UNCERTAINTY ANALYSIS IN BURIED LANDMINE BLAST CHARACTERIZATION DRDC-RDDC-2016-N029

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1 UNCERTAINTY ANALYSIS IN BURIED LANDMINE BLAST CHARACTERIZATION DRDC-RDDC-2016-N029 M. Ceh, T. Josey, W. Roberts Defence Research and Development Canada, Suffield Research Centre, PO Box 4000, Stn Main, Medicine Hat, Alberta, T1A 8K6, Canada ABSTRACT Detailed procedures for evaluating the protection levels for occupant survivability exist in Volume 2 of the Allied Engineering Publication 55 Procedures for Evaluating the Protection Level of Armoured Vehicles (AEP-55). Results in the past have shown an unexpectedly high variation in total impulse across similar test conditions. The variation in these results leaves questions about the type of explosive, experimental methods, and soil preparation procedures used in testing. Work was undertaken at the Suffield Research Centre of Defence Research and Development Canada to characterize this variation and to explore the test protocol so as to reduce this variability and improve understanding of the mechanisms affecting the repeatability of the impulse from a Level 2 blast test specified in AEP-55 Volume 2. In addition to field tests, a computer model was developed to provide a means to determine the most influential parameters that contribute to the variability seen in field tests. The developed computer model was used to determine the magnitude of the uncertainty associated with impulse from buried landmine blasts. These goals were achieved by combining a predictive model (Westine) and an uncertainty analysis framework (Monte Carlo Simulation). OBJECTIVE The procurement and employment of vehicles for use in military operations by the Canadian Armed Forces (CAF) requires a detailed understanding of the protection offered by these vehicles against threats on the modern battlefield. Operations in theatres as diverse as Bosnia, Eritrea, and Afghanistan have shown that CAF vehicles and their occupants are subjected to a variety of potentially lethal buried explosive threats including landmines and improvised explosive devices (IEDs). To ensure mission success, an improvement of the survivability of vehicles for CAF members is essential. This will be achieved through increased understanding of these threats and the resulting development of appropriate protection and mitigation strategies. Canada is an active participant in several international efforts to characterize and improve the survivability of military vehicles. NATO Standardization Agreement 4569 Protection Levels for Occupants of Armoured Vehicles (STANAG 4569) [1] specifies standardized protection levels from various threats. Although kinetic energy (artillery and direct fire) and blast mine protection levels are specified within STANAG 4569, the procedures for evaluating the protection levels and additional details on other types of threats are specified in Allied Engineering Publication 55 Procedures for Evaluating the Protection Level of Armoured Vehicles (AEP-55) [2]. AEP-55 is separated into several volumes - Volume 1 addresses kinetic energy and artillery threats, Volume 2 focuses on mine threats, Volume 3 concentrates on IED threats, while Volume 4 deals with chemical energy threats. AEP-55 Volume 2 addresses a number of topics related to vehicle testing against buried landmines including the test plan, evaluating occupant survivability Her Majesty the Queen in Right of Canada, as represented by the Minister of National Defence, 2016 Sa Majesté la Reine (en droit du Canada), telle que représentée par le ministre de la Défense nationale, 2016

