J. M. Thomsen, R. H. Franzen and D. L. Orphal- High Explosive Simulation of a Nuclear Surface Burst:...

8/3/2019 J. M. Thomsen, R. H. Franzen and D. L. Orphal- High Explosive Simulation of a Nuclear Surface Burst: A Feasibiiity

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. '!'DNA, 501

S/ HIGH EXPLOSIVE SIMULATION OFA NUCLEAR SURFACE BURSTA Feasibility Study,Physics International Company - /"2700 Merced StreetSan Leandro, California 94577 , / T . -i . ... --.. / -4,;: .

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(~ Final ep t Y 1 MarAM077-30 Junin79. 77"i--'~~~~~~~~~~~~~~~ ................. o 1--10......... ..........-CONTRACT N9 DNA qo1-77-C-15\li . ' -- L/.:'T- CO NTRACT N

APPROVED FOR PUBLIC RE L EASE;D(STRIBUTION UNLIMiTED. I

THIS WORK SPONSORED BY THE DEFENSE h.U..EAR AGENCYUNDER RDT&E RMSS CODE B34407744-Y99QA0XS 07035 H2590D.

DTICPrepared for ELEC-TEDirector / AUG271980DEFENSE NUCLEAR AGENCYWashington, D. C. 20305 8

Li~~ / 18~3 070


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Destroy this report when it is o longerneeded. Do not return to sender.PLEASE NOTIFY THE DEFENSE NUCLEAR AGENCN9ATTN: TISI, WASHINGTON, D.C. 20305, IFYOUR ADDRESS IS INCORRECT, !F OU WISH TOBE DELETED FROM THE DISTRIBUTION LIST, ORIF THE ADDRESSEE IS O LONGER EMPLOYED BYYOUR ORGANIZATION.

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UNCLASSIFIEDSECURITY CLASSIFICATION OF THIS PAGE (When Data Entered)REPORT DOCUMENTATION PAGE READ INSTRUCTIONS

BEFORE COMPLETING FORMI. REPORT NUMBER 2. GOVT ACCESSION NO, 3. RECIPIENT'S CATALOG NUMBERDNA 5016F T

4. TITLE (and Subtitle) S. TYPE OF REPORT & PERIOD COVEF 0HIGH EXPLOSIVE SIMULATION OF A NUCLEAR Final Keport for PeriodSURFACE BURST 1 Mar 77--30 Jun 79A Feasibiiity Study 6. PERFORMING ORG. REPORT NUMBERPIFR-1035 (DNA 5016F)

7. AUTHOR(s) 8. CONTRACT OR GRANT NUMBER(s)J. M. ThomsenR. H. Franzen DNA 001-77-C-0150D. L. Orphal9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT, PROJECT, TASKPhysics International Company , AREA & WORK UNIT NUMBERS2700 Merced Street Subtask Y99QAXSDO70-35San Leandro, California 94577I1 CONTROLLING OFFICE NAME AND ADDRESS 12. P.PORT DATEDirector 30 June 1979Defense Nuclear Agency 13. NUMBER OF PAGESWashington, D.C. 20305 20614. MONITORING AGENCY NAME & ADDRESS(if different from Cottrolling Office) 15. SECURITY CLAS S 'of his report)

UNCLASS;FIEDI5a. DECLASSIFICATION DOWNGRADING

SCHEDULE

16, DISTRIBUTION STATEMENT (of this Report)

Approved for public release; distribution unlimited.17. DISTRIBUTIO4 STATEMENT (of the abstract entered In Block 20, If ifferent from Report)

18. SUPPLEMENTARY NOTESThis work sponsored by the Defense Nuclear Agency under RDT&E RMSS CodeB344077464 Y99QAXSD07035 H2590D.

19. KEY WORDS (Continue on reverse side If necessary and Identify by block number)ANFO Experiments Explosive EffectsNuclear Effects Simulation Mine Throw Technique"Airblast Airblast Induced MotionsGround Coupling Computer Calculations

2 ABSTRACT (Continue on reverse aide If necessary aid identity by block number)The feasibility of designing and constructing a high explosive source whichfaithfullv reproduces the direct- and airblast-induced ground motions result-ing from a l-kt rliclear surface burst has been investigated. A preliminarycharge design ;ncorporating subsurface and surface high explosive charges wasdeveloped, and shown to theoretically reproduce the desired simulation corndi-tions. The subsurface charge employs techniques first used in tne MINETHROW I simulation of the JOHNIE BOY nuclear event. The surface charge

DD 1N 1473 EDITION OF I NOV 65 IS OBSOLETE UNCLASSIFIEDSE.CURITY CLASSIFICATION OF THIS PAGE (Wten Data Enter

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UNCLASSIFIEDSECURITY CLASSIFICATION OF I8HIS PAGE(When Data Entered)

- -. 20. ABSTRACT (Continued)consists of an elevated disc of explosive (ANFO) with a thickness varying from1 m to 0.1 m with a total diameter of about 40 m. Detonation spacings and aninitiation system for this novel charge design were investigated. A completefieldable charge was not constructed because of difficulties in experimentallydetermining the detonation properties of thin sheets of ANFO. Steps leadingto a future fieldable charge which simulate airblast, ground motion, andcratering effects of a 1-kt nuclear surface burst are made, based on theresults of this initial effort.

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PREFACE

The work in this report was performed from January, 1977to October 1978 unde~r contract to the Strategic Structures Division(SPSS) of the Defense Nuclear Agency. The contract was monitoredfirst by Major George Goss and later by CDR Thomas Deevy.

The authors wi-sh to thank the following Physics Internationalpersonnel for their participation in this multifaceted program:C. Vincent, J. Kochly, P. Cayere, B. Drake, F. Milistefr and R.Funston for instrumentation support, P. Vigil for Tracy Test Sitesupport, K. Abbott, R. Brown, S. Hancock and S. Ruhl for calculationalsupport, and F. Sauer for providing technical direction and ro-viewof the final report.

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TABLE OF CONTENTSPage

PrefaceList of Illustrations 3List of Tables 8

SECTION 1 INTRODUCTION 11SECTION 2 SURFACE CHARGE CONCEPT AND PRELIMINARYINVESTIGATION 18

2.1 Brief Description of th e Charge DesignProcess 192.2 Results of th e Preliminary Investigation 212.3 Summary of Key Unknowns 61SECTION 3 FURTHER INVESTIGATION OF TECHNICAL FEASIBILITY 63

3.1 Early Thin ANFO Investigation 633.2 Final Thin ANFO Experiment 923.3 Initiation System 1143.4 Low Overpressure Airblast Characterist ics 119SECTION 4 HE SIMULATION OF DIRECTLY COUPLED ENERGY FROM

A NUCLEAR EVENT 1324.1 Two-dimensional Calculation of JANGLE S 1324.2 HE Simulation of Direct- and Cratering-

induced Ground Motions 158SECTION 5 SUMMARY AND RECOMMENDATIONS 168REFERENCES 171APPENDIX OVERPRESSURE WAVEFORMS ANy OVERPRESSUREIMPULSE FROM STANDiRD SOURCE AIRBLAST TESTS 173

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LIST OF ILLUSTRATIONS

Figure Page1-1 High Explosive Simulation of Nuclear Detonations 121-2 MINE THROW I--Direct- and Cratering-induced GroundMotion, Cratering, and Ejecta 141-3 Concept for Applying the Close-in Airblast

