shape, and point of detonation within the charge. Chock and Kapania (2001) reviewed the blast-scaling methods: the Hopkinson-Cranz and the Sachs blast scaling. Sachs scaling was used by Baker (1973), and Hopkinson-Cranz scaling was used by Kingery and Bulmash. The blast-loading profiles resulting from these two methods were compared. The findings suggested that the magnitudes of the peak pressures were similar with differing specific impulses. It was also found that a much lower impulse and an earlier time of arrival were obtained by using Baker’s method than Kingery and Bulmash’s method. It is difficult to determine a more accurate approach for blast prediction because both methods are based on experimental data with minimal or unrepeated tests. Therefore, uncertainties associated with some aforementioned parameters are difficult to assess.
Woomera Blast Trial This arena test was carried out in the Woomera Prohibited Area of South Australia. The authors were members of the core group involved in planning, taking measurements, and conducting the tests. This is the first time the results are reported in open literature.
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The blast trial was carried out under a U.K./Australian agreement as part of the Anglo-Australian Memorandum of Understanding on Research (AAMOUR). The arena test included target containers with the dimensions of 4 × 2 × 2 m. The performance of these targets is not reported in this paper as they have negligible effects on the blast measurements. The trial was intended to simulate a surface burst. Ideally, a hemispherically shaped stack of explosives would be deployed to enable a comparison with other data sets; however, a cylindrical stack was used, which is a reasonable approximation for far-field measurements. Fig. 1 shows the TNT charge, which consisted of 16 quarter-cylinder packets stacked into a cylindrical shape with an approximate diameter of 2 m and a height of 1 m. The weapon was placed on level ground composed of sandy loam soil, which is prevalent in the Woomera Prohibited Area. The ambient temperature during the trial was 29.3°C, with 28% humidity. The ambient pressure was 101 kPa, and there was a north-easterly wind of 5.3 m=s, gusting to 6.7 m=s. Twelve freefield pressure measurements were made. The pressure probes were 8 mm in diameter and 30 mm in length. The pressure transducers were embedded flush with the reflector panels (Fig. 2), which were then oriented to the required angle of incidence. To monitor incident pressure, the transducer was oriented parallel to the outward propagating wave. The transducers were located along two
orthogonal lines, lines 1 and 2, at standoff distances of 25, 50, 75, 100, and 150 m, which represent scaled distances of 1.5, 2.9, 4.4, 5.8, and 8.8 m=kg1=3 , respectively. There were two additional transducers at a 92-m standoff distance (5.4 m=kg1=3 ), which were located in the vicinity of blast line 2. Fig. 3 shows the location of the transducers and the numbering scheme used; GZ4 is ground zero. The pressure capacities for the transducers were varied because much higher pressures were expected close to the charge (transducers 3 and 8 in Fig. 3) than far away. The pressure limit of the transducers at target points 3 and 8 (scaled distance of 1.5 m=kg1=3 ) was 3,400 kPa. The peak pressure that could be measured by the transducers at target points 7 and 12 (scaled distance of 8.8 m=kg1=3 ) was 345 kPa. The pressure limit on the remaining transducers was 690 kPa. The sampling rate for the data acquisition system was 2 MHz. The blast parameters that were recorded in the trial are summarized in Table 1. The signal from the transducer at target 2 was interrupted, which prevented the calculation of specific impulse and all negative phase data. The signals from targets 8 and 9 were also interrupted, but reliable positive phase data were recorded. The pressure histories recorded by the transducers that were located along lines 1 and 2 are shown in Figs. 4 and 5, respectively. Because of the vicinity of target 1 to line 2, the pressure histories recorded at the transducer are also presented in Fig. 5. The crater, which is shown in Fig. 6, is approximately 3 m deep with a 4.5-m radius. A comparison between the pressure histories along lines 1 and 2 suggests that the blast-wave propagation was not symmetrical. Fig. 7 shows a high-resolution photograph of the explosion. The difference between the extent of soil particle disturbance along lines 1 and 2, which can be observed in Fig. 7, indicates that the pressure-wave propagation is asymmetrical. This asymmetricality was also shown in analyses conducted by Sherkar et al. (2010). The pressure histories on line 2 (shown in Fig. 8) decay from the peak overpressure, and are slower than those on line 1. The impulse recorded on line 1 is typically less than that recorded on line 2. Although the trial was a controlled detonation, significant variations in values of the blast parameters were measured, which reinforces the hypothesis that detonations will be uncertain in terms of overpressures and impulses.
