numerical study of soil modelling approaches using ls-dyna: part...

Numerical Study of Soil Modelling Approaches

using LS-DYNA: Part 2

Project Lead: Laura Donahue

Prepared by:

Martec Limited 400-1888 Brunswick Street Halifax, NS B3J 3J8Tel: (902) 425-5101, Ext. 279Québec, QC G1P 4P5

Contract number: W7701-063750/001/QCL(Task1) Scientific Authority: Amal Bouamoul, 418-844-4000 Ext. 4588

Grant McIntosh, 418-844-4000 Ext. 4278

Defence R&D Canada – ValcartierContract Report

DRDC Valcartier CR 2009-164April 2009

The scientific or technical validity of this Contract Report is entirely the responsibility of the contractor and thecontents do not necessarily have the approval or endorsement of Defence R&D Canada.

Numerical Study of Soil ModellingApproaches using LS-DYNA: Part 2

Contract: W7701-063750/001/QCL (Task 1)

Project Lead: Laura DonahueMartec Limited400-1888 Brunswick StreetHalifax, NS B3J 3J8Tel: (902) 425-5101, ext 279

Scientific Authorities: Dr. Amal Bouamoul / Dr. Grant McIntoshWeapons Effects and Protection Section, DRDC ValcartierTel: (418) 844-4000

UNCLASSIFIED

The scientific or technical validity of this Contract Report is entirely the responsibility ofthe contractor, and the contents do not necessarily have the approval or endorsement ofDefence R&D Canada

L’entrepreneur est entièrement responsable de la validité scientifique ou technique de cerapport de contrat, et le contenu de ce rapport n’est pas nécessairement approuvé nientériné par R et D pour la défense Canada.

Defence R&D Canada - Valcartier

Contract Report

DRDC Valcartier CR 2009-164

April 2009

Authors

Dr. Rick Link, P. Eng. Dustin Pearson

Co-Authored and Reviewed by

Laura Donahue, P. Eng.

Project Lead

Publication approved by

David Whitehouse, P. Eng.

Manager, Combustion Dynamics Group

Terms of Release: This document contains proprietary information. It is provided tothe recipient on the understanding that proprietary and patent rights will be respected.

Conditions de diffusion: Ce document renferme de l’information exclusive. Lesdroits de propriété et les droits attachés au brevet doivent être respectés.

© Her Majesty the Queen as represented by the Minister of National Defence, 2009

© Sa majesté la reine, représentée par le ministre de la Défense nationale, 2009

1.0 Abstract

This report is a continuation of a previous modelling study (Martec Technical ReportTR-07-21) for sand under high strain rate loading. The objective of this project is toinvestigate the suitability of several LS-DYNA material models to simulate Valcartiersoil response under landmine loading conditions.

Parameters for the two soil material models were determined using in-situ soilmeasurements, validated for simple triaxial tests, and used to simulate a DRDCValcartier experiment with a 6.0 kg landmine charge.

The material models used gave comparable crater sizes and shapes. The craterdepths agreed relatively well with experimental data; however, there were significantdifferences between predicted and measured crater radii. Limited parametric studieswere performed on soil strength and mine detonation model, but these did not yieldagreement with experiment.

The cause of the discrepancy between the numerical and experimental crater sizes isunknown at this time. Differences could be due to additional soil physics that are notconsidered in the numerical models, or by unknown factors in the experimentalconfiguration. For comparison purposes, a brief literature survey was performed, andcrater shapes from other numerical simulations included.

2.0 Résumé

Ce rapport est la continuation d’une étude antérieure de modélisation (MartecRapport Technique TR-07-21) du sable soumis à de grandes déformations. L’objectifdu projet est d'évaluer le potentiel de plusieurs modèles de LS-DYNA à simuler laréponse du sol de RDDC Valcartier pour des mines enfuis.

Les paramètres utilisés pour deux modèles de sol ont été évalués en utilisant desmesures géotechniques du sol local. Les modèles du sol ont été vérifiés avec destests fondamentaux de compression, cisaillement, et tension, et utilisés pour lasimulation d’essais faits à RDDC Valcartier pour une mine enfuit de 6.0 kg.

Les résultats des modèles ont donnés des tailles et formes de cratères comparables.La profondeur des cratères correspond relativement bien avec les mesuresexpérimentales. Cependant, il y a des différences significatives entre les rayons descratères prédis et ceux mesurés. Des études paramétriques limitées ont été réaliséessur la force du sol et des modèles de détonation de mines, mais ceux-ci n'ont pasaméliorées la corrélation avec les essais.

L'écart obtenu entre les résultats numériques et expérimentaux des dimensions descratères est inconnu actuellement. Les différences pourraient être dues à des

paramètres de la physique des sols non considérés dans les modèles numériques,ou par des facteurs inconnus dans la configuration expérimentale. Pour fin decomparaison, une petite recherche bibliographique a été complétée, et des formesde cratères générés par d'autres simulations numériques ont été incluses.

Smart Solutions for Engineering, Science and Computing

Smart Solutions for Engineering, Science & Computing

Martec Limited tel. 902.425.5101 1888 Brunswick Street, Suite 400 fax. 902.421.1923

Halifax, Nova Scotia B3J 3J8 Canada email. [email protected] www.martec.com

Numerical Study of Soil Modeling Approaches Using LS-DYNA: Part 2

Martec Technical Report TR-09-23

April 2009

Prepared for:

Amal Bouamoul Grant McIntosh

DRDC Valcartier – WEP Section 2459 Boul. Pie XI North

Quebec, QC Canada G3J 1X5

Martec is a member of the Lloyd’s Register Group

REVISION CONTROL

REVISION REVISION DATE

PROPRIETARY NOTICE

This report was prepared under Contract W7701-063750/001 (Task 1) – DRDC Valcartier andcontains information proprietary to Martec Limited.