Overpressures to the Ground 162-1 HE Results Required fo r Surface Charge Design fromExperiments and/or Calculations 202-2 General Calculational Gecmetry for Standard SourceOne-dimensional HE Calculations using Plane Symmetry 232-3 Peak Pressure versus V/A from One-dimensional ANFOCalculations 262-4 Total Impulse Delivered to the Ground versus A (V=0)(from one-dimensional calculations) 282-3 Closure Time, TOA', versus V from One-dimensionalStandard Source Calculations (ANFO/VOID/RIGIDBoundry 302-6 ANFO Air Shock TOA in Air from One-dimensionalCalculation 312-7 Airblast Peak Pressure versus Range from a 1-ktNuclear Surface Burst 332-8 Airbiast Time-of-arrival for l-kt Nuclear Surface

Burst 342-9 Airbiast Impulse versus Range from a l-kt NuclearSurface Burst 352-10 Detonation Trajectory for Undiluted 94/6 ANFO 382-11 Explosive Thickness versus Range, Charge Design IA 40

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Figure Page2-12 Standard Source Charge Design LA (note expandedvertical scale) 412-13 Charge Design 1A 432-14 Initiation Time versus Range, Charge Design 1A 442-15 Calculations Examining Infinite and 3(A+V) DetonatorSpacing; Peak Prersure at Ground Surface versusRange 472-16 Calculations Examining Infinite, I(A+V) and 2(A+V)Detonator Spacing; Peak Pressure at Ground Surfaceversus Range 482-17 Effect of Detonator Spacing on Impulse, Spacing =2(A+V), Calculation No. 3 492-18 Concept of Initiation Geometry 512-19 Two-dimensional Charge Performance Calculation;Computed Time-of-arrival at th e Ground Surface versusRange compared with 1-kt Nuclear Time-of-arrival 542-20 Two-dimensional Charge Performance Calculation;Computed Overpressure versus Range at th e GroundSurface compared with l -kt Nuclear Overpressures 552-21 Two-dimensional Charge Performance Calculation;

Computed Total Impulse versus Range at the GroundSurface at Five Times, compared with Total l-ktNuclear Impulse 562-22 Typical Panel for Supporting ANFO 592-23 Conceptual Layout of Standard Source Charge 603-1 Thin Film ANFO with TOA Pins and Booster 653-2 Instrumented Witness Plate, Shot 23 673-3 Ionization Pin System 693-4 Time-of-arrival Pin System 703-5 P.C,,B. Pressure Recording System 7123-6 Carbon Stress Gage Recording Systc,., 723-7 Calibration Curves for Copper Crush Balls 74

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IFigure Page

3-8 Experimental Setup, Shot 13 753-9 Propagation Velocity in ANFO versus Distance fromBooster, Tests 4, 5, and 6 783-10 Detonation Velocity in ANFO-versus Distance fromBooster, Tests 7-11 803-11 Detonation Velocity in ANFO Charge, Tests 16B and16C (aluminized ANFO) 853-12 Detonation Velocity in ANFO versus Distant_ fromBooster, Tests 21, 22, and 24 863-13 TOA Data from Pins on and above the SegmentedAluminum Plate, Test 25 883-14 Geometries for Thin ANFO Calculations 913-15 Side-on Photograph of the Setup of the Final ThinANFO Experiment 933-16 Final Thin ANFO Segmented AluminumPlate 943-17 Standard Source Background Grid 963-18 Fast Camera Frame l(t=0 is) Side-on Setup View ofThin ANFO, Test 26 983-19 Fast Camera, Frame 6 (t=150 is) Showing EarlySpherical Expansion of ANFO Detonation Products 993-20 Fast Camera Frame 8 (t=200 ps) 1003-21 Fast Camera Frame 11 (t=275 ps) Sh-wing InitialFormation of Mach Stem along Aluminum Plate 1023-22 Fast Camera Frame 14 (t=350 ps), Showing FurtherMach Stem Development beneath the ANFO Charge 1033-23 Fast Cameza Frame 16 (t=400 ps) 1043-24 TOA versus Range in Thin ANFO Test 26 10 73-25 TOA in ANFO Test 26 (average of three pin lines) 10 83-26 Comparison of Average ANFO Pin Data in Charge withData from Framing Camera Photographs 11 0

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Figure Page3-27 Data Digitized from Framing Camera Photos along

Lines 3 and 4, near the Aluminum Plate il13-28 Comparison of Gage and Framing Camera TOA Data nearthe Aluminum Plate 1123-29 Concept of Initiation Geometry 1153-30 Initiation System Test Layout 1173-31 Design of Model Standard Source Surface Charge UsingLayers of EL506C-1 Sheet Explosive 1223-32 Model Standard Source Charge, Test 19 1233-33 Comparison of Test 18 and Test 19 Measured PeakOverpressures with Predictions 1293-34 Comparison+ of Expected and Measured Positive Phase+Impulse (I), Tests 18 and 19 1304-1 Initial Geometry and Euler Zoning for JANGLE S2DELK Calculation 1344-2 Shock Arrival Time in the Vicinity of the JANGLE SNuclear Source, Based on One-dimensional Calculations 1374-3 Initial Coupled Lagrange/Euler Grid for the JANGLE S2DELK Calculation 1404-4 Schematic of CIST-15 Hydrostat 14 34-5 Schematic of CIST-15 Yi ld Surface 14 64-6 CIST-15 Hydrostatic Compressibility Curve 1484-7 Comparison of CIST-5 and CIST-15 CompressibilityCurves 15 04-8 PICES 2DELK Vector Velocity and Material Boundary

Plot from JANGLE S Calculation 1524-9 The Intersection of the Hugoniot Curves fo r theCIST-15 Soil and ANFO Yields a Pressure of 7.2 GPa.fo r the Reflection of the Detonation Wave 1544-10 The 7.2 GPa Contour fo r the Nuclear SourceCalculation 155

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Figure Page4-11 Arrival Time and Impulse along Smoothed 7.2 GPa

Contour from JANGLE S Nuclear Source Calculation 1564-12 Geometry of Design 1 1594-13 Comparison of the Impulse fo r Designs 1, 2, 3,and 4 with the Desired Impulse Curve 1604-14 Geometry of Design 2 1624-15 Geometry of Design 3 1634-16 Comparison of the Impulse versus Time Curves forthe Nuclear Source Calculation and Design 3 onthe Axis of Symmetry 1644-17 Comparison of the Impulse versus Time Curves forthe Nuclear Source Calculation and Design 3 ate 70 degrees 16 54-18 Geometry of Design 4 167

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LIST OF TABLES

Table Page2-1 JWL Parameters fo r Ideal ANFO 222-2 Results of Standard Source One-dimensional

Calculations 242-3 Table of 1-kt Nuclear Airblast Conditions to aRange of 25 m 362-4 Summary of Two-dimensional Detonator SpacingCalculations Performed 462-5 Standard Source Detonator and Booster Tiiing 523-1 Thin ANFO Experiments - Summary Table 763-2 Copper Crush Gage Results: Test 13 823-3 Copper Crush Gage Results: Test 15 (DilutedNitromethane) 823-4 Time-of-arrival in Test 26, Data from Fast CameraPhotographs 1053-5 TOA Pin Data in Thin ANIO, Test 26 1063-6 Summary of TOA Measurements On and Near theSegmented Aluminum Plate, Test 26 1133-7 Data Summary Initiation System Tests 1183-8 Dimensions and Design of t.,e Scale Model StandardSource Surface Charge (Test 19) 1213-9 Experiment Plan fo r Tests 18 and 19 1253-10 Experiment Plan fo r Test 20 1263-11 Summary Results fo- 10.5 kg Nitromethane Charge(Test 18) 127