Fig. 1. 5,000-kg cylindrical TNT charge on site
Fig. 2. Blast pressure sensor/transducer © ASCE
Fig. 3. Blast pressure transducer and target locations 04015009-3
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Table 1. Summary of Experimental Results Positive phase
a
Negative phase
Scaled distance (m=kg1=3 )
Time of arrival (ms)
Peak overpressure (kPa)
Specific impulse (kPa-ms)
Peak underpressure (kPa)
Specific impulse (kPa-ms)
5.4 5.4 1.5 2.9 4.4 5.8 8.8 1.5 2.9 4.4 5.8 8.8
151.8 151.9 13.9 53.4 108.8 172.4 304.3 13.1 52.3 108.6 170.7 300.8
44 41 1,167 175 54 33 19 1,064 166 58 36 20
857 N/A 2,130 736 469 366 254 2,678 955 903 838 488
−10 N/A −78 −17 −9 −6 −4 N/A N/A −8 −8 −5
−968 N/A −3,541 −415 −468 −596 −352 N/A N/A −238 −654 −408
1 2 3 4 5 6 7 8 9 10 11 12 See Fig. 3.
Numerical Simulation Numerical simulations were performed using the computational fluid dynamics (CFD) code Air3D. This code uses a simplified balloon blast source model, in which the explosive is replaced by a uniformly pressurized sphere of gas at high pressure and
temperature (Rose 2006). The pressure in the balloon is calculated by equating the specific internal energy of the pressurized ideal gas to the detonation energy of the explosive (Brode 1959). The diameter of the balloon is set equal to the diameter of the explosive being modeled, whereas the specific internal energy, given by Eq. (1), is set equal to the energy yield of the explosive
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E¼
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Fig. 4. Pressure history recorded on blast line 1
ΔP ρðγ − 1Þ
ð1Þ
where E = specific internal energy; ΔP = difference between the pressure within the balloon and ambient pressure; ρ = density of the explosive; and γ = adiabatic constant of the ambient medium. Air3D can only simulate spherical or hemispherical shapes of explosives. For the simulations reported in this study, the cylindrical weapon from Fig. 1 was then replaced by a hemispherical charge with a radius equal to 1.1 m, to achieve the equivalent blast-loading effects. The adiabatic constant, γ, was set equal to 1.4. The density and the specific internal energy of the explosive presented in Baker et al. (1983) were adopted in the analysis. The density of the explosive was set equal to 1,600 kg=m3 , and the specific internal energy was set equal to 4.52 MJ=kg. These explosive and ambient parameters can be substituted into Eq. (1) to obtain a resultant pressure difference of 2.9 GPa.
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Target pointa
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Fig. 5. Pressure history recorded on blast line 2 © ASCE
Fig. 6. Cratering effect at ground zero 04015009-4
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Fig. 7. Asymmetric blast wave propagation in Woomera blast trial (image by Raymond Lumantarna)
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Fig. 8. Overpressure histories recorded along blast lines 1 and 2: (a) 25-m standoff distance; (b) 50-m standoff distance; (c) 75-m standoff distance; (d) 100-m standoff distance; (e) 150-m standoff distance © ASCE
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longitudinal range of the domain (x-axis) was 200 m. Fig. 9 shows the typical analysis domain, with a transmitting boundary at the upper x and y perimeters. This represents the infinite air domain for blast-wave propagation out of the boundary without reflections, and a reflecting boundary was used at the lower x and y perimeters to simulate the ground and the axis of symmetry, respectively. The cell sizes in the CFD models were determined based on a mesh sensitivity analysis. The baseline value was the peak pressure obtained from spherical 1D CFD analysis with a mesh size of 10 mm. The mesh convergence factor (CF), which is summarized in Table 2, is the ratio of the peak overpressures obtained with varying cell size and peak overpressure obtained with the baseline cell size. A 50 × 50 mm cell size was adopted for both 2D models, Model RF1.8 and Model RF2, with a maximum difference of 7% relative to the 1D model. The differences between the 2D model’s CF (with 50 × 50 mm cell size) diminishes with increasing scaled distance, as given in Table 3. The choice of cell size was influenced by computational effort, as it was found that reducing the cell size would result in a significant increase in computational demand with little improvement in precision. The pressure histories obtained from Model RF2 are presented in Fig. 10.