The information contained herein may be used and/or further developed by DRDC Valcartierfor their purposes only.

Complete use and disclosure limitations are contained in Contract W7701-063750/001 (Task1) – DRDC Valcartier.

EXECUTIVE SUMMARY

This is an interim report for Task Authorization Contract (W7701-063750/001) Task 1,“Numerical Study of Soil Modeling Approaches using LS-DYNA: Part 2”. The objective ofthis project was to investigate the suitability of several LS-DYNA material models to simulateValcartier soil effects under landmine loading conditions. This project is a continuation of aprevious modeling study (described in Martec Technical report TR-07-21 [1]), in whichmodels for sand were developed.

This report describes the re-derivation of parameters and the verification testing performed forthe two material models, using the new Valcartier soil test results. The material modelsinvestigated were then used in the simulation of a DRDC Valcartier experiment involving a6.0 kg landmine charge.

The material models studied gave comparable crater sizes and shapes. While the crater depthsagreed relatively well with experimental data (within 16%), there were significant differencesbetween the predicted and measured crater radii. An investigation into the effect of soilstrength was performed by parametrically varying the soil friction angle in the soil models.Although reducing the soil strength did produce larger diameter craters, agreement with theexperimental measurement was not obtained.

The effect of the explosive modelling approach was determined using Chinook. Simulationresults using the standard balloon analogue approach (explosive represented by high-pressure,high-temperature detonation products), were compared to results obtained by explicitlymodelling the detonation propagation through the explosive. The resulting crater shape wasidentical between methods.

The exact cause of the discrepancy between the numerical and experimental crater sizes isunknown at this time. Differences could be due to additional soil physics which are notaccounted for in the numerical models, or alternatively by factors in the experimentalconfiguration which have not been accounted for. For comparison purposes, a brief literaturesurvey was performed and crater shapes from other numerical exercises included.

TABLE OF CONTENTS

1.0 INTRODUCTION.....................................................................................................................................1

2.0 SOIL MODEL VERIFICATION TESTS...............................................................................................2

2.1 COMPRESSION TESTS ..............................................................................................................................32.2 SHEAR TESTS ..........................................................................................................................................32.3 TENSILE TESTS........................................................................................................................................4

3.0 VALIDATION SIMULATIONS .............................................................................................................5

3.1 DESCRIPTION OF DRDC TEST.................................................................................................................53.2 NUMERICAL DOMAIN DESCRIPTION........................................................................................................63.3 RESULTS OF BASELINE TESTS .................................................................................................................93.4 FRICTION ANGLE VARIATION ...............................................................................................................12

4.0 EFFECT OF MODELING CHARGE DETONATION ......................................................................17

5.0 DISCUSSION AND CONCLUSIONS ..................................................................................................21

5.1 BRIEF LITERATURE SEARCH RESULTS ..................................................................................................215.2 CONWEP STUDY .................................................................................................................................235.3 CONCLUSIONS AND RECOMMENDATIONS..............................................................................................23

6.0 REFERENCES........................................................................................................................................24

APPENDIX A: CORRECTIONS TO FINAL REPORT FROM STUDY PART 1

APPENDIX B: LS-DYNA MATERIAL KEYWORDS FOR VALIDATION CASE

LIST OF FIGURES

FIGURE 2-1: VERIFICATION TEST GEOMETRY ............................................................................................................2FIGURE 2-2: COMPACTION CURVE COMPARISON .......................................................................................................3FIGURE 3-1: TEST CONFIGURATION ...........................................................................................................................5FIGURE 3-2: EXPERIMENTAL CRATER PROFILE ..........................................................................................................6FIGURE 3-3: QUARTER-SYMMETRIC MODEL..............................................................................................................7FIGURE 3-4: DIMENSIONED MODEL PROFILE .............................................................................................................8FIGURE 3-5: TIME STEP VARIANCE DURING ANALYSIS ..............................................................................................9FIGURE 3-6: TIME-HISTORY OF CRATER RADIUS – 42.8º FRICTION ANGLE..............................................................10FIGURE 3-7: TIME-HISTORY OF CRATER DEPTH – 42.8º FRICTION ANGLE ...............................................................10FIGURE 3-8: CRATER AT T = 6 MS (LEFT) MAT_PSEUDO_TENSOR (RIGHT) MAT_SOIL_AND_FOAM............11FIGURE 3-9: CRATER AT T = 30 MS (LEFT) MAT_PSEUDO_TENSOR (RIGHT) MAT_SOIL_AND_FOAM..........12FIGURE 3-10: MEASURED CRATER DEPTH WITH SOIL FRICTION ANGLE VARIATION ...............................................13FIGURE 3-11: MEASURED CRATER RADIUS WITH SOIL FRICTION ANGLE VARIATION .............................................13FIGURE 3-12: 2° FRICTION ANGLE (LEFT) T = 6 MS, (MIDDLE) T = 30 MS, (RIGHT) T = 50 MS ....................................14FIGURE 3-13: 20° FRICTION ANGLE (LEFT) T = 6 MS, (MIDDLE) T = 30 MS, (RIGHT) T = 50 MS ..................................15FIGURE 3-14: 42.8° FRICTION ANGLE (LEFT) T = 6 MS, (MIDDLE) T = 30 MS, (RIGHT) T = 50 MS ...............................15FIGURE 3-15: 60° FRICTION ANGLE (LEFT) T = 6 MS, (MIDDLE) T = 30 MS, (RIGHT) T = 50 MS ..................................16FIGURE 3-16: 80° FRICTION ANGLE (LEFT) T = 6 MS, (MIDDLE) T = 30 MS, (RIGHT) T = 50 MS ..................................16FIGURE 4-1: CHINOOK MESH IN CHARGE VICINITY .................................................................................................18FIGURE 4-2: EARLY-TIME SOIL SHAPE (LEFT) BALLOON (RIGHT) DETONATION ......................................................18FIGURE 4-3: LATER-TIME CRATER SHAPES - BALLOON MODEL ..............................................................................19FIGURE 4-4: LATER-TIME CRATER SHAPES – DETONATION MODEL ........................................................................19FIGURE 4-5: COMPARISON OF CHINOOK BALLOON MODEL AND LS-DYNA CRATER DEPTHS ................................20FIGURE 4-6: COMPARISON OF CHINOOK BALLOON MODEL AND LS-DYNA CRATER RADII....................................20FIGURE 5-1: CRATER SHAPE AND EXPERIMENTAL COMPARISON FROM [6]..............................................................21FIGURE 5-2: AUTODYN CRATER SHAPE FROM [7].................................................................................................22FIGURE 5-3: CRATER SHAPE COMPARISON FROM [7] ...............................................................................................22