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Table page3-12 Summary Results for 10.5 kg Model Charge (Test 19) 1284-1 Initial Conditions for Materials in JANGLE SCalculation 1364-2 Summary of Euler Rezones Performed in the 2DELKJANGLE S Calculation 1394-3 CIST Model Constants for Event 15, Used toDescrize the Alluvium at the JANGLE S Site 1474-4 Coordinates, Impulse, and Arrival Time along th eSmoothed 7.2 GPa Contour - JANGLE S 157

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SECTION 1INTRODUCTION

Since the advent of the Atmospheric Nuclear Test Ban Treaty,the Defense Nuclear Agency and the Armed Service Laboratorieshave relied on chemical explosives as energy sources for theproof testing of structures and military equipment against- thenuclear airblast and ground shock environment. The phenomeno-logical investigation of nuclear effects, especiallyinvestigations concerning cratering and ground motion, nave alsorelied upon chemical explosives to simulate the nuclear source.In both usages, si.. 1ulation implies replication of only thenuclear effects of interest. This is illustrated inFigure 1-1. How well high explosi--e (HE) simulation sourcesreplicate the airblast from nuclear weapons can be readily eval-uatei since considerable data exist for atmospheric nuclear testsmade prior to the Nuclear Test Ban Treaty. In addition, bothnigh explosive and nuclear airblast effects have been studiedcalculationally in considerable detail.

In May 1970 -PhysicsnternaLional Company (PI) proposed amethod of using chemical explosives to reproduce the crater,ejecta, and the cratering related and direct-induced groundmotions of a nuclear near-surface burst. This method becameknown as the MINE THROW technique.

P1


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IfI\AIRBL.AST.

INDUCED--. D~r-.T AN .. GROUND"....................SHOCK

INDUCEDGRUDSH')CK I'-----


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The first test of this technique was the MINE THROW Ievent. This event had as its objective the v.eproduction of thecrater and the cratering-related ground mrotions 1'roduced by theJOHNIE BOY nuclear event, a 500 ton nuclear explosion buried at58.5 cm in Area 18 alluvium at the Nevada Test Site. No attemptwas made to match the JOHN.TE BOY airbiast environment on MINETHROW I because the coupled airbiast energy did not appear to besignificant. It was postulated that the crater formation forthis event was dominated by the direct-induced mo~tions and wouldnot be severely influenced by the differenre in airblast betweenthe JOHNIE BOY event and MINE THROW 1.

The specific technique for designing the MINE THROW I exper-Iiment was as follows: The contour of constant peak pressurecorresponding to the detonation pressure of the explosive usedwas obtained from the finite difference calculations of theJOHNIE BOY event. At each point along that contour, both theprescure as a function of time, P(t), and the time integral ofIP(t), or specific impulse, were determined from these

!;I

calculations. An explosive charge was then shaped in such a waythat it reproduced the nuclear pressure history (approximately)and the total specific impulse along this contour. In practice,an iterative series of finite difference HE calculations wereperformed, tailoring the HE : to producc the s-ame boundary andinitial conditions along the above described contour.

II

The final charge configuration is shown in Figure 1-2. Acomparison of the final craters for MINE THROW I and JOHNIE BOYshowed an agreement in volume and shape within 11 percent. heAlthough JOHNIE BO Y had only a few ground motion gages, and these

13

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. . .. ....

BOOSTERS - 2.3kgCAST PENTOLITE

- CONSTRUCTEDFROM 27.7kg BAGS

67 METER

STATUS: FULL SCALE FIELD SIMULATION OF 0.5 kt JOHNIEBOY NUCLEAR EVENT SUCCESSFULLY CONDUCTEDON DECEMBER 15,1971RESULTS: JOHNIE BOY DIRECT AND CRATE RI NG-IN DUCEDGROUND MOTION AND FINAL CRATER WELL SIM-ULATED. NO ATTEMPT TO SIMULATE AIRBLAST-INDUCED GROUND MOTION

"Figure 1-2 MINE THROW I--Direct and cratering-induc~edground motion, craterjinq, and ejecta.

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were placed at large radii from the source, the correspondinggages on MINE THROW I showed very similar displacements andground iaotion waveforms (Reference I).

The results show that'. the MINE THROW technique is a validtechnique for reproducing the direct-induced ground motion andcratering ::esulting from a near surface nuclear burst. of a knowndegree of coupling.

Subsequent to the MINE THROW I experiment, PI performedcalculations (Reference 2) on an explosive configuration whichwould simulate the craten-ing and the direct-induced ground motionon the CACTUS event, a 17 kt above-surface nuclear explosion atthe Pacific Proving Ground. In this case, the relative airblast-induced motions were much larger than for JOHNI BOY. It becameclear from these calculations that the airblast-induced motionson the horizontal plane added a sig,.l-ficant impulse th.t shouldbe included in the simulation technique. Thus, for targetresponse tests, investigating the the effects of airblist, andairblast-induced ground motions, there are impoctant phenomeno-logical reasons why a standard nuclear simulation techniqueshould include the proper pressure profiles and timing cf theclose-in airblast.

In March 1976, Physics International Compan! proposed amethod fo r applying the required close-in airblast loading to theground surface in conjunction with the MINE THROW technique inorder to better simulate the cratering-induced and airblast-induced ground motions. This technique is shown in Figure 1-3.The MINE THROW charge is coupled at its edges to the surface HE

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AN FO TIME: t =0

TIME-PHASED CHARGE DETONATION

~. ~ * . .A RBLAST" -INDUCEDIGRONDSHOCK

i~ue- Coneptfor applying the close-in airbiast

overpressures to the ground.

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charge which extends in a thin sheet above the ground surface.The subsurface charge design is accomplished by using the tech-nology developed fo r MINE THROW I.

The surface charge design required development of a newtechnology. This effort has been underway fo r about two years.During that time a series of one- a.,d two-cdimensionalcalculations were performed to establish the design elements suchas the explosive thickness, the standoff distance, and initiationpattern fo r an ANFO surface explosive charge. As a result ofthat work, a preliminary surface charge design was developed.This work is reported in Section 2.

To design an initial field experiment to test the concept, afollow-on effort was then performed to investigate specificdesign details. The details of greatest concern are discussed atthe end of Section 2, followed by a comprehensive discussion ofwork performed in Section 3. Also, it was desirable to designthe MINE THROW, or subsurface charge fo r a specific past nuclearevent so that this charge could be integrated with the surfacecharge, simulating the specified nuclear effects of the nuclear-event and making it a concept validation test. Work performed insupport of this effort is presented in Sectior 4.

Because of unexpected difficuities in obtaining neededexperimental data on the ANFO, it was not possible to develop animproved design fo r the surface charge. Thus, the fullvalidation test remains to be designed. A summary of workperformed, and some recommendations as to how the validation testcan be designed are included in Section 5.