Table 2. Mesh Convergence Table Mesh convergence factor (CF)
Mesh size Baseline 1D CFD—10 mm 2D CFD—50 × 50 mm 2D CFD—100 × 100 mm 2D CFD—200 × 200 mm
1 0.93 0.89 0.82
Table 3. Solution Accuracy with 50 × 50 mm Mesh Size Mesh convergence factor (CF)
Scaled distance (m=kg1=3 ) 1.5 2.9 4.4 5.4 5.8 8.8
0.929 0.989 0.993 0.994 0.995 0.998
800 700 P3 P4 P5 P1 P6 P7
600 500
Pressure (kPa)
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Air3d uses an explicit finite-volume formulation to solve the Euler equations of mass, momentum, and energy (Rose 2006). Although Air3D enables an implementation of the JonesWilkins-Lee (JWL) Equation of State (Lee et al. 1968), the ideal gas Equation of State was used in this study because the focus was on far-field calculations. To model obstacles, Air3d uses dead cells with reflective boundaries to represent perfectly rigid obstacles and perfectly reflective soil. Two models were analyzed, one based on a weight factor of 1.8 (Model RF1.8) and the other with a weight factor of 2 (Model RF2). These scale factors are used to take into account the effect of wave reflection from the surface in a hemispherical surface burst (Kingery and Bulmash 1984). Specifically, this factor will give the amount of energy in a hemispherical blast from a spherical blast model and is not addressed in the Kingery and Bulmash data set and model. However, it is included because the model was developed from an empirical approach, based on hemispherical blast trials. Moreover, the factor is less than the idealized value of 2.0 because part of the energy associated with a surface burst is lost through the ground and in digging a crater. Model RF2 represents a surface burst with no energy loss and Model RF1.8 represents a surface burst with energy loss, such as in the formation of the blast crater. Air3D cannot simulate blast energy dissipation. Therefore, to take the energy dissipation into account, the weight factor has to be incorporated into the Air3D model. Radial symmetry was assumed. The recommended cell size for spherical analysis in Air3D is expressed in terms of the scaled radial distance, which is equal to 1E-3 m=kg1=3 (Rose 2006). For example, for a 1.8 × 5,000 kg TNT equivalent charge, the recommended cell size is 21 mm ½¼ 1E-3 × ð1.8 × 5,000Þ1=3 . Each simulation consisted of two phases: one-dimensional (1D) analysis with spherical symmetry, and a subsequent two-dimensional (2D) analysis with radial symmetry. An average cell size of 10 mm, which is finer than the recommended cell size, was used for the 1D analysis. A domain range of 24 m was used for the 1D analysis. Once the shock front reaches the boundary of the domain, the results of the 1D analysis are mapped to the 2D domain. The domain range of 24 m was chosen so that the recorded overpressure from the nearest target point (25-m standoff distance) would be recorded in the 2D phase. An average cell size of 50 mm was used for the 2D analysis phase. The height of the domain (y-axis) was 60 m, and the
(25m) (50m) (75m) (92m) (100m) (150m)
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Fig. 9. Air3D analysis domain with boundary conditions © ASCE
Fig. 10. Overpressure histories from CFD Model RF2 04015009-6
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Results Differences between the experimental results and those calculated using the UFC 3-340-02 are evident in Fig. 8. Those uncertainties are quantified in this study in terms of a relative error (RE) given in Eq. (2), in which positive and negative REs represent an underestimation and overestimation of the blast parameters, respectively. This approach has been used in the literature (Kingery 1966; Bogosian et al. 2002; Netherton and Stewart 2009), and is adopted in this study for consistency. An accurate predictive model will yield an absolute value of the RE that is very close to zero y − y0 y0
ð2Þ
where y = experimental data point; and y0 = predicted value. The pressure histories at monitoring locations P1 and P3 are presented in Figs. 11 and 12, respectively. These two target points are chosen because they represent extreme cases: At P1, the peak overpressure, specific impulse, and arrival time obtained from Model RF2 are in general agreement with the Woomera blast trial data, whereas at P3, significant differences are observed. Fig. 11 shows the overpressure histories calculated using Model RF1.8,