LIST OF TABLES

TABLE 3-1: CHARGE DETAILS ....................................................................................................................................5TABLE 3-2: EXPERIMENTAL BLAST SOIL PARAMETERS .............................................................................................6TABLE 3-3: EXPERIMENTAL CRATER DIMENSIONS ....................................................................................................6TABLE 3-4: ELEMENT DIMENSIONS............................................................................................................................8TABLE 5-1: CONWEP CRATER CALCULATIONS FOR 6.0 KG C4 AT A 0.2 M DEPTH OF BURIAL ...............................23

Numerical Study of Soil Modeling ApproachesUsing LS-DYNA: Part 2 1

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1.0 INTRODUCTION

The objective of this project is to investigate the suitability of several LS-DYNA materialmodels to simulate Valcartier soil. Specifically, the performance of these models insimulations of landmine blasts is tested. This project is a continuation of a previous modelingstudy (described in Martec Technical Report TR-07-21 [1]), in which models describing sandwere developed. To evaluate the effectiveness of the models, simulations of a DRDC Suffieldpiston-apparatus trial involving small-scale charges in sand were performed.

In the first phase of the project, parameters for the two models investigated in the previousstudy (*MAT_SOIL_AND_FOAM and *MAT_PSEUDO_TENSOR) were re-derived usingthe new Valcartier soil test results. In the second phase, the soil models were verified bysimulating fundamental compression, shear, and tensile tests on small three-dimensional cubesamples. Finally, the two models were used in the simulation of a 6.0 kg landmine experiment,with comparisons made to the observed crater size.


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2.0 SOIL MODEL VERIFICATION TESTS

Three 3-D, one element tests were performed using both *MAT_SOIL_AND_FOAM and*MAT_PSEUDO_TENSOR. These included:

1) Hydrostatic compression – the soil is compressed using equal loading and confiningstresses i.e.

321

2) Shearing – the soil is compressed using a stress path that violates the yield surfacecriterion. For a successful test, the stresses should be scaled back so that the yield criterion(Equation A.2) is attained i.e. the computed friction angle should be identical to the one inputinto LS-DYNA.

3) Tension – the soil is loaded with a small hydrostatic tensile stress. The calculated stressshould be zero for cohesionless soils i.e. the soil cannot support tension.

The numerical model geometry is shown in Figure 2-1. The element is a 1.0 m cube, withsliding boundary conditions along the planes x = 0, y = 0, and z = 0.

Figure 2-1: Verification Test Geometry

The Excel file “Valcartier Soil Model.xls” generated in the previous study was used togenerate the necessary constitutive input for both models using the Queformat data for theValcartier soil. Several corrections to the equations given in the previous report [1] are givenin Appendix A.

3

3

1

x

y

z


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The relevant soil test parameters input to the spreadsheet are:

Wet Density: 2265.0 kg/m3

Dry Density: 2104.0 kg/m3

Internal Friction Angle: 42.8º

2.1 COMPRESSION TESTS

The soil is compressed isotropically to 6.95x108 Pa. Figure 2-2 gives a plot of pressure as afunction of volumetric strain; only one set of output data is plotted, since the results areidentical. It is apparent that the output curve follows the input curve, meaning the materialmodels have passed the test.

Figure 2-2: Compaction Curve Comparison

2.2 SHEAR TESTS

The stress path chosen is one that violates the yield criterion of Equation A.2

71 1095.6 Pa

732 1050.0 Pa


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resulting in a stress path angle on the p-q plot of 40.9 degrees. The stress output values forboth models are

71 1095.6 Pa

732 10327.1 Pa

resulting in a computed internal friction angle of 42.8 degrees, which is the input angle of thefailure envelope. Therefore, both models pass this test. It is noted here that the elementundergoes rapid lateral expansion as a result of the lateral stresses not being in equilibrium.

2.3 TENSILE TESTS

The element is isotropically expanded with the stresses

4321 1000.1 Pa

The resulting stresses from both models are zero, indicating that the cohesionless soil cannotsupport tension. As well, the element undergoes large expansions due to the internal stressesand external loads not being in equilibrium. Both models pass this test.