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SECTION 2SURFACE CHARGE CONCEPT AND PRELIMINARY INVESTIGATI ON

The surface charge concept is an extension of the MINE THROWdesign in that it is designed to match specified nuclear effectsat a specified contour, or interface. It is specifically desiredthat a reasonable approximation to the nuclear surface burstairblast at the ground surface be obtained within the regionoccupied by the final crater. These nuclear effects include:

i. The correct time of arrival of the airblast2. The correct peak pressure as a function of range3. The correct impulse as a function of range

It is also desirable, but not re-quired, that the airblast atgreater ranges from the ground zero (down to approximately10 psi) be a reasonable approximation to a nuclear surfaceburst, This section discusses briefly how the surface charge isdesigned to meet the above requirements, and the results of acalculational effort which was performed to generate apreliminary design tor a l-kt surface burst.

Since this preliminary design was based entirely on calcu-lations, many important details of the charge design were notspecified. These could only be answered by a dedicated exper-imental program. Section 2.3 reviews the most critical designitems which remained after completion of this preliminaryinvestigation.

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r- .... .-..I. ',-.,,-. - ,..... .... * '' " ' ' - - '

S2.1 BRIEF DESCRIPTION OF TH E CHARGE DESIGN PROCESS

Nuclear airbiast condi t ions of peak pressure , P, totalimpulse, I, and time o arrival, TOA, along th e ground surfaceare obtained either from nuclear data or from empir ical modelssuch as those developed by Brode (Reference 3). For a givenyield, th e above condi t ions can be accurately described asfunctions of range, r, from th e source. These are th e conditionswhich must be matched in th e high explosive s imulat ion. It wasshown early in th e program that these nuclear condi t ions could beadequately simulated by a "sheet" charge of high explosivelocated above th e ground surface. The radial extent of thesheet, and its thickness an d elevation above th e ground surface,must be specified. These can be determined, once a particulartype of high explosive has been chosen, by calculations and/orexperiments.

The required HE results are shown in Figure 2-1, where V isth e dis tance of the charge above th e ground surface, and A is th etotal charge thickness. It was shown very early in th e programth a for a reasonable range of V an d A, th e peak pressure , P',could be adequately represented as a function of V/A, while theimpulse, I', was directly related to A. The t ime of arrival ofth e airblast wave at th e surface, TOA, is directly related toV+A.

Once these HE results are known, it is a straightforwardprocedure to develop th e basic charge design to accomplish th esimulation of th e basel ine nuclear condi t ions . By setting

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P1 I' TOA'

'V/A A V + A

Figure 2-! HE results required fo r surface charge designfrom experiments and/or calculations.'

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P' = P one is able to obtain V/A as a function of range, whilesetting I' = I gives A versus range. Knowing both V/A and Acompletely specifies the charge design. What remains is todetermine when che HE charge is detonated as a function ofrange. This is obtained by subtracting TOA' from TOA.

Over the intended range of simulation, this procedure willlead to a high explosive change design which, when executed inthe field, will match the close-in airblast from a nuclear deto-nation at the ground surface. This ciose-in airblast generatesthe correct boundary condition fo r the airblast-induced groundmotion, which will vary at different sites because of changes inthe subsurface geology.2.2 RESULTS OF THE PRELIMINARY INVESTIGATION

This section shows how the charge design process outlined inSection 2.1 is actually performed. First, the results of someone-dimensional HE calculations and computational analyses aredescribed. These efforts lead to the derivation of thepreliminary charge dimensions. Some results from two-dimensionalcalculations investigating detonator spacing requirements arethen presented. A fully two-dimensional calculation using thepreliminary charqe dimensions and the necessary detonator spacingis then described in detail. Finally, the preliminary STANDARDSOURCE charge design is presented and discussed in detail.

2.2.1 One-Dimensional HE Calculations. This sectiondescribes the results of some one-dimensional calculationsperformed to determine the relationship between the thickness of

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the explosive sheet, A, and its standoff distance above theground surface, V, cn the parameters of interest, namely the peakpressure, the total impulse, and the TOA at the ground surface.The explosive considered in these calculations was ANFO.

Figure 2-2 shows the general calculational geometry forthese calculations. In all cases, the air in the standoff volumewas modeled as a void. The ground surface in the calculationswac modeled either as a rigid boundary or as an alluvial-typesoil. The alluvial soil model used was the CIST-15 model(Reference 4), discussed in detail in Section 4. The ANFO wasmodeled as an ideal explosive using the JWL high-explosiveequation-of-state (Reference 5). The JWL constants used in thecalculations are given in Table 2-1 (Reference 6).

TABLE 2-1JWL PARAMETERS FOR IDEAL ANFO

P = 0.782 Mg/M 3 A 0.7519P = 5.5 GPa B -0.008175D = 5.0 mm/"s R1 = 4.1E = 2.9 x 109 J/m 3 R2 = 1.25S =2.554 w = 0.44

Table 2-2 contains a summary of the calculations performed,and the essential results of these calculations in terms of peakpressure P', impulse, I', and the closure or contact time of theANFO explosive gases with the ground surface, TCA'. The ANFOexplosive slabs were modeled with three thicknesses: I meter,

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-'- - - '"' -.. ,'.... ". . . . , ,' '

K ANFO A

VOID V

GROUNDSUI IFACE-

GROUND SURFACE MODELED AS EITHERA RIGID BOLNDARYOR ASA SOIL. (CIST-15MODEL)

Figure 2-2 General calculational Qreometrv fo r standardsource one-dimensional HE calculations usinaplane symmetry.

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TABLE 2-2RESULTS OF STANDARD SOURCE ONE-DIMENSIONAL CALCULATIONS

ANFO THICKNESS,A VOID THICKNESS,V V/A ' P'dt-I' TOA'(m) (m) (GPa) (kPa-sec) (ms)

RIGID CROUND SURFACE MODEL1 0 0 10.09 >1610 --1 0.25 0.25 2.78 >141.0 0.2811 0.5 0.5 1.58 >1383 0.3321 1 1 0.93 >1350 0.4251 2 2 0.56 >1320 0.6021 3 3 0.41 >1290 0.7731 4 4 0.33 >1260 0.9421 5 5 0.28 >1240 1.1081 10 10 0.16 >1150 1.925

0.3 0 0 10.09 521 --0.3 0.9 3 0.43 > 437 0.7440.3 1.5 5 0.29 > 430 0.3370.3 2.4 8 0.20 > 420 0.4850.3 3 10 0.16 > 412 0.5820.1 0 0 10.12 169 --0.1 0.3 3 0.42 143 0.0780.1 3 30 0.06 > 132 0.512

CIST-15 SOIL GROUND SURFACE MODEL1 0 0 6.15 >1430 --1 0.5 0.5 1.10 >1400 --1 1 1 0.74 >1350 ---1 3 3 0.36 >14001 10 10 0.14 >1330

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0.3 meter, and 0.1 meter. These calculations were performed inorder to determine the relationship between the ANFO slabthickness and the total impulse, and also to verify that themaximum pressure at the ground surface was a function only of theratio (V/A) of the void thickness to the ANFO thickness. Thecalculations using the CIST-15 model for the ground surface wereperformed only at a thickness of 1 meter.

Figure 2-3 shows the peak pressure calculated at the groundsurface as a function of V/A. For the rigid boundarycalculations, and for values of V/A from 0.25 to 30.0, a fit tothe data gives

P' = 0.96 (V/A)- 0 7 7 (2.1)

where P' is in GPa. A similar, but slightly differentrelationship is found for the CIST-15 calculations, where V/A i'varied between 0.5 and 10.0. It was found that these were wellrepresented by the equation (see Figure 2-3):

P' 0.75 (V/A)-0- 6 9 GPa. (2.2)Thus, it was verified that for an adequately wide range of valuesof both V and A, the peak pressure at the ground surface was afunction only of the ratio V/A. Although this type ofrelationship is not required to define the STANDARD SOURCE chargedimensions, it does simplify the charge design process.