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32 24 16 8 0 -8 -16 120
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Fig. 11. Overpressure histories at target point P1 (92-m standoff distance; 5.4-m=kg1=3 scaled distance)
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Ta (msec/kg1/3) Pso (kPa) is (kPa msec/kg1/3) Ta - Exp (msec/kg1/3) Pso - Exp (kPa) is - Exp (kPa msec/kg1/3) Ta - CFD (msec/kg1/3) Pso - CFD (kPa) is - CFD (kPa msec/kg1/3)
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RE ¼
Model RF2, UFC 3-340-02, and measured in the experiment at target point P1 (92-m standoff distance, Z ¼ 5.4 m=kg1=3 ). Fig. 12 presents identical information at target point P3 (25-m standoff distance, Z ¼ 1.5 m=kg1=3 ). The peak overpressures, specific impulses, and arrival times obtained from all target points are summarized in Fig. 13. The summary of shockwave parameters measured in the experiment in comparison with the results of the CFD Model RF2 and the UFC 3-340-02 charts is shown in Fig. 13, and the model errors of model RF1.8, model RF2, and the UFC 3-340-02 charts are summarized in Table 4. Table 4 indicates that Model RF1.8 significantly underestimates the peak overpressures recorded at P3 and P8 (scaled distance of 1.5 m=kg1=3 ) by 88 and 72%, respectively, whereas the peak overpressures at P4 and P9 (scaled distance of 2.9 m=kg1=3 ) are underestimated by approximately 43%. The peak overpressures obtained from Model RF1.8 underestimates the peak overpressures recorded on the remaining data points, with errors of less than 17%. Model RF2 underestimates the peak overpressures recorded at P3 and P8 (1.5 m=kg1=3 ) by 73 and 57%, respectively, whereas the peak overpressures at P4 and P9 (2.9 m=kg1=3 ) are underestimated by approximately 33%. The peak overpressures obtained from Model RF2 are in general agreement with the peak overpressures recorded on the remaining data points. UFC 3-34002 charts underestimate the peak overpressures recorded at P3 and P8 (1.5 m=kg1=3 ) by 100 and 82%, respectively, whereas the peak overpressures at P4 and P9 (2.9 m=kg1=3 ) are underestimated by approximately 40%. The peak overpressures calculated using the UFC 3-340-02 charts slightly underestimate the peak overpressures recorded on the remaining data points. These findings indicate that the peak-overpressure predictions from the CFD analysis and UFC 3-340-02 charts are more reliable at scaled distances greater than 2.9 m=kg1=3 . The specific impulses obtained from Model RF1.8, Model RF2, and the UFC 3-340-02 charts generally overestimate the specific impulse recorded in the trial, with the exception of target points P1, P8, and P11. On blast line 1 (i.e., P3, P4, P5, P6, P7), the specific impulses obtained from Model RF1.8 significantly overestimate the specific impulses measured in the trial by approximately 50% except at P3, where the Model RF1.8 overestimates the specific incident impulse measured in the trial by 7%. Model RF2 overestimates the specific impulses measured on blast line 1
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Fig. 12. Overpressure histories at target point P3 (25-m standoff distance; 1.5 m=kg1=3 scaled distance) © ASCE
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Fig. 13. Summary of measured parameters, UFC 3-340-02 data, and results of CFD analysis of Model RF2
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Table 4. Relative Error of the Predictions with Blast Parameters Recorded in the Experiment
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Target point P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 Average a
T a (%)
Pso (%)
is (%)
CFD RF1.8
CFD RF2
UFC 3-340-02
CFD RF1.8
CFD RF2
UFC 3-340-02
CFD RF1.8
CFD RF2
UFC 3-340-02
−2 −2 −5 −4 −3 −2 −2 −10 −6 −3 −3 −3 −4
0 0 −2 −2 −1 0 0 −8 −4 −1 −1 −2 −2
−4 −4 −14 −8 −5 −3 −3 −19 −10 −5 −4 −4 −7
17 10 88 47 0 2 7 72 39 8 9 73 31
10 4 73 36 −6 −4 2 57 29 1 3 64 22
15 9 100 44 −1 1 4 82 36 6 8 69 31
6 N/Aa −7 −47 −52 −51 −50 17 −31 −8 12 −4 −20
−1 N/Aa −13 −50 −55 −54 −53 9 −35 −14 4 −10 −25
−10 N/Aa −31 −55 −59 −58 −58 −13 −41 −21 −5 −19 −38
A Measurement at P2 was interrupted before the specific impulse can be determined.