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3.0 VALIDATION SIMULATIONS

To evaluate the effectiveness of the two material models, simulations of a DRDC Valcartier6.0 kg landmine experiment in soil were performed. The experimental parameters are given inSection 3.1, and the numerical configuration in Section 3.2. Calculation results using the actualexperimental soil conditions are given in Section 3.3, followed by results of a parameter studyin which the soil friction angle was varied to investigate the effect of soil strength on theresults.

3.1 DESCRIPTION OF DRDC TEST

The main parameters required to simulate the landmine blast are the soil overburden, and thetype, mass and dimensions of the explosive. The DRDC experimental configuration is given inFigure 3-1 and Table 3-1. This data corresponds to experimental test T-1 performed on April25, 2008.

Figure 3-1: Test Configuration

Table 3-1: Charge Details

Type C4Diameter (mm) 245Height (mm) 75Soil Overburden (mm) 205Depth of Burst (mm) 242NEQ (kg) 6.0

In order to accurately simulate the soil response, the soil conditions from the experimentalblast are required. This data is provided below in Table 3-2.


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Table 3-2: Experimental Blast Soil Parameters

Location Wet Density (kg/m^3) Moisture (%)

South-East 2219 2.2South 2133 2.1

North-West 2175 2Average 2176 2.1

The crater depth, radius and profile are used to compare the simulation to the experimentalblast. The experimentally-observed crater dimensions are shown below in Table 3-3 and theprofile displayed in Figure 3-2.

Table 3-3: Experimental Crater Dimensions

Minimum 2012Apparent Radius (mm)

Maximum 2138Apparent Depth (mm) 529

Figure 3-2: Experimental Crater Profile

3.2 NUMERICAL DOMAIN DESCRIPTION

Analyses were executed using LS-DYNA version 971. The computational mesh was createdusing Hypermesh 9.0 exclusively.

Ideally, simulations would be performed by taking advantage of the axial-symmetry of theproblem. However, the axisymmetric element formulation is not available for ALEcalculations. Therefore the model was created using quarter symmetry (Figure 3-3). Modellingquarter symmetry requires manipulating the boundary conditions applied to the element nodesalong the planes of symmetry. A mesh bias was also utilized to increase the computationalefficiency. By gradually increasing the element size in the far field, the charge and near-fieldregion could be meshed with a relatively high-resolution mesh while maintaining a practicalcell count. The details of the bias, cell size, and count follow in Figure 3-4 and Table 3-4. Themodel must be as efficient as possible because it is so large and an increased cell countincreases the required analysis time. Simulating the landmine blast involves a large model to


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reduce the effect of boundary interactions. The domain boundaries were reflecting and placedfar from the region of interest.

Figure 3-3: Quarter-Symmetric Model

Figure 3-4 below is the dimensioned profile of the landmine blast model. The details of thecell dimensions are given in Table 3-4 with reference to the sections assigned in the figure.These sections, contain a mesh bias that pertains to a particular section and direction. Thedirection arrow below or beside the assigned section indicates the direction in which theelements are described in the table.

The quarter symmetric model contains a total of 346,762 cells. The charge was meshed with1.5 cm cells (8 cells in radius x 5 cells in height), for a total of 280 cells. The chargedimensions modeled (126.2 mm radius, 77.3 mm height) were slightly different than the actualcharge dimensions (122.5 mm radius, 75 mm height). The experimental dimensions and massgive an explosive density of 1687 kg/m3, which exceeds the theoretical maximum density ofC4 (~1657 kg/m3). The charge dimensions were modified to give a density equal to that usedin the previous project (density of 1550 kg/m3). The charge dimensions and placement weremodified such that the charge mass, aspect ratio, and soil overburden were conserved.


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Figure 3-4: Dimensioned Model Profile

Table 3-4: Element Dimensions

Element Dimension Variation (mm)Section

From To

Section Length(mm)

T1 17.98 650 7873.8T2 15.77 15.77 126.2A1 18.08 24.7 659.7A2 32.38 359.6 4900S1 17.67 22.13 205S2 15.46 15.46 77.3S3 19.71 26.7 358S4 33.04 367 5000


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3.3 RESULTS OF BASELINE TESTS

Simulations of the experimental configuration using the MAT_PSEUDO_TENSOR and theMAT_SOIL_AND_FOAM materials were performed. The parameters for these models aregiven in Appendix B. The parameters were determined assuming a soil friction angle of 42.8°,as was found in the Quéformat soil tests. The effect of soil friction angle is investigated inSection 3.4.

A large difference between the two materials is the required analysis time, and moreimportantly the time step size determined by LS-DYNA. While MAT_PSEUDO_TENSORhas a constant time step throughout the analysis, MAT_SOIL_AND_FOAM has a decreasingtime step. A decrease in time step is a notable issue because it extends the required run timewhich decreases the efficiency of the analysis. Figure 3-5 displays the two material time steptrends.

Figure 3-5: Time Step Variance during Analysis

The overall trend in the MAT_SOIL_AND_FOAM curve is a decreasing time step. The modelwas not analysed until the minimum time step was reached due to the resulting excessive runtimes.

Other than the varying time step, the two models also calculated different but similar craterradii and depths for the same analysis duration. Figure 3-6 and Figure 3-7 describe the time-histories of the crater depth and radius patterns for each material. The crater radius wasmeasured at ground level from the charge center axis to the inner edge of the crater, as shownin Figure 3-2.