It was intuitively felt that the total impulse deliveredthrough the ground surface, fo r reasonable standoff distances,

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10.0 I I Ii 0.

P=0.96 (V/A)-0 7 700GPa (ANFO/VOID!'RIGID BOUNDARY)

.. 1.0 - 10.0LU .

Ld

OA 0.3mS0.10- OA=O.1 m1.

LU .

P 0.75 (V/A- 0.69GPa (ANFO/VOID/SOIL) 100*

V/A

F-iaure 2-3 P-3ak pressure versus VAfrom one-dimensionalANFO calculations.

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would be only a function of the ANFO thickness itself.Figure 2-4 plots the specific impulse, I', versus A, for the caseof zero standoff distance. For the 1-meter-thick ANFO slab,specific impulse had not achieved its final value in the 28 mssimulated in the calculations. Taking this into account, thecomputational results suggest that

I' (kPa-sec) 1730 A(m). (2.3)Thus, fo r the case of no standoff, a 1-meter-thick ANFO slab willdeliver an impulse of 1730 kPa-sec to the ground surface. Thisvalu- is consistent with previous results, such as those obtainedduring the MINE THROW simulation of JOHNIE BO Y (Reference 1).All of the calculations using realistic standoff distances weresimulated only to a real time of 28 ms. Although the totalimpulse was delivered in only a few of the calculations, it wasfound that the specific impulse delivered during this time wasonly s'lightly dependent upon standoff distance, since the greaterthe standoff, the longer the time before the explosive gasescontacted the ground surface. For the calculations using therigid boundary representation of the ground surface, the totaliI impulse was adequately represented by Equation 2.3. For thecalculations using the CIST-15 soil representation of the groundsurface, it was found that the total impulse was betterrepresented by

I'(kPa-sec) 1500 A(m). (2.4)Thus, the use of a realistic soil equation of state slightlylowers the total impulse delivered to the ground surface.

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1800

1600c. 1400

1200

L" 1000 '= 1730AS"00

W.- 600"% 400

2000

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0A ANFO CHARGE THICKNESS, m

Figure 2-4 Total impulse delivered to the ground versus A(V=0) (from one dimensional calculations) .28T

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*' , ' ' ' ... __________________________ . .... . . ..

Figure 2-5 is a plot of the time of arrival of the explosivegases at the rigid boundary, TOA' versus the void thickness V.Data are shown fo r all three ANFO thicknesses studied. The dataare consistent with a "closure velocity" of about 5.8 m/ms. Thedifferences in intercepts fo r the different ANFO thicknessesreflect the time required fo r the detonation wave to reach thefront suriace of the ANFO slab. The detonation velocity in theANFO was 5.1 m/ms. Therefore, fo r a 1-meter-thick slab, thedetonation wave arrives at the front surface at about 0.2 ms.Similarly, fo r a 0.3-meter-thick ANFO slab, the front surfacebegins to move at about 0.06 ms following the initiation of thedetonation at the rear surface. For the 0.1-meter-thick slab,the front surface begins to rrove about 0.02 ms after rear surfaceinitiation. The closure time results for the one-dimensionalcalculation using the CIST-15 soil equation of state groundsurface are not reported or plotted because they are exactly thesame as those fo r the rigid boundary calculations.

It was recognized that using a void to represent the airwithin the standoff distance would lead to too large a closurevelocity. To determine a more representative closure velocity,another one-dimensional calculation was performed. This calcu-lation contained a 1-meter-thick ANFO slab surrounded by air. Arealistic equation of state was used for the air. Figure 2-6plots the air shock time of arrival versus the distance from theANFO front surface. The propagation velocity of the air shock isnearly constant, at about 5.3 m/ms. As expected, this was2 slightly slower than the closure velocity obtained in theprevious charge design calculations.

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2.0

~1.8 =10.68=0

CA,0. =mCL SRE

0.2

1.01

0.4 -

Figure 2-5 Closure tix~e, TOA' , versus N7 f-rom one-dimensionalst-andard source calculations (ANFO/VOID/,RI0!Dboundary).

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ii~

2.01.8

, 1.6-E> 1.2 VEL 5.3 m/ms

" 1.0u.08_ 0.6

S0.401.20 r I I I I I I - I I I ....

0 1 2 3 4 5 6 7 8 9 10 1DISTANCE FROM ORIGINAL ANFO FRONT SURFACE, m

ii,

Figure 2-6 ANFO air shock TOA in air from one-dimensionalcalculation.

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2.2.2 Nuclear Airblast Conditions. This section containsthe data used to derive the nuclear conditions to be matched inthe HE simulation. They include the peak airblast overpressure,P, the total impulse of the positive phase, I, and the airblasttime of arrival, TOA. These were obtained from formulaspresented by Brode (Reference 3), using a yield of 1.0 kt.

The peak overpressure versus range is shown in Figure 2-7.This is well represented by a simple functional form, as shown inthe figure. Figure 2-8 presents the airblast TOA as a functionof range. Figure 2-9 presents the total positive phase impulse,I, as a function of range. Table 2-3 presents the nuclearairblast conditions from a range of 4 meters to 25 meters.

2.2.3 Preliminary STANDARD SOURCE Charge Dimensions. Usingthe results of Sections 2.2.1 and 2.2.2, a candidate chargedesign could be developed. Before this design was developed, anattempt was made to account fo r the non-ideal nature of ANFO.This was done by uniformly lowering the HE peak pressures, P',developed in Section 2.2.2. Then the procedure described inSection 2.1 was applied. This charge design was r-ferred to as"first order corrected" STANDARD SOURCE charge design (ChargeDesign A).

The work of McKay, et al., (Reference 7) strongly suggestedthat an ANFO detonation gradually progressed to steady state overa distance of 1 to 1.5 meters. Thus, for ANFO thicknesses lessthan 1 meter, the detonation velocity, and hence the detonationpressure, were less than those attained under Chapman-Jouget(C-J) conditions. TOA data within an ANFO charge, are shown in

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102P (GPa) 5.648 X 102 R- 2 .9 5 8

101

S100cuU;

0 o-uJ

10-2

10-31 S10 100 1000RANGE, m

i4

Figure 2-7 Airblast peak pressure versus range from al-kt nuclear surface burst.

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10

100

E

S10-1

10-2 4 0 0 ( N r-

cc CM H 00 W -

00f C m~'j C)

E-4 l

~ 0

HD0D 0 0C0E-U 01 0n0 'z ~ ta C N (N (NCNHS 4JH4

P4)

Q) 4 ,o*4

0

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>1n 0D 0 co Li N' r-

0

4- H 0 a 0 0 0 0

GQw 0nC 0 CD 0 0c CNm 1 N CN (N (

en -I - 4 ,4 W D 00 in126 F4r-


130/205

02 a ~ - r '10 0 *

H m N C dLi 0rd cJ 0, L) N "I

00 J1 00 0 ~ - 1r- r- 10 L cp. m r0 Cn C CN

H0 00 1~0 ko 0m- C4 N -42

gm ND n N H H

HoCI2 N 0 A N Lr4 E-4t *4 k

(n CD' P- N C'N r-.02)1A40 0D r-4 (nH HL

9 09E-i 114 4r En o 0) H0 H N Hr- A4 02) 0 0 H a 1 LP4C r- 4 N a- q

LA Ad r- w m H

oN Ln c o c44~ r-40 -I C

ML

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H r - U) rn IN LA 0f., L4 0 0 (N O C

'- n w om - l-

lH .4J1 r- 14 ONi mv0C d I H- rn 009 E-1 E-4P 4 ' 4' C40 (r, C)

E-4

r.i.4 0 H r-4 ko *cl U) ( IN r, I 4 N LA0. 04 r ')V)4 S4 acc

g (a In i LA0 .0~a) (N H, I m' 00v. H CD (NLA

w'C1

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RANGE, ft0 10 20 30 40 50 60 70_ I I II !