by approximately 54% except at P3, where the specific impulse is overestimated by 13%. The UFC 3-340-02 charts overestimate the specific impulses measured on blast line 1 by approximately 58%, except at P3, where the specific impulse is overestimated by 31%. On blast line 2 (i.e., P1, P8, P9, P10, P11, P12) the specific impulses obtained from Model RF1.8 are in general agreement with the Woomera trial results, with the exception of P9, where Model RF1.8 underestimates the specific impulse by 31%. The specific impulses obtained from Model RF2 are in general agreement with the Woomera trial results, with the exception of P9, where Model RF1.8 underestimates the specific impulse by 35%. The UFC 3-340-02 charts overestimate the specific impulses measured on blast line 2 by approximately 15%, except at P9, where the specific impulse is overestimated by 41%. Table 4 also lists the average value of the REs, which can be used to identify the most reliable analytical approach. For prediction of peak overpressure and arrival time, Model RF2 contains the least errors in comparison to Model RF1.8 and UFC 3-340-2. However, for predicting the specific impulse, Model RF1.8 provides a more accurate prediction than Model RF2 and UFC 3-340-02 because the average REs from Model RF1.8 are less than the other approaches. Although tools such as CONWEP and the UFC 3-340-02 charts generally make reasonable predictions of the peak-incident overpressures and impulses under controlled conditions for scaled distances greater than 3 m=kg1=3 , the findings of the analysis indicate that discrepancies were observed between the blast loadings recorded in the trial and the UFC 3-340-02 charts at a close standoff distance. These discrepancies are speculated as the results of the asymmetricality of blast-wave propagation that can be observed in the propagation of the contact surface in Fig. 7. The stacking of the TNT bricks and the firing sequence of the detonators may have contributed to the asymmetry of the blast waves.
The K-B polynomials, which are implemented in the UFC 3-340-02, are based on mean responses at a given scaled distance in the K-B data set. Kingery (1966) demonstrated the reliability and unbiased nature of the model by quantifying the uncertainties associated with the model in terms of the mean relative error (MRE), mean positive relative error (MPRE), and mean negative relative error (MNRE). The MPRE and MNRE describe how the experimental data sets are distributed around the predicted value. Table 5 summarizes the model error of the peak overpressure and specific impulse collected in the K-B data set (Kingery and Pannill 1964; Kingery and Bulmash 1984). The numbers of positive (negative) points represent data that are greater (less) than the prediction. The MRE of the peak overpressure chart from the UFC 3-340-02 relative to the K-B data set is 0%, which indicates that the UFC 3-340-02 chart is an unbiased estimator of the K-B data set. For the specific impulse, the MRE of the UFC 3-340-02 chart relative to the K-B data set is 0.14%, which indicates that the UFC 3-340-02 chart slightly overestimates the K-B data set. The standard deviation of the REs can be derived by using the average values of the MPRE and the MNRE, which leads to a standard deviation of 9% for the RE of peak-incident overpressure and 10% for the RE of specific-incident impulse. Bogosian et al. (2002) collected data from different experiments. The BFS data set contained trials of varying blast source, charge shape and height of burst, which represent blast events varying from a scaled distance of 1 to approximately 25 m=kg1=3. Relative to the BFS data set, the model error of the peak overpressure chart from UFC 3-340-02 is equivalent to an MRE of 19% with a standard deviation of 33%, whereas the model error for the specific impulse chart is equivalent to an MRE of −14% with a standard deviation of 18% (Bogosian et al. 2002). Table 6 summarizes the statistical parameters of the errors of the UFC 3-340-02 charts relative to the K-B data set, BFS data sets,
Comparisons of Blast Load Prediction Methods and Their Uncertainties
Table 5. Model Error Parameters (Data from Kingery and Pannill 1964; Kingery 1966)
There is significant variability in the pressure histories along lines 1 and 2 at identical standoff distances, in addition to differences between calculations performed using the UFC 3-340-02 and the CFD code Air3D. In this section, the K-B and BFS data sets are analyzed to judge their inherent uncertainties. The results are compared with those from the Woomera trial. The analysis is conducted using the error parameters given in Eq. (2) for each data set relative to the charts provided in the UFC 3-340-02. © ASCE
Parameters Sample size Number of positive points Number of negative points MPRE MNRE MRE
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Peak-incident overpressure
Specific-incident impulse
273 136 137 6.14% 6.65% 0%
94 41 53 7.6% 6.1% −0.14% J. Struct. Eng.