2 using Anthropomorphic Test Devices (ATDs), injury criteria, instrumentation, explosive charge configuration, and test site preparation. Although AEP-55 Volume 2 specifies the test conditions for occupant survivability testing against landmines, some questions about the ability of the test protocol to generate repeatable results exist. DRDC Project 12RL was created to examine several aspects of the buried landmine testing including total impulse and impulse distribution in order to better understand the effects of buried landmines on vehicles. Tests at the DRDC Valcartier Research Centre showed an unexpectedly high variability between tests results in the total impulse imparted on a simple vehicle-like target from an explosive charge buried in soil. Therefore, additional work was undertaken to adjust the test protocol so as to reduce this variability. A project subcomponent (12RL03) examined the effects of test bed preparation on total impulse, while other parts of the parent project examined impulse distribution. Project 12RL03 at the DRDC Suffield Research Centre focussed on developing an understanding of the mechanisms affecting the repeatability of the impulse from a Level 2 blast test specified in AEP-55 Volume 2. This tasking involved two aspects, development and use of a software application tool, and field tests. The primary goal was to develop an understanding of these mechanisms so that a test condition for a landmine buried in soil could be reliably used to evaluate the survivability of a CAF vehicle. The project was completed and results were reported to the CAF [3]. The purpose of the computer modeling component of this project is to provide a means to determine the most influential parameters that contribute to the variability seen in experimental field tests. The developed computer model can also be used in determining the magnitude of the uncertainty associated with impulse from buried landmine blasts. These goals are achieved by combining a predictive computer model and an uncertainty analysis framework. The objective of this paper is to describe the development of the computer program used in this study, and discuss the results and their impact on the understanding of the mechanisms affecting the repeatability of the impulse from a Level 2 blast test. METHOD The purpose of the sensitivity and uncertainty analysis component of this project is to provide a means to determine the most influential parameters that contribute to the impulse result variability recorded in experimental field tests, and determine the magnitude of the uncertainty associated with impulse from buried landmine blasts. These goals are achieved by combining a predictive blast-impulse model and an uncertainty analysis framework into a software application tool. A software application tool was developed to investigate the uncertainty in impulse loading on a steel target plate (representative of a vehicle foot print) due to variability in experimental parameters and to provide insight into the uncertainty of loading experienced on the target used in experimental field trials. The general concept of the tool, shown graphically in Figure 1, is the use of a predictive blast-impulse model in association with uncertainty analysis methods. Uncertainty in stochastic input parameters (e.g., soil density, explosive mass and energy, target stand-off, and depth of explosive charge burial) is represented with user determined probability distributions.

3 A predictive blast-impulse model was chosen that reflects the test conditions used in the experimental field trials. In general, the test setup (Figure 2) consists of a cylindrical explosive charge of known size, mass, and depth of burial, emplaced in a prepared soil pit. The soil conditions (soil type, moisture content, particle size distribution, and density) are known. The explosive charge is positioned under a target of known mass and shape with a known stand-off from the surface of the soil pit. The target is designed in a way to allow the vertical displacement of the target to be measured during the explosive event. Figure 1: Predictive and uncertainty analysis model concept. Figure 2: Test apparatus (left) and soil pit (right).

4 Modified Westine Model The US Army Tank-Automotive Command Research and Development Center (TARDEC) developed a numerical model (i.e., the Westine model) to predict the loading from a buried landmine on a target plate [4]. The main goal of this model was to predict the impulsive load on the hull of a vehicle subjected to the explosion from a cylindrical shaped landmine. During the detonation of a landmine under a vehicle, the main load is impulsive in nature due to the soil ejecta impacting the underside of the vehicle. The output of the empirical model is the vertical scaled specific impulse at the point of impulse prediction. The model is specific to cylindrical type buried charges, and is capable of simulating a variety of explosives; along with the dimensions of the charge, the total energy release of the explosive are the only parameters required. The impulse loading model was developed using similitude theory (a model analysis and curve fitting of experimental test results) and experimental data from impulse plug tests. [4] A schematic of the Westine model and its parameters are shown in Figure 3. Figure 3: Westine model schematic. The inputs to the empirical model include soil and explosive parameters. The parameters are: W, energy release of the explosive S, standoff distance of the target from the center of the explosive A, cross-sectional area of the explosive d, depth of burial to the center of the explosive ρ, soil density X, lateral distance to the location of impulse prediction.

5 Using the energy release of the explosive parameter (W) allows any number of explosives to be represented and permits the Westine model to be explosive-type independent. For practical purposes, the energy release of the explosive can be correlated to the mass of the explosive through its heat of detonation as is shown in Equation (1). The explosive heat of detonation can be determined experimentally. Alternatively, if the heat of detonation for a particular explosive is unknown, a TNT equivalence factor can be used and multiplied to the heat of detonation of TNT to estimate the heat of detonation for the particular explosive. These equivalent factors can be found in the literature. Ultimately the Westine model relies on the energy release of the explosive and not the mass or type. (1) Limits to the empirical model are: The impulse load computed using the Westine model has large bounds on the results. The bounds are: The bounds provide insight into the accuracy of the model and are based on the scatter and variability of the experimental results. The empirical model has limited parameters to accurately represent soil conditions. The only parameter that can be varied is the soil density (i.e., there is no separate parameter for soil moisture, cohesion, or voids). The model states that the compressibility effects in the soil are secondary. The loading on the target occurs from the inertial effects of soil impact; hence the dominant soil property is mass. The Westine model was incorporated into a computer application to provide a distribution of impulse over a two-dimensional target plate. Example output from the application is shown in Figure 4. To determine the total impulse delivered to the plate the specific impulse per unit area is summed. The model predicts that the majority of the loading occurs directly above the mine, where the majority of the impulse from the soil ejecta is directed upwards. Past the edge of the mine the loading falls off rapidly as the distance from the mine is increased, as the area of highest specific impulse is directly above the mine.