3000 - 10.5 Kg NM charge (test 18) - 5002000 10.5 Kg model standard 3002 -source (test 19)

200ya - 1000 '

- 045.5 Kg spherical -50uw 00 ',Mx 300- charge predictions20..

S200- 0LS10.5 Kg 2000 spherical 20100 charge 1- prediction 10

50- 00 f I I 50 5 10 15 20RANGE, m

Figure 3-33 Comparison of Test 18 and Test 19measured peak overpressures withpredicit ions.

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- - -.. . . '. . . ..

900. 10.5 Kg NM charge (test 18)

800- 0 10.5 Kg model standardsource charge (test 19)700

S600E E Prediction,C45.5 Kg TN T sphere

" 500-J 0

S400 0Prediction10.5 Kg NM300o sphere

000200 0

100-00

0 5 10 15RANGE, m

Figure 3-34 Comparison of expected andmeasured positive phase impulse(I+), Tests 18 and 19.

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SECTION 4A SIMULATION OF DIRECTLY COUPLED ENERGYFROM ANUCLEAR EVENT

4.1 TWO-DIMENSIONAL CALCULATION OV JANGLE S

The specific objectives of the JANULE i ualuulatiun,following those used in the Mine Throw I duiu_!! QL'UVL(Reference 1), are listed below:

1. Calculate the total fractiozi oi thu InIuuaL' tJUOL'UUenergy coupled to the alluvium.2. Calculate the two-dimensionlal contouu ini tihu a liuvlullcorresponding to a peak prossuru ok 7.2 GPa (72 kba,) "izdthe arrival time of the shock front at thiu uuotLouLv,3. Calculate the total impulse dullvur.ud aLu)ow thu abuvwcontour.The above information from the nulu.avL ualuulatLiun iu

sufficient to design the ANFO charge required to uiiluulaLu tLhucratering and direct-induced ground motion, a InucuuavLy L)rz.'t (LAthe total STANDARD SOURCE simulation. To obtaizn hiu ieLIoviLaLionlit is necessary only to investigate the coupliny pr,uuhu OuL'-Iiqits early formative stages, i.e., the first I uL 2 m11U.Therefore, the calculation was not carried to late timuu sand theprocesses associated with late stage crater dovulopmoznt wuo'u nuotinvestigated as part of this effort.

4.1.1 Zoning and Initial Conditions. LSCIS 2D ELK i; acoupled Euler-Lagrange two-dimensional continuum muiclunicu

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OttUt11AILO UU0 Thia iw uxtrezruly advantageous for surface-burstL1LLLwvuiiuiziiy (whvi~w thu zunu uizu vemainu fixed in time, but theIuIIAW A wU~h 2uni vaiiuu with Lime) can be uuud ain the regionUuaUu Lo wid iAiiluUdIIW theu wxLjluuivu uouLce, where violent,LuL~bulwoL wutlu~iun a9UUiAtd with uahouk vaporization ordwtuiiaL iul j)LdwUminAj JvuunUzi bayrangu di1EfuLrncing (wher-e theislawk uL' Wullt zuliw L'mil Uin i tatin but the zone shape call ch~ange)W~ Ju UWWU IUL' '.thui L'uyiunta, rnabling unu to acc.urately monitorJjL'Wd~dUL'Q Miid vwiwjiL~y wavouLvuinu at uLpeUil~iud potiitions within the'JL Ikii hW14L auii LuqL'dIIQ L'uyiO111 uan Uu uouplud avrouG mutualfI LQLLakuwo A1 .wiikJ LvaniIuiziwiunl uf uhuc~k wavuu VLtom one rugionLw Lhu uthuL'.

Thu Luuui~ud Nuuv.~-LiAYLUIIWtJ option in 2DLKL1 wau usuduiawutivo4y iI I thu JANULWLi J u~aluulatiou, IViYULQ 4-1 uhawu thu

Lt L4 wintua L,y tid L, 1WL' ZU tintj. ThU Y1iUi UXtUzIdUd to a~ rnyauL J.. Lw 4.b nwuLwL~ "Ltuvu thue yL'uild uurt~auu and U.7 inutur bulowLiiu IWL'UIIdI MULA"PUW, Th w l"UUlJtiUII wiaU UonuI(UtUd inl CylindriCalWymmituLL~y, with Lhw Axlit4 uL uymmtinLry luautd at R N C.0 i. The11uu1WIiAL W4UUL'.UW w~au iik4dulud j.iA a upiliuvu with anl initia~l radius ofIJ4,V0 LuLwL' ~UwiL1L'UL4 ui n Lh, aXisi at a diata.neu ot 1.0670 motor4iLLJVu L1hu ()L'UUjLI 1:UL'I24Uu. TIhiai yuonutLvy ifi consiut'~nt With theautu~tia nuu luu'.A iuv Iuu LjtoumuLL'Y. Th'lo mi ti~ia OI~u.Lu ?Qliny in thlevio2iniLy utL hu IUQIJL'~hUUL1.LIt Wid Lho 4liuvium wa.i 5U inin (610 by

111111I~iAhz). Buwinnini aL a diutancu ot 2.135 in a~bove the,ji.ouund mut.'Lauli thu 4oni:nq in LhQ Z-diI~u~jion waui yaoznetL-icallyIiniLJLuaaud b' 4 L,4aiu ci I.045il. Thu total number of zones inLhu 1( dii'uw'tion, iniitia.U1.y, wau S0, and in the Z-diruction, 78.

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4.5iz =0.156 mIE 24 ZONES,NAR

- AIR RATIO= 1.045UL

AZ = 0.057mM 2.134 --J

SORC:AR54 ZONESu,,, A0m0.0525 m

S0.377 50 ZONES0.0R 0.0500 m -

ALLUVIUMN00 2.5

. . 0RANGE(),m.0.

Fiaur, 4-1 initial geometry and Euler zonina for JANGLE S2DELK calculation.

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The spherical nuclear source was assumed to have a uniformL initial density (2.16834 g/cc) and internal energy

(1.6806 x 101 ergs/gm), but no initial velocities. Initialconditions for the nuclear source, air, and alluvium aresummarized in Table 4-1.

As the calculation progressed, the size of the Euler gridwas increased in order to follow the shock wave in the air closeto the ground surface and in the underlying alluvium. To aid inthis rezone effort, two one-dimensional calculations wereperformed to conservatively estimate shock arrival times.