Peak-incident pressure Specific-incident impulse
9.4 10.1
Peak-incident pressure Specific-incident impulse
BFS data set 19% −14%
33 18
Woomera trial data set Peak-incident pressure 33% Specific-incident impulse −33%
36 21
BFS data set and Woomera trial data set Peak-incident pressure 20% Specific-incident impulse −16%
34 19
1/3
Standard deviation (%)
Scaled specific impulse (kPa-msec/kg
Mean relative error K-B data set 0% −0.14%
3000 2000 UFC 3-340-02 UFC3-340-02 BFS Woomera trial blast line 1 Woomera trial blast line 2
1000 700 500 300 200 100 70 50 30 20 10 7 5 3 2.1 0.85 1
2
3
4
5
6 7 8 9 10
20
30
Scaled distance (m/kg1/3)
Fig. 15. BFS-specific impulse data (data from Bogosian et al. 2002)
Woomera trial data, and the combined BFS and Woomera trial data set. Table 6 indicates that the MREs of the peak overpressure and specific impulse obtained from the UFC 3-340-02 charts relative to the BFS data set are not close to zero, which implies that the UFC 3-340-02 is a biased estimator of the BFS data set sample. Furthermore, the standard deviation of the RE of the UFC 3-340-02 charts relative to the BFS data set is greater than that of the K-B data set, which implies that greater variabilities were observed in the BFS data set than in the K-B data set. A comparison of results from the Woomera trial and the BFS data set is shown in Figs. 14 and 15. The peak overpressures and specific impulses obtained in the Woomera blast trial are in general agreement with the BFS data set. The Woomera trial data can be added to the BFS data set to define improved statistical parameters that represent the peak overpressure and specific impulse of a blast event. The statistical parameters of the combined BFS and Woomera trial data set are also given in Table 6. Inspection of the combined data set suggests that the bias of the peak overpressure from the UFC 3-340-02 chart was exhibited only in data obtained from experiments with a scaled distance of 3 m=kg1=3 or less. This trend was not observed in the specificimpulse parameter, in which overestimation of the specific incident impulse was observed consistently throughout the data range. Fig. 15 shows that general agreement was observed in the specific impulses recorded along blast line 1, whereas the specific impulses recorded along blast line 2 were generally lower than the BFS data set. 3000 2000
UFC 3-340-02 UFC3-340-02 BFS Woomera trial blast line 1 Woomera trial blast line 2
1000 700 500
Overpressure (kPa)
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Parameters
)
Table 6. Summary of Statistical Parameters
300 200 100 70 50 30 20 10 7 5 3 2.1 0.85 1
2
3
4
5
6 7 8 9 10
20
30
Scaled distance (m/kg1/3)
Fig. 14. BFS overpressure data (data from Bogosian et al. 2002) © ASCE
Several sources of error contributed to the discrepancies between the UFC 3-340-02 charts and the Woomera trial results and the BFS data set. The first source of error is the uncertainties in the blast parameter charts provided in UFC 3-340-02. The peak overpressures in the K-B data set, which is the basis of the UFC 3-340-02 charts, were inferred from the arrival time rather than being directly measured. The K-B data set contains uncertainties of the arrival-time measurement, which was carried over when the peak overpressures were inferred using the Rankine-Hugoniot relationship. The uncertainties of the arrival-time measurement are not significant, considering that the parameter can be measured with good accuracy in the trials. Therefore, uncertainties in the peak overpressure data and the specific-impulse data are minimal, which is evident in the unbiased means and the low standard deviation in the peak overpressure and specific-impulse REs of the K-B data set that are given in Table 6. However, the K-B data set contains additional uncertainties that are not represented in the statistical distribution of the REs. These uncertainties can be associated with the calculation of the overpressure data, in which factors, such as the adiabatic constant, density of explosives, ambient pressure and speed of sound in the medium, are assumed. In the Woomera blast trial and BFS data sets, uncertainties in the calculation of pressure data are mitigated by directly measuring pressure. Unlike the K-B data set, which addresses charges of idealized shapes, the Woomera and BFS data sets include variabilities associated with a varying charge shape, detonation point, and height of burst. The second source of error is the result of a variability in the charge configuration in the Woomera blast trial and the BFS data set. The third source of error can be associated with the effect of an asymmetrical blast-wave propagation. Asymmetrical blast-wave propagation was not reported in Kingery and Pannill (1964), Kingery (1966), and Bogosian et al. (2002). However, the K-B and BFS data sets may have contained asymmetrical data, especially in the BFS data set, in which the blast detonation point and charge shape were not reported. Given the differences between the blast data (from the Woomera blast trial and BFS data set) and peak overpressure predicted using the UFC 3-340-02 chart, an alternate approach to quantify the uncertainties in the BFS data set is adopted. In this approach, the data set is split into two parts: (1) data points for a scaled distance, Z, between 1 and 3 m=kg1=3 ; and (2) data points for a scaled distance between 3 and 25 m=kg1=3 . Table 7 summarizes the results of this study, which indicate that the model is a more reliable and less
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Table 7. Summary of Peak Overpressure RE Sample
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Sample 1 (1 < Z ≤ 3 m=kg3 ) Sample 2 (3 m=kg3 < Z < 25 m=kg3 )
Mean (%)
Standard deviation (%)
34 7
37 19
biased estimator of the peak overpressure of the sample at scaled distances greater than 3 m=kg1=3 , compared with scaled distances of less than 3 m=kg1=3 . In design, Section 2-13.3 of UFC 3-340-02 recommends that the charge weight be multiplied by a factor of 1.2 to take into account the errors in the charts. This weighting factor provides only a minor increase in the peak overpressure and specific impulse. Considering the REs identified previously in predicting the peak overpressure, the application of the weight factor may still result in a significant underestimation of the peak overpressure. The weight factor is also not suitable for the specific-impulse parameter, because it would increase the specific impulse of an already conservative model. Alternatively, a better estimate of blast parameters can be obtained by modifying the UFC 3-340-02 charts based on the statistics of actual blast data, as provided in Table 6.