6 Figure 4: Impulse distribution contour on a plate as predicted by the modified Westine Model. Uncertainty Analysis Framework The purpose of the Uncertainty Analysis Framework component of the software tool is to discover and analyze the parameters that contribute the most to the overall uncertainty in impulse distribution results from the modified Westine Model. This framework uses a parameter sensitivity analysis and quantifies uncertainty using uncertainty propagation analysis. The framework uses Perturbation Analysis [5] in the parameter sensitivity function of the framework to emphasize the most influential parameters. A Perturbation Analysis determines the effect of variability in single parameter values on the overall result. The parameter values are individually varied by a marginal amount (e.g., ±5%) while recording the resulting change in model output. The two goals of this analysis are to rank the parameters according to their influence on the results and to provide insight into these parameters (i.e., magnitude of influence) to inform about the implications of parameter variation. A sensitivity ratio, represented by SR, for each parameter is calculated using the following equation [5]: where represents the result after the perturbation; represents the result prior to perturbation; represents the parameter value after perturbation; and represents the parameter value prior to perturbation. (2)

7 Parameters chosen to be investigated are ranked based on their relative influence (i.e., higher SRs denote higher relative influence). Further analyses on the most influential parameters can then be conducted with uncertainty quantification techniques such as uncertainty propagation. In this analysis, uncertainty in designated parameters is represented with user specified probability distributions. The specified distributions are derived from available information (i.e., existing experimental data, literature, and expert judgment). Uncertainty propagation in the framework is achieved using Monte Carlo Simulation (MCS). Monte Carlo methods are computational algorithms that use repeated random sampling of input probability distributions to derive a resulting probability distribution of the model outcome [6]. In general, a large number (>10 4 ) of random samples, N, from chosen parameters (i.e., those of most interest, or the largest source of uncertainty) are passed through the modified Westine Model N times, resulting in N outcomes. Uncertainty in the model outcomes (total impulse for a given threat) are represented graphically with histograms. Quantification of the uncertainty for a given scenario can be assessed by calculating the likelihood of total impulse within a range of various confidence intervals. Modeled Parameters For the purpose of this study, parameters are segregated into two separate categories; trial procedure and material property parameters. Trial procedure parameters include target standoff from the explosive charge and charge mass, and are directly controlled by the experimental trial team through trial procedures. However, they are subject to variation due to error in trial procedure execution and error in measurement. The lateral offset of the explosive charge (from centre of target) is also a trial procedure parameter but has been determined to have a low influence on the outcome, and thus not included in the uncertainty analysis in this study. Material property parameters include test pit soil density and the explosive heat of detonation. Soil density is controlled through experimental trial setup procedures, but is prone to natural variation that is more difficult to reduce. Uncertainties in the actual values of parameters used in the Uncertainty Analysis Framework (analogous to those in the field trials) are represented using probability distributions (i.e., uniform, Weibull, normal, etc.) and are summarised in Table 1. The choice of distribution type is based on the nature of the natural parameter variability. Since a large amount of focus of this paper is on the procedures in place to reduce variation in impulse results, this uncertainty analysis uses different cases of uncertainty in these parameters to show the effect that inaccuracy has on the variation in results. Specifically, a baseline case of ±2.5% parameter variability is used, along with a mid-case of ±5% and high case of ±10%. For example, field trial experience indicates that the actual standoff of the target can vary by ±2.5% from the requirement of 40cm. Thus a representative probability distribution would be one that represents a high confidence range between 39cm to 41cm. In this study, a uniform distribution is used for the standoff distance since little is known about the nature of the actual variation in stand-off (i.e., the probability of a given value within the range). Since it is possible that the standoff distance could vary by more than the baseline ±2.5%, additional cases are explored (±5% and ±10%) to determine the effect of wider ranges in positioning inaccuracy on the impulse seen by the target.