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Figure 3-6: Time-History of Crater Radius – 42.8º Friction Angle

Figure 3-7: Time-History of Crater Depth – 42.8º Friction Angle


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Neither soil model correctly predicted the experimental crater radius or depth. The physicalblast created a minimum crater radius of 2012 mm and the model predicted a radius of 675mm; incomparable to the experimental blast. The simulated depth was, however, similar to theexperiment. A crater depth of 529 mm was measured in the test blast while 615 mm was thedepth achieved by the MAT_SOIL_AND_FOAM analysis; a difference of 16%. Both craterradius and depth curves depict the same trend with MAT_PSEUDO_TENSOR producing alarger crater in terms of depth and radius. For both materials, the largest crater deformationoccurs in the first ~ 10 ms.

When comparing the crater profiles, the differences between the two materials becomes moreapparent, as shown in Figure 3-8 and Figure 3-9 (contours illustrate the volume fraction ofsoil). At approximately t = 6 ms, the crater profile for MAT_SOIL_AND_FOAM is identicalto that of MAT_PSEUDO_TENSOR, demonstrating how similar the two materials behave atthe initial stages of the analysis. The craters have identical depths, radius and slopes, and bothsoil models have soil ejecta dispersed in much the same pattern.

At later times, differences in the two models become more apparent. From Figure 3-6 andFigure 3-7, the depth and radius are shown to reach a fairly constant value at later times;however this does not indicate a fully-formed crater. Comparison of the t = 6 ms and 30 msprofiles shows that crater slope does not only change due to the increase in radius and depthbut due to the material diffusion. At t = 30 ms the difference between the two materialdefinitions becomes more apparent as the crater shape, slope, radius, depth, and soil ejectapattern differs.

Figure 3-8: Crater at t = 6 ms (left) MAT_PSEUDO_TENSOR (right)MAT_SOIL_AND_FOAM


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Figure 3-9: Crater at t = 30 ms (left) MAT_PSEUDO_TENSOR (right)MAT_SOIL_AND_FOAM

3.4 FRICTION ANGLE VARIATION

Although the crater depth predicted in the LS-DYNA analyses agreed reasonably well with theexperimental observations, there were considerable differences in the crater radius. Todetermine the effect of the soil friction angle on the results, a series of additional calculationswere performed. Because of the faster computation times, this study was performed using onlythe MAT_PSEUDO_TENSOR model.

The original data set, described in Section 3.3, was created using a friction angle of 42.8°.Modelling the soil with friction angles of 2°, 20°, 60° and 80° was performed to determine thefriction angle impact on crater radius and depth. Figure 3-10 and Figure 3-11 give the craterradius and depth histories as a function of the friction angle.


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Figure 3-10: Measured Crater Depth with Soil Friction Angle Variation

Figure 3-11: Measured Crater Radius with Soil Friction Angle Variation


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By varying the soil friction angle both the crater radius and depth are influenced. In general, anincrease in friction angle leads to a decrease in both crater radius and depth. However, this wasnot the case for the friction angle of 80°. At this angle, the radius and depth were larger than asoil with 60° friction angle. Although the craters for both angles are very similar in shape andsize, this anomaly should be noted.

Even by varying the soil friction angle, the experimental radius and depth were still notcaptured. A large friction angle produced a crater depth that was similar but did not have acomparable crater radius. At even the smallest friction angle, the experimental blast craterradius was not achieved.

From Figure 3-10 and Figure 3-11, it can be concluded that the increase in friction angleincreases the speed at which the maximum crater size is obtained. However, the increase in thefriction angle also leads to instabilities in the crater profile. The following figures give thecrater profiles for the friction angles simulated:

Figure 3-12 to Figure 3-16 display the crater profiles (given by the volume fraction of soil), forsoil models with friction angles of 2°, 20°, 42.8° (angle used in main study), 60°, and 80° att = 6, 30 and 50 ms. These figures have been presented to display how the crater profilechanges throughout the analysis. For soil models with a friction angle less than 42.8°, thecrater shape remains parabolic. For soil models with a friction angle greater than 20°, thedispersed ejecta decreases and the crater shape does not remain parabolic throughout theanalysis. With a friction angle greater than 42.8°, the crater shape is initially erratic anddissimilar to the lower friction angle crater profiles.

Figure 3-12: 2° Friction Angle (left) t = 6 ms, (middle) t = 30 ms, (right) t = 50 ms


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Figure 3-14: 42.8° Friction Angle (left) t = 6 ms, (middle) t = 30 ms, (right) t = 50 ms


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4.0 EFFECT OF MODELING CHARGE DETONATION

In all simulations performed in both Parts 1 and 2 of the soil modeling study, the detonation ofthe explosive was not explicitly modeled. In a common explosives-modeling technique, thecharge was represented by a volume of high pressure, high temperature gas with a mass andenergy equal to that of the actual explosive (“balloon-analogue” model). Because of thediscrepancy between the numerical and experimental results, the assumption that the chargecould be adequately modeled using the balloon analogue approach was tested.

The effect of the balloon analogue model was investigated by performing a simulation wherethe actual charge detonation was captured, and comparing the crater shapes from the twoapproaches. In both Chinook simulations (balloon and detonation), the explosive productswere solved using the JWL equation of state. In order to effectively model the detonation, ahigh mesh resolution in the charge was necessary, and it was not practical to simulate the blastin three dimensions. Because 2D axisymmetric ALE simulations cannot be performed in LS-DYNA, the effect of modelling the detonation was investigated using Chinook.

The Chinook multi-material approach has been used in previous landmine projects [3, 4]. Invalidation simulations, the predicted impulse delivered to a target due to a buried chargeagreed well with experimental values. However, because strength effects are not included inthe Chinook model, the crater shapes should be comparable to the low friction angle LS-DYNA calculations. The Chinook simulations were performed to determine the relative effectof modelling the detonation, as opposed to directly comparing the results to the experimentaldata.