Closing Remarks UFC 3-340-02 (UFC 2008) and its predecessor [TM 5-1300 (USACE 1990)] have been used widely to generate overpressures and impulses for blast resistant design. The main limitation of the charts provided in UFC 3-340-02 is that they are based on an idealized TNT charge with an assumed spherical free-air or hemispherical surface burst. The charts are also based on field trials, in which pressure data were not directly measured, but were inferred from the arrival-time data. This paper presents the results of a controlled detonation of a large, highly explosive device (5,000 kg TNT) in Woomera, South Australia, and identifies some of the variabilities in the blast-wave parameters that must be expected in blast resistant design. Pressure measurements were made along two lines at identical standoff distances. The measured results along blast lines 1 and 2 at the same standoff distances were different, showing an asymmetrical blast-wave propagation. If such asymmetry in the response occurs with a controlled explosion, higher variability must be expected with an uncontrolled explosion. CFD analyses and charts from UFC 3-340-02 were used to estimate pressure histories for the Woomera trial. Two CFD models were developed, namely, (1) Model RF1.8 and (2) Model RF2. Model RF1.8 was developed using a factor of 1.8 on the charge weight, which was based on the assumption that some energy was lost in the formation of a crater. Model RF2 was developed using a factor of 2 for the charge weight. The analysis shows that the results of Model RF1.8 and the UFC 3-340-02 charts are in general agreement. Although significant discrepancies were evident in comparison to the Woomera trial results, Model RF2 provided relatively more accurate estimates of the peak overpressures and arrival time than the other methods; in contrast, Model RF1.8 and the UFC 3-340-02 charts provided better estimates of the specific impulse than Model RF2. CFD analysis and the UFC 3-340-02 charts generally underestimate the peak overpressure, with REs of less than 15% for most data points at scaled distances greater than 3 m=kg1=3 . However, there are significant differences between these computations and the results of the Woomera trial at scaled distances of 1.5 © ASCE
and 2.9 m=kg1=3 . At a scaled distance of 1.5 m=kg1=3 , the CFD analysis underestimates the peak overpressure at P3 (P8) by 73% (57%), whereas the UFC 3-340-02 charts underestimate the peak overpressures by 100% (82%). At a scaled distance of 2.9 m=kg1=3 , the CFD analysis underestimates the peak overpressure at P4 (P9) by 36% (29%), whereas the UFC 3-340-02 charts underestimate the peak overpressure by 44% (36%). The predictions of the specific impulse generally overestimate the trial results. The CFD analyses overestimate the specific impulse measured on blast line 1 by approximately 50%, whereas the UFC 3-34002 chart overestimates the specific impulse by approximately 58%. The results of the CFD analysis are in general agreement with the specific impulse recorded on blast line 2 in the Woomera trials, except on P9, where the CFD analysis overestimates the specific impulse by approximately 35%. The UFC 3-340-02 chart generally overestimates the specific impulse obtained on blast line 2 by approximately 15%, except at P9, where the trial result is overestimated by 41%. To establish an understanding of the variabilities of blast data recorded in the Woomera blast trial, the Woomera trial data set is compared against the previously published BFS and K-B data sets. The comparison between the Woomera trial results and the BFS data set showed that the predictions of both data sets deviated from UFC 3-340-02: The peak overpressure of the trial is significantly underestimated at less than 3-m=kg1=3 scaled distance, and the specific impulse of the trial is generally overestimated. The aforementioned trend of errors is not observed in the K-B data set, which contains a much lower standard deviation than the BFS data set. The following sources of error contribute to the discrepancies between the UFC 3-340-02 charts, the Woomera trial results, and the BFS data set: • Uncertainties in the K-B data set that resulted from the pressure and impulse data in the K-B data set being inferred from the arrival-time data; • Uncertainties associated with asymmetrical blast-wave propagation, which was observed in the Woomera trial; and • Variabilities associated with varying charge configurations, which were reported in the BFS data set. The statistical parameters obtained by dividing the data set into two samples (the first sample to represent the data points at standoff distances of 3 m=kg1=3 or less, and the second sample to represent the remaining data points) suggest that the UFC 3-340-02 predictions of the peak incident overpressures are more reliable at scaled distances greater than 3 m=kg1=3 . UFC 3-340-02 uses a factor of 1.2 on the charge weight to address uncertainties in the K-B data set. The data presented in this paper indicate that this factor is not large enough for the peak overpressure, and conservative for the specific impulse. Thus, it is not possible to suggest a universal weighting factor to address these uncertainties. One alternative and a more viable strategy than modifying the weighting factors to address these uncertainties would be to revise the charts to provide percentiles on blast loadings.