The first calculation contained only the nuclear sourcesurrounded by a large void region. Its purpose was to obtain therate of free expansion of the nuclear source. The initial condi-tions for the nuclear source were the same as for the two-dimen-sional calculation. A a gamma-law equation of state (EOS) wasused (constant Y = 1.5). This will be discussed in more detailin Section 4.3. The result of this calculation was that at about10 P.s, the nuclear source debris reached a limiting velocity ofabout 9 cm/i's. The second calculation, also performed inspherical symmetry, placed alluvium beyond the void region at arange of 1.067 meter. The purpose of this calculation was toobtain a conservative estimate of the shock arrival time and peakshock pressure in the alluvium directly beneath the nuclearsource. The nuclear source was again treated as a gamma-law gas;the alluvium EQS model was the same as used in the two-dimensional calculation. it will be discussed in Section 4.3.Aresult of this calculation is summarized in Figure 4-2, whichplots the calculated arrival time of the peak pressure in theI~ ground.

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TABLE 4-.INITIAL CONDITIONS FO R MATERIALS IN JANGLE S CALCULATION

INITIAL INITIAL INITIALATERIAL DENSITY INTERNAL ENERGY VELOCITYNuclearSource 2.16834 Mg/m3 16.806 eu*/g 0.0 cm/usAir 1.293 x 10-3 Mg/m3 0.002 eu/g 0.0 cm/usAlluvium 2.13 Mg/nm 0.0 eu/g 0.0 cm/us

*i eu/g 1012 ergs/gm

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10,000

a - ARRIVAL TIME VS. DISTANCEw BELOW GROUND SURFACEBENEATH NUCLEAR SOURCEW (10 CALC 2) \2W 1000w

10 0

ARRIVAL TIME OF NUCLEAR - SOURCE DEBRIS ALONGSURFACE (1D CALC 1)10 - . III1I1"!

0 1 2 3 4 5 6 7DISTANCE, m

Figure 4-2 Shock arrival time in the vicinityof the JANGLE S nuclear source, based on one-dimensional calculations.

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Also plotted in this figure is the arrival time of thenuclear source debris close to the surface as obtained from thefirst one-dimensional calculation. It is easily seen that theexpansion of the debris is much more rapid than the propagationof the direct-induced shock into the alluvium. For example, thedebris arrives at a point 2 meters from the center of the sourceat a time of about 30 Pis, whereas the shock wave reaches a point2 meters below the ground surface directly below the device inabout 220 4s.

Figure 4-2 aided considerably in design the rezone schedulefor the Euler grid. This schedule is shown in Table 4-2. It canbe seen from this table and Figure 4-2 that Euler rezones wereperformed before the shock reached the edge of the grid duringthe first 0.6 ms of the calculation. When coupling from theairbiast and source debris predominate. The extent of the gridabove the ground surface was held constant at 4.5 meters, so thatafter about 0.6 ins, energy was allowed to escape through thisboundary.

Below the ground surface, a Lagrange grid was dimensioned tomonitor the shock wave for peak shock pressures of less than orequal to 7.2 GPa (72 kbar) and to monitor the total impulsedelivered to the alluvium beyond the 7.2 GPa peak pressurecontour. As shown in Figure 4-3, the Lagrange grid was a hemi-spherical shell lying below the ground surface with an initialinner radius of 2.0 meters and an outer radius of 5.0 meters.There were 21 zones in the circumferential (0) direction and 15zones in the radial direction. In the circumferential direction,the zone size was a constant 0.20 meter; in the radial direction,

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00r-L4 N~4.


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EULERSOURCE GI

RANGE, m0 1 2 3 400 INERCTVBOUNDARY / /

U-

4.4

Figure 4-3 Initial coupled Lagranae/Euler arid, for thieJANGLE S 2DELK calculation.

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the zone size varied from about 0.15 meter at R =2.0 meters toabout 0.4 meter at R = 5.0 meters. Also shown in Figure 4-3 is sketch of the Euler grid discussed previously. The interactiveboundary defined between the Euler and Lagrange regions is alsoindicated. The number of radial Lagrange zones was increased anthe size of the grid expanded as the calculation progressed. Thmaximum number of radial Lagrange zones was 33, and the maximumradial extent of the grid was 10 meters.

4.1.2 Equations of State. To perform the JANGLE Scalculation, equations of state for the nuclear source material,air, and NTS alluvium are required. This section describeb theequations of state for each of these materials.

Briefly summarizing, the alluvium model useu was the CIST15model developed at the Air Force Weapons Laboratory(References 11 and 121) to characterize layered alluviums found athe White Sands Missile Range. The nuclear source was describedby the ideal gas EQS with a constant gamma. The air was alsodescribed as an ideal gas, but with variable gamma. Because allthree materials exist in the Euler grid, and only two materialsper cell are currently allowed, both the air and the source weredesignated to be the same material in the computationaldescription and a criterion based on the cell material densitywas devised to differentiate between the two.

NTS Alluvium EQS. The AFWL CIST (Cylindrical In-situ Test)soil model was programmed for 2DELK in order to describe the NTSalluvium. It calculates pressure as a function of P'(compression) and, optionally, as a function of e (specific

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internal energy). The pressure is the sum of two components: ahydrostatic component which depends only on 4, and an energydependent term. The hydrostatic component, p1 , is calculateddirectly using a piecewise continuous fit to experimental data.The hydrostatic loading/unloading curves are history-dependent.The energy-dependent pressure term is a standard, condensed phaseTillotson form equation-of-state (Reference 13). The generalform of the pressure equation is:

P= PH + Goe + e T

p E total pressureP hydrostatic pressureG Gruneisen coefficientT Tillotson Coefficienteo -constant

e specific internal energy0 mass density

The hydrostatic pressure versus compressioility equationscomprise a four interval, piecewise, continuous function.Figure 4-4 shows a gene,,alized plot of the hydrostatic pressure,P,' versus compression, '. The equations are listed below:

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a_P3 K L2

P2 P

PH1 HYPOTHETICAL UNLOADINGK/ CURVE FROM (p H

I it'1/lr P2 "3

r-,.

y,-

Figure 4-4 Schematic of CIST-'I5 hvdrostat.

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1. .1> `3 , loading and unloadingPH P3 + KM(P-P 3 ) - (Km - Kz) 's (. -

Ae exp [() -2. P* < < 43 (virgin loading curve)

P2+KL I2 P2 <

3. (unloading curve)PH= Ku (-L4r)

- pl*/Kui.s the x-intercept of the unloading curve of slope K whichpasses through (P*r P1j*), where P* is tne lesser of the twovalues of 4max, the maximum compression the soil element hasexperienced, and the current value of 4.

.The constants, q' "2 43, Ps' Km , Kz, t'u, KLI, KL2, Pl, P2,P3 , G, T, and e. are defined separately fo r each CIT test.The shear modulus is calculated as a function of , and isthe lesser of.the values of a x K and 4 x Kz, where

]3

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andKLl i

K= KL2 42 < A 13Km - (Km-Kz)exp [(P3-A)/Ps] 4 > 43

and Kz and v (Poisson's ratio) are constants.

The yield stress is calculated as a function of p, andoptionally, e. Figure 4-5 shows a generalized plot of yieldstress versus pressure. The equations are:

Y = Y' (no energy dependence)Y = Y' x (1 - e/es) (with energy dependence), and

Y' = max 0, C1 (I-P/Tl) P Umin (c1 + siP, Y1 ) P > 0

The constants Cl, TI, Y1 and S1 describe the unconfinedcompressive strength, the tensile strength, the maximum yieldstrength, and the shape of the failure curve in the intermediatepressure region, respectively.