8 The quality of the TNT cast (i.e., cracks, voids, and impurities) introduces a factor of uncertainty in the explosive output of the charge. This uncertainty is expressed using variability in the explosive heat of detonation. The uncertainty in the value of explosive heat of detonation is represented using a uniform distribution with bounds of ±1% [7]. The uncertainty associated with the mass of the explosive is due to the difference in masses between each trial, and the addition of the C4 booster. Based on measurements taken in the field and in the laboratory, explosive mass for 6kg nominal TNT charges (including C4 booster) are between 6.05kg and 6.30kg. A uniform probability distribution was chosen with a baseline range between 6.0kg and 6.15kg (based on the AEP 55 specification for Level 2 charge mass [2]). Additional ranges were explored using different cases to determine the effect of off spec explosive charges. A 2-parameter Weibull probability distribution is used to represent the uncertainty in the soil density of the pit. This distribution type was chosen based on the fit characteristics with the available density data gathered from a nuclear densometer. This analysis does not vary the uncertainty in this parameter as in the other parameters above. Other parameters such as explosive density, explosive depth, and explosive factor are kept constant. The target size is also kept constant since this is unchanging throughout the experimental trial series. Parameter Table 1: Representation of uncertainty in parameters used in the Uncertainty Analysis Framework. Initial Value Probability Distribution Distribution Parameters Explosive Density (kg/m 3 ) 1570 Constant Explosive Depth (m) 0.1 Constant Explosive Factor 1 Constant Explosive Heat of Detonation (m-kg/kg) 4.346E5 Uniform Min = 4.281E5 Max = 4.411E5 Explosive Mass (kg) 6 Uniform Min = 6.0 Max = 6.15 Soil Density (kg/ m 3 ) 2237 Weibull k = 65.1 λ = 2335 Target Width and Length (m) Constant Target Standoff (m) 0.4 Uniform Min = 0.39 Max = 0.41

9 RESULTS Results from the perturbation analysis are presented below in Figure 5. These results show that the impulse results are most sensitive to variation in the target standoff, with a SR of Thus a 1% variation in standoff results in a 0.6% variation in impulse. The negative sign indicates that an increase in standoff results in a decrease in impulse. Impulse results are less sensitive to the explosive heat of detonation, soil density, and charge mass, which have an SR of This is followed by target size (0.43), depth of burial (0.36), and charge offset (0.03). Parameter Standoff Explosive Heat of Detonation Soil Density Charge Mass Plate Size Depth of Burial Charge Offset SR Figure 5: Perturbation Results from the Uncertainty Analysis Framework. In this exercise, an uncertainty propagation analysis is performed to investigate the effect of and quantify the uncertainty within the target standoff, explosive heat of detonation, soil density, and charge mass parameters used in the modified Westine Model. Results of the baseline uncertainty propagation analysis are presented in Figure 6 and Table 2. Based on the baseline level of parameter uncertainty (see Table 1), there is a 95% confidence that the experienced impulse will be 2.6% under the average impulse and 2.3% above the average. Frequency Impulse (N s) Frequency Cumulative % % 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% Figure 6: Baseline Uncertainty Propagation Results