The Chinook domain extended approximately 20 m from the charge in all directions to ensurethat no boundary interactions would influence the results. The domain was meshed using acombination of triangular and quadrilateral elements, with small cells located near the chargeand larger cells at the domain boundaries (approximately 160,000 total cells). Figure 4-1illustrates the mesh in the vicinity of the charge. A cell size of 2 mm was used in the charge toeffectively capture the detonation propagation due to initiation from a point at the bottomcentre (63 cells in radius, 39 in height). The detonation modeling approach, described in [5],has been used in multiple previous projects and papers.

The early-time deformed soil shapes are shown in Figure 4-2 for both methods. The contoursgive the volume fraction of the solid component; in Chinook, soil is modelled as a mixture ofair, water, and a solid. There are very slight differences in the soil shapes when modelling theexplosive detonation. However, these very small differences cannot be perceived at later times(Figure 4-3 and Figure 4-4).


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Figure 4-1: Chinook Mesh in Charge Vicinity

Figure 4-2: Early-Time Soil Shape (left) Balloon (right) Detonation

Initiation Point


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Figure 4-3: Later-Time Crater Shapes - Balloon Model

Figure 4-4: Later-Time Crater Shapes – Detonation Model

Figure 4-5 and Figure 4-6 illustrate the crater radius and depth histories presented earlier(Figure 3-10 and Figure 3-11), with the addition of the Chinook results. As expected, theChinook results correspond well with the low friction angle results from LS-DYNA, sincestrength effects are not included in the Chinook model.


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Figure 4-5: Comparison of Chinook Balloon Model and LS-DYNA Crater Depths

Figure 4-6: Comparison of Chinook Balloon Model and LS-DYNA Crater Radii


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5.0 DISCUSSION AND CONCLUSIONS

The results of the numerical simulations show some significant differences with the measuredexperimental crater shapes. While there was reasonable agreement in the crater depths, thecrater radii were quite different. There was a slight difference in the results obtained using thetwo soil material models, and a greater variance in the crater results when the friction anglewas modified. However, no simulation resulted in the experimentally-observed shallow cratergiven in Figure 3-2.

The effect of modeling the explosive using the balloon analogue approach as opposed tosimulating the detonation propagation through the explosive was analysed using Chinook. In ahigh-resolution, 2D axisymmetric calculation, it was determined that the crater shapes areidentical for the two explosive modeling methods. As expected, the Chinook results alsoagreed well with the low friction angle LS-DYNA results, since the Chinook model does notaccount for strength effects.

Overall, all simulations tended to produce craters with an approximate 1:1 radius-to-depthratio, very different from the experimental results (4:1 ratio). The literature was brieflysearched for other studies in which numerical predictions of landmine craters were made, anda series of CONWEP crater calculations were also performed for comparison.

5.1 BRIEF LITERATURE SEARCH RESULTS

Wang [6] from DSTO performed simulations of DRDC-Suffield experiments using LS-Dyna3D. The experiments involved 100 g C4 charges buried in buckets of dry sand. Thecharge aspect ratio (d:h) was approximately 3:1, and the depth of burial was roughly equal tothe height (3 cm). The resulting crater shape, as well as the comparison between the numericaland experimental crater widths, is given in Figure 5-1. The simulations predicted a crater withan approximate 1:1 radius-to-depth ratio, and also under-predicted the crater width (measuredfrom the outside edge of the crater), although not as significantly.

Figure 5-1: Crater Shape and Experimental Comparison from [6]


TR-09-23

Fiserova [7] from Canfield University also performed simulations of landmine blasts,including crater comparisons. Results from AUTODYN simulations of a different DRDCSuffield trial involving 1 kg C4 buried in prairie soil are given in Figure 5-2. The charge had ad:h aspect ratio of 3:1, and a depth of burial approximately equal to the explosive height. Theresulting crater shape again shows a radius-to-depth ratio of about 1:1, although in thisscenario there is also interaction between the ejecta and the raised plate.

Figure 5-2: AUTODYN Crater Shape from [7]

Fiserova also performed simulations of the same 100 g C4 experiment as Wang [6], with craterwidth results shown in Figure 5-3. The LS-DYNA results are comparable to those of Wang,and the AUTODYN results further under-predict the crater width.

Figure 5-3: Crater Shape Comparison from [7]


TR-09-23

5.2 CONWEP STUDY

A series of CONWEP crater calculations were also performed for varying soil conditions(Table 5-1), as another point of reference. The apparent depth and radius most closelymatching the experimental values are given in the shaded cells in Table 5-1. The depth mostclosely representing the experimental value corresponds to dry sand conditions, while the soilconditions matching the experimental radius are on the other extreme (wet clay). Overall,CONWEP tends to predict a crater radius-to-depth ratio of approximately 1.5:1.

Table 5-1: CONWEP Crater Calculations for 6.0 kg C4 at a 0.2 m Depth of Burial

Apparent Depth(m)

ApparentDiameter (m)

ApparentRadius (m)

Radius-to-DepthRatio

Dry Sand 0.6369 2.017 1.009 1.58Dry Sandy Clay 0.7581 2.193 1.097 1.45Wet Sand 0.8510 2.475 1.238 1.45Dry Clay 0.9581 2.740 1.370 1.43Wet Sandy Clay 1.087 3.010 1.505 1.38Wet Clay 1.324 3.979 1.990 1.50

5.3 CONCLUSIONS AND RECOMMENDATIONS

The brief literature search did not find papers in which the numerical simulations predicted ashallow (high radius-to-depth aspect ratio) crater. Shallow craters were also not predicted byCONWEP crater calculations. Assuming the validity of the experimental measurements, thismay indicate that there are additional soil physics which need to be accounted for in thenumerical models which have been overlooked. Alternatively, this may point to some otherfactor present in the experiments which is not included in the model.