The CIST data used were those derived for the top soi l layerfo r Event 15, performed at the White Sands Missile Range. Theconstants used in the calculation are summarized in Table 4-3.Figure 4-6 shows the CIST-15 compressibility curve from 0 to 20.0GPa (0 to 200 kbar). It is this region which is important forthe JANGLE S calculation because the pressure contour of interest(7.2 GPa) and the total impulse across it are defined by thehydrostat in this pressure region.

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cc I)

Figure 4-5 Schematic of CIST-iS yield 3urface.

146

IL4M5JAAfIbI&


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TABLE 4-3CIST MODEL CONSTANTS FO R EVENT 15,USED TO DESCRIBE TH E ALLUVIUM AT THE JANGLE S SITE

CIST Constant 2DELK Value SI Value

3 3Pc 2.13 g/= 2.13 Mg/Mv 0.3 0.3K 0'.01588 Mbar 1.588 GP aUK 0.01588 Mbar 1.588 GPaKLI 4.9 x l0-3 Mbar 0.49 GPaK 2 1.764 x 10-3 Mbar 0.176 GPaLK .6897 Mbar 68.97 GPam ~-8i 6.897 x 10 Mbar 6.897 kPaP 2 6.8969 x 10 Mbar 68.97 kPa-4P, 2.650586 x 10 PMbar 26.5 MPa

- -64.3432 x 10-, 4.3432 x 1021.3102 x 10- 4 1..3102 x 10- 4P3 0.15 0.15

0.25 0.25A 0.5 0.5B 1.3 1.3-7 S6.69710 Mbar 68.97 kPaT -6.897 x 10 Mbar -68.97 kPaS 0.6y 1.38 x 10 Mbar 13.8 MPae 1.0 x 10 eu/g 100 joules/ges 0.1 eu/g 10,000 joules/g

o 0.1333 0.1333

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20.0

15.0

D 10.0Lu xI

5.0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7COMPRESSIBILITY, p

I"I

Figaure 4-6 CIST-15 hydrostat ic compressibili t , curve.

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After the JAINGLE b calculations were completed, informationfrom CIST Event 5, performed in Area 10 of the Nevada Test Site,was maue available. The compressibility curve from this test isgiven in Figure 4-7. The data from CIST Event 15 are alsoincluded for comparison. The Event 15 data are very similar tothe Event 3 data; thus, it was unnecessary to rerun the JANGLE 6calculation. The CIbT 15 data were used throughout the programto assure consistency and comparability of results.

Nuclear Source and Air Eub. To miodel Coth the nuclearsource material and the air as a single material, a specialequation-of-state routine was written fo r PISCES 2DELK. T etollowing information was relied upon in developing the model:

i. The nuclear source can be treated as iron using anideal gas EOS with a constant gamma (' 1.5).2. Initially, there is a considerable density mismatchbetween the air and nuclear source.3. Once the nucleat source material expanded to 2 to 3times its initial radius, it could be treated as air.

The model consisted of the following density criteria:1. For o 0.2U4 g/cc, cell is nuclear source material(iron). Use ideal gas EoU with a constant r = 1.35.2. For U.08159 g/cc, cell is air, use ideal gas EOiwith a variaole gamma, corresponding to a real air LuS.3. For 0.8i59 g/cc u.4,04 g/cc, cell is -i:ixec aic ananuclear source material. Use an ideal gas wiLh variaolegamma in tnis "transition region," witn gamma given oy:

1 :-0.0819-( A (Aj 0.12241

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20.0

10.0

5.0

0 I0 0.1 0.2 0.2 0.4 0.5 0.6 0.7COMPRESSIBILITY, pu

iu r e 4 - 7 Comparison of CIST-5 and CIST -15 compressibillit";curves.

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where YA is equal to the real air EQS Y at P 0.08159 g/cc andthe current cell internal energy, e.

A check was made to ensure that the above EQS formulationdid not introduce large artificial gradients into the pressure.

4.1.3 Some Results of the JANGLE S 2DELK Calculation. Fromthe JANGLE S calculation the specific results required to designthe high explosive charge, as discussed in Section 4.1.1, are thecontour in the ground on which the peak pressure was 7.2 GPa(72 kbar), the time of arrival (TOA) of the peak pressure on thatcontour, and the total impulse delivered across the contour.These results were obtained and are compared in Section 4.2 withthe results of the HE calculations performed in order to designthe "MINE THROW" charge.

Figure 4-8 shows a two-dimensional vector velocity andmaterial boundary plot at 15 as. The nuclear source has expandedradially outward and vertically upward to a distance of about2 meters, and has begun to interact with the alluvium below.

The total energy coupled to the alluviumn reached a peak ofU.044 kt (3.67 percent of the total yield of 1.2 kt) at 0.067 ins,and then slowly decreased, leveling off at 0.0328 kt (2.73percent of the total yield) at 0.8 mns.

For the HE simulation, the contour of the ANFO/Soilinterface is determined by the requiremnent' that the peak pressurealong the contour should be the same in both the MINE THROW sinu-

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3.0A~IR

E.4 NU0CLEARLu 2. OURCE- -

0 .~~~~-~--.------ - --- ./0. 5

OALLUVIUMi

-0.S-1.0

INNER-1.5 -LAGRANGE'BOUNDARY --2.0 1 __ I2.5 2.0 1.5 1.0 0.5 0

RANGE, m

Ficrure 4-3 PISCES 2DELN vector velocity and materialboundary plot from JANGLE S calculation.

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lation and in the nuclear event. The value of the peak pressurewill be equal to the pressure which occurs when a detonation wavein ANFO reflects from the ANFO/soil interface.

The pressure of reflection of a normally incident detonationwave in ANFO on a soil interface can be found graphically as theintersection of the Hugoniot curves of the two materials inpressure velocity space. Figure 4-9 shows the Hugoniot curvesfo r the CIST-15 soil model and the ANFO, which is modeled with aJWL equation-of-state. The pressure at the intersection of thesecurves is 7.2 GP a (72 kbar). This value was confirmed with aone-dimensional hydrodynamic calculation.

Since the peak pressure in the MINE THROW simulation and thenuclear event should be equal, the ANFO/soil contour should betaken to be the contour of the JANGLE S calculation where thepeak pressure equals 7.2 GP a (72 kbar). (The complexity of anon-normally incident detonation wave is not considered in theMINE THROW simulation method.) The 7.2 GP a pressure contour fromthe nuclear calculation is shown in Figure 4-10. This contour isirregular near the surface and was replaced with a contour whichwas smoothed in that region. Figure 4-1 1 shows the time ofarrival and impulse per unit area around the smoothed contour.Table 4-4 gives the coordinates, impulse and arrival times aroundthe smoothed contour.

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72 kbar -- NF810 6

wj C-J POINT/CL

2

0 0.05 0.1 0.15VELOCITY, cm/gsec

S'icure 4-9 The intersection of th e Huaoniot curves for theCIST-15 soil and ANFO yields a pressure of7.2 GPa for th e reflection of th e detonation wave.

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Fi,;ire 4-10 The 7.2 GPa contour ffor te nuclear sour.,alculiation, (The "dashes Iine near the surfacefldicatez the *sRjoot,e 'cOn our.'


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J. M. Thomsen, R. H. Franzen and D. L. Orphal- High Explosive Simulation of a Nuclear Surface Burst:...

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