References Baker, W. E. (1973). Explosions in air, University of Texas Press, Austin, TX. Baker, W. E., Cox, P. A., Westine, P. S., Kulesz, J. J., and Strehlow, R. A. (1983). Explosion hazards and evaluation, Elsevier, New York. Beshara, F. B. A. (1994). “Modelling of blast loading on above ground structures. I: General phenomenology and external blast.” Comput. Struct., 51(5), 585–596.
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Bogosian, D., et al. (2002). “Measuring uncertainty and conservatism in simplified blast models.” U.S. Dept. of Defense 30th Explosives Safety Seminar, Atlanta. Brode, H. L. (1959). “Blast wave from a spherical charge.” Phys. Fluids, 2(2), 217–229. Chock, J. M. K., and Kapania, R. K. (2001). “Review of two methods for calculating explosive air blast.” Shock Vib. Digest, 33(2), 91–102. Davis, W. C. (1981). “High explosives: The interaction of chemistry and mechanics.” Los Alamos Sci., 2(1), 48–75. Davis, W. C. (1998). “Shock waves; rarefaction waves; equations of state.” Explosive effects and applications, J. A. Zukas and W. P. Walters, eds., Springer, New York. Donahue, L. K. (2009). “Afterburning of TNT detonation products in air.” M.Sc. thesis, Dalhousie Univ., Halifax, NS. Glasstone, S., and Dolan, P. J. (1977). The effects of nuclear weapons, U.S. Dept. of Defense and the Energy Research and Development Administration, Washington, DC. Kingery, C. N. (1966). Airblast parameters versus distance for hemispherical TNT surface bursts, Ballistic Research Laboratory, Aberdeen Proving Ground, MD. Kingery, C. N., and Bulmash, G. (1984). Airblast parameters from TNT spherical air burst and hemispherical surface burst, Ballistic Research Laboratory, Aberdeen Proving Ground, MD.
© ASCE
Kingery, C. N., and Coulter, G. A. (1983). Reflected overpressure impulse on a finite structure, Ballistic Research Laboratory, Aberdeen Proving Ground, MD. Kingery, C. N., and Pannill, B. F. (1964). Peak overpressure vs scaled distance for TNT surface burst (hemispherical charges), Ballistic Research Laboratory, Aberdeen Proving Ground, MD. Lee, E. L., Hornig, H. C., and Kury, J. W. (1968). “Adiabatic expansion of high explosive detonation products.” Lawrence Radiation Lab, California Univ., Livermore, CA. Needham, C. E. (2010). Blast waves, Springer, Heidelberg, Germany. Netherton, M. D., and Stewart, M. G. (2009). “The effects of explosive blast load variability on safety hazard and damage risks for monolithic window glazing.” Int. J. Impact Eng., 36(12), 1346–1354. Rose, T. A. (2006). A computational tool for airblast calculations, Air3d version 9 users’ guide, Cranfield Univ., Swindon, U.K. Sherkar, P, Whittaker, A. S., and Aref, A. J. (2010). “Modelling the effects of detonations of high explosives to inform blast-resistant design.” Technical Rep. MCEER-10-0009, New York. UFC (Unified Facilities Code). (2008). “Structures to resists the effect of accidental explosion.” UFC 3-340-02, Washington, DC. USACE (United States Army Corps of Engineers). (1990). “TM 5-1300 structures to resists the effect of accidental explosion.” TM 5-1300, Washington, DC.
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