A possible explanation is that the edges of the crater (high-slope region predicted in thenumerical models) are not stable, and may collapse into the crater at a late time. This collapsewould occur in the relatively long term, and is not captured in the numerical simulations. Otherpotential issues may be differences in the soil density below the charge versus the overburden,or other soil non-uniformities. It is also possible that subsurface conditions (high water table,bedrock), could affect the experimental measurements if undetected.

Future simulations could be performed for other experimental conditions (soil conditions,explosive mass and placement), to determine if LS-DYNA consistently under-predicts thecrater size.


TR-09-23

6.0 REFERENCES

[1] Dunbar, T.E., and Link, R.A., “Numerical Study of Soil Modeling Approaches in LS-DYNA”, Martec Technical Report TR-07-21, Halifax, NS, 2007.

[2] Holtz, R.D., and Kovacs, W.D. An Introduction to Geotechnical Engineering. Prentice-Hall, p. 733, 1981.

[3] Ripley, R.C., Donahue, L., Zhang, F., “A Hybrid Equation-of-State Detonation Modelfor Homogeneous Explosives”, 2005 Combustion Institute / Canadian Section SpringTechnical Meeting, Halifax, Canada, May 15 – 18, 2005.

[4] Donahue, L., Link, R., Hlady, S.L., “Numerical Modelling of Soils Subjected toExplosive Loading”, 18th International Symposium on the Military Aspects of Blastand Shock, Bad Reichenhall, Germany, September 27 – October 1, 2004.

[5] Donahue, L., Dunbar, T.E., “Numerical Simulation of LAV III Rear Suspension”,Martec TR-05-48 Rev 3, June, 2005.

[6] Wang, J., “Simulation of Landmine Explosion Using LS-DYNA3D Software –Benchmark Work of Simulation of Explosion in Soil and Air”, DSTO TechnicalReport DSTO-TR-1168, Fishermans Bend, Autstralia, 2001.

[7] Fiserova, D., “Numerical Analyses of Buried Mine Explosions with Emphasis onEffect of Soil Properties on Loading”, PhD Thesis, Cranfield University, 2006.

APPENDIX A

CORRECTIONS TO FINAL REPORT FROM STUDY PART 1

CORRECTIONS TO PREVIOUS FINAL REPORT

Upon further review of the final report from the previous soil modeling contract [1], a smallerror was uncovered. These corrections are made in the current work.

In the previous report, the expression

tanpq (A.1)

was used to determine the strength parameters for both models 5 and 16. This was later foundto be in error; the expression should be

tanpq (A.2)

Where is related to as follows

tansin (A.3)

This affects the determination of 2a for model 5 (MAT_SOIL_AND_FOAM) as

2

2

sin3

11

sin

3

4

a (A.4)

and the strength relationship for model 16 (MAT_PSEUDO_TENSOR) as

XYS

sin3

11

sin2(A.5)

APPENDIX B

LS-DYNA MATERIAL KEYWORDS FOR VALIDATION CASE

The following parameters were determined using the “Valcartier Soil Model.xls” spreadsheet:

*MAT_PSEUDO_TENSOR (42.8º Friction Angle)

*MAT_PSEUDO_TENSOR$$ mid ro g pr

2 2175.8 4.068E+07 0.180E+00$$ sigf a0 a1 a2 a0f a1f b1 per

0.0E+00 0.0 0.0 0.0 0.0 0.0 0.0 0.0$$ er prr sigy etan lcp lcr

0.0 0.0 0.0 0.0 0.0 0.0$$ x1 x2 x3 x4 x5 x6 x7 x80.000E+00 1.019E+05 1.000E+09 2.000E+09 3.000E+09 4.000E+09 5.000E+09 6.000E+09$$ x9 x10 x11 x12 x13 x14 x15 x167.000E+09 8.000E+09 9.000E+09 1.000E+10 1.100E+10 1.200E+10 1.300E+10 1.400E+10$$ ys1 ys2 ys3 ys4 ys5 ys6 ys7 ys80.000E+00 1.019e+03 1.757E+09 3.514E+09 5.270E+09 7.027E+09 8.784E+09 1.054E+10$$ ys9 ys10 ys11 ys12 ys13 ys14 ys15 ys161.230E+10 1.405E+10 1.581E+10 1.757E+10 1.932E+10 2.108E+10 2.284E+10 2.459E+10

*EOS_TABULATED_COMPACTION$$ eosid gama e0 v0

2 0.000E+00 0.000E+00 1.0$$ ev1 ev2 ev3 ev4 ev5

0.000E+00 -1.2243E-02 -3.7177E-02 -5.9497E-02 -8.5632E-02$$ ev6 ev7 ev8 ev9 ev10

-1.0434E-01 -1.4586E-01 -1.8015E-01 -1.8317E-01 -1.000E+00$$ c1 c2 c3 c4 c5

0.000E+00 4.580E+06 1.500E+07 2.920E+07 5.920E+07$$ c6 c7 c8 c9 c10

9.810E+07 2.894E+08 6.507E+08 6.950E+08 4.1536E+10$$ t1 t2 t3 t4 t5

0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00$$ t6 t7 t8 t9 t10

0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00$$ k1 k2 k3 k4 k5

5.000E+10 5.000E+10 5.000E+10 5.000E+10 5.000E+10$$ k6 k7 k8 k9 k10

5.000E+10 5.000E+10 5.000E+10 5.000E+10 5.000E+10

*MAT_SOIL_AND_FOAM (42.8º Friction Angle)