10 Table 2: 95% Confidence Range for the Baseline Case Range Case 95% Confidence Range Low (% of Mean) High (% of Mean) Baseline (2.5%) % Further information about the effects of uncertainty in target standoff can be derived with two additional variability cases (±5% and ±10%). These cases represent situations where accuracy in placing the target and/or explosive charge is low or unknown. The results shown in Figure 7 and Table 3 and demonstrate that accuracy and repeatability in target standoff play a significant role in the repeatability of impulse, with total variability about the average in impulse results of 8% and 13% for the mid and high cases respectively. As with standoff, an analysis on the effect of uncertainty in explosive mass was conducted, with +5% and +10% range cases. The results are shown in in Figure 7 and Table 3. A +10% range in standoff increases the uncertainty in impulse results, with a high value in the 95% confidence range of a 7.5% variation about the average. It is likely that a combination of inaccuracies in target standoff and explosive mass exist. Further analysis uses the combined ranges explored above to perform an aggregated uncertainty analysis for higher levels of uncertainty. Results are shown in Figure 7 and Table 3. These results show that in the high uncertainty case (10%), the confidence range increases to a 14.5% total variation about the average. Table 3: 95% Confidence Range for Variation about the Average Total Impulse for Stand-off, Explosive Mass, and Combined Parameter Uncertainty Stand-off Variation Explosive Mass Combined Variation Variation Range Case Low High Low High Low High Baseline (2.5%) -2.6% 2.3% -3.1% 2.3% -3.1% 2.3% Mid (5%) -3.6% 4.4% -3.1% 2.8% -4.1% 4.0% High (10%) -6.2% 7.0% -4.1% 3.4% -7.7% 6.9%

11 Cumulative Frequency 100% 80% 60% 40% 20% Standoff Variation 0% Impulse (N s) Cumulative Frequency 100% 80% 60% 40% 20% Explosive Mass Variation 0% Impulse (N s) Cumulative Frequency 100% 80% 60% 40% 20% Combined Variation 0% Impulse (N s) Baseline Mid High Figure 7: Uncertainty in Impulse from Variation in Uncertainty in Stand-off (top), Explosive Mass (middle), and Combined Parameters (bottom). CONCLUSIONS Computer modeling and experimental testing indicates that the resulting impulse imparted to a target from an exploding buried charge is sensitive to small changes in some parameters, which likely explains experimental field trial variability. These parameters need to be closely controlled and monitored to ensure that tests of military vehicles are both realistic and repeatable. Due to the

12 size of the test apparatus and soil pits there is a high probability that inconsistencies and errors in target placement and explosive charge mass will occur and will contribute to variability in results. Based on the results of computer modelling, the vertical position of the test apparatus in relation to the explosive charge has been indicated as being very influential to the imparted impulse. An inaccurate measurement or inconsistency in the vertical position of the test apparatus between trials will result in a variation of trial results. Measuring and controlling the standoff of the target relative to the charge position requires a high degree of precision. Therefore, the surface of the test pit must be flat and level. With an uneven surface, this cannot be accurately measured and controlled. Additionally, the computer model assumed that the target was level to the soil. Any rotation of the target off of level will add to the variability of the impulse results. The variation in target stand-off will likely be in addition to other effects, such as from soil pit properties, explosive charge mass and energy variations (due to inconsistencies in charge construction and materials). The additional uncertainty introduced through these other parameters has the potential to push the bounds of confidence in impulse results to unacceptable levels. In order to limit the variation in impulse results in AEP-55 testing, researchers and engineers should strive to reduce controllable variability in key test parameters. The likely consequence of failing to do so will be unacceptable scatter in results, leading to further uncertainty in comparison of vehicle blast resistance performance. REFERENCES [1] NATO Standardization Agency, 2011, Protection Levels for Occupants of Armoured Vehicles. [2] NATO Standardization Agency, 2011, Procedures for Evaluating the Protection Level of Armoured Vehicles, AEP-55, Volume 2. [3] Ceh, M., W. Roberts and T. Josey, 2016, Characterization of Buried Charge Loading: Examination of Level Two Charges, DRDC - Suffield Research Centre, DRDC-RDDC-2016-R043 (C). [4] Westine, P. S., B. L. Morris, C. P.A. and P. E.Z., 1985, Development of Computer Program for Floor Plate Response from Land Mine Explosions, Southwest Research Institute for US Army Tank Automotive Command Research and Development Center, [5] Heijungs, R. and R. Kleijn, 2001, Numerical approaches towards life cycle interpretation five examples, The International Journal of Life Cycle Assessment, 6, [6] Morgan, M. G., M. Henrion and M. Small, 2003, Uncertainty: A Guide to Dealing with Uncertainty in Quantitative Risk and Policy Analysis, Cambridge, UK, Cambridge University Press. [7] Cooper, P. W., 1996, Explosives Engineering, USA, Wiley-VCH.