*MAT_SOIL_AND_FOAM$$ mid ro g bulk a0 a1 a2 pc ok

2 2.176E+03 4.068E+10 5.000E+10 0.000E+00 0.000E+00 1.029E+00 0.000E+00$$ vcr ref ok

0.0 0.0$$ eps1 eps2 eps3 eps4 eps5 eps6 eps7 eps8 ok0.000E+00-1.234E-02-3.718E-02-5.950E-02-8.563E-02-1.043E-01-1.459E-01-1.802E-01$$ eps9 eps10 ok-1.832E-01-1.000E+00$$ p1 p2 p3 p4 p5 p6 p7 p8 ok0.000E+00 4.580E+06 1.500E+07 2.920E+07 5.920E+07 9.810E+07 2.894E+08 6.507E+08$$ p9 p10 ok6.950E+08 4.154E+10

dcd03e rev.(10-1999)

UNCLASSIFIED SECURITY CLASSIFICATION OF FORM

(Highest Classification of Title, Abstract, Keywords)

DOCUMENT CONTROL DATA

1. ORIGINATOR (name and address) Defence R&D Canada Valcartier 2459 Pie-XI Blvd. North Quebec City, QC G3J 1X8

2. SECURITY CLASSIFICATION (Including special warning terms if applicable) Unclassified

3. TITLE (Its classification should be indicated by the appropriate abbreviation (S, C, R or U) Numerical study of soil modeling approaches using LS-DYNA: Part 2 (U)

4. AUTHORS (Last name, first name, middle initial. If military, show rank, e.g. Doe, Maj. John E.) Donohue, Laura

5. DATE OF PUBLICATION (month and year) April 2009

6a. NO. OF PAGES 39

6b .NO. OF REFERENCES 7

7. DESCRIPTIVE NOTES (the category of the document, e.g. technical report, technical note or memorandum. Give the inclusive dates when a specific reporting period is covered.)

Contract Report

8. SPONSORING ACTIVITY (name and address)

9a. PROJECT OR GRANT NO. (Please specify whether project or grant)

9b. CONTRACT NO. W7701-063750/001/QCL(Task1)

10a. ORIGINATOR’S DOCUMENT NUMBER CR 2009-164

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N/A

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Unlimited distribution Restricted to contractors in approved countries (specify) Restricted to Canadian contractors (with need-to-know) Restricted to Government (with need-to-know) Restricted to Defense departments Others

12. DOCUMENT ANNOUNCEMENT (any limitation to the bibliographic announcement of this document. This will normally correspond to the Document Availability (11). However, where further distribution (beyond the audience specified in 11) is possible, a wider announcement audience may be selected.)

Unlimited

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SECURITY CLASSIFICATION OF FORM (Highest Classification of Title, Abstract, Keywords)

dcd03e rev.(10-1999)

UNCLASSIFIED SECURITY CLASSIFICATION OF FORM

(Highest Classification of Title, Abstract, Keywords)

13. ABSTRACT (a brief and factual summary of the document. It may also appear elsewhere in the body of the document itself. It is highly desirable that the abstract of classified documents be unclassified. Each paragraph of the abstract shall begin with an indication of the security classification of the information in the paragraph (unless the document itself is unclassified) represented as (S), (C), (R), or (U). It is not necessary to include here abstracts in both official languages unless the text is bilingual).

The objective of this project was to investigate the suitability of several LS-DYNA material models to simulate Valcartier soil effects under landmine loading conditions. This report describes the re-derivation of parameters and the verification testing performed for two soil material models, using the new Valcartier soil test results. The material models investigated were then used in the simulation of a DRDC Valcartier experiment involving a 6.0 kg landmine charge. The material models studied gave comparable crater sizes and shapes. While the crater depths agreed relatively well with experimental data (within 16%), there were significant differences between the predicted and measured crater radii. An investigation into the effect of soil strength was performed by parametrically varying the soil friction angle in the soil models. Although reducing the soil strength did produce larger diameter craters, agreement with the experimental measurement was not obtained. The effect of the explosive modelling approach was determined using Chinook. Simulation results using the standard balloon analogue approach (explosive represented by high-pressure, high-temperature detonation products), were compared to results obtained by explicitly modelling the detonation propagation through the explosive. The resulting crater shape was identical between methods. The exact cause of the discrepancy between the numerical and experimental crater sizes is unknown at this time. Differences could be due to additional soil physics which are not accounted for in the numerical models, or alternatively by factors in the experimental configuration which have not been accounted for. For comparison purposes, a brief literature survey was performed and crater shapes from other numerical exercises included.

14. KEYWORDS, DESCRIPTORS or IDENTIFIERS (technically meaningful terms or short phrases that characterize a document and could be helpful in cataloguing the document. They should be selected so that no security classification is required. Identifiers, such as equipment model designation, trade name, military project code name, geographic location may also be included. If possible keywords should be selected from a published thesaurus, e.g. Thesaurus of Engineering and Scientific Terms (TEST) and that thesaurus-identified. If it is not possible to select indexing terms which are Unclassified, the classification of each should be indicated as with the title.)

landmines "soil modeling" "numerical simulations" "crater formation"

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