IN THE ESKIMO TESTS - Defense Technical Information Center · 67 7170 84 E,,__-3 , ... in the ESKIMO Tests May 1975 to may 19764 ... IST41111UTON SATC CNT at A* astrct ntered in Stock

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U.S. DEPARTMENT OF COMMERCENational Technical Information Service

AD-A030 885

DYNAMIC ANALYSES OF MAGAZINE HEADWALLS

IN THE ESKIMO TESTS

AGBABIAN AssocIATES,

EL SEGUNDO, CALIFORNIA

MAY 1976

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DEPARTE"OF DEESE E (PLOSIVESSAErBOR i :

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REPRODUCED BY

o NATIONAL TECHNICALo8 5) 80 INFORMATION SERVICE 3 8 985 86k.S. DEPARTMENT OF COMMERCE 38

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AGBABIAN AS OCIATES104 105 1Q§0 North Nalf(afreet .08 109

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R-755,-1"4182

DYNAMIC ANALYSES OFMAGAZINE HEADWALLSIN THE ESKIMO TESTS

Prepared for

ADEPARTMENT OF UEFENSE EXPLOSIVES SAFETY BOARD

Wat.hington, D.C. 20314

Iq:S White pectloe [

e•:' Iloll Sn~l• [

.• . ...,. • . .. . . . .. .. . . . . . Final Report

... ... May 1976

Damoder P. Reddy i

AGBABIAN ASSOCIATES2.50 North Nash Street 4.110 o• . ,

El Segundo, California 90245 Approw:,-. ! i

UNCLASSIFIEDSCCUIMITY CLASSIFICATION Or ?l.IS PAME (r7hon netsa Pne.,eE)

READ INSTRUCTIONSREPORT DOCUMENTATION PAGE BEF'ORE COMIPLETING FOR%1 1

1.04PN UMI(N1 a.OVT ACCISSION NO.l 3. *CIPItmNi CATA600 HUMSCA

R-7556-i-4i82 yEO IO?4PA0CvNOJ

4. TITlt (and Saabfl IS.)TYEO C Q &P iO og

Dynamic Analyses of Magazine Hleadwalls FINALin the ESKIMO Tests May 1975 to may 19764

_________________________________________ R-7556-1 -4182-7. AUTHOft(o) S. CONTRACT OR GRANT 4MSPa

1'amoder P. Reddy DAABO9-75-C-0025

*. PERFORMNING ORGOANIZATION NAME AND ADDRESS 10. PROGRAM ElEMENT. PR0JE , T ASK

Agbabian Associates AE OKUI U61

250 N. Nash Street RDT&E 4A765702M857ElSegundo,_California 90245 _____________

It. CONVTROLLNG OPFICE NA#AE ANO ADDRESS 12. REPORT DATE

Dtpartment of Defense Explosives Safety Board My17Washington, D.C. 20314 .NUERFAS

-14. -MONO TORINO A44ENCY NAME AOORCSS(ti different (0101 ContralIind Office) IS. SECURITY CLASS. tat thle report)

Unclassified

IS*. 041CLASSIFICATION. 0OWN4GMAOlNG

"Apoe :f::or:public r:lease; distribution unlimited. L

17. IST41111UTON SATC CNT at A* astrct ntered in Stock 20.itdise ra Rpo)

r ~~~18 SuPPI.SMIENTANY NOTESr int Eemn

It. KCY WORDS (Continue en lowers@ stdo It necessary and Identify by black number)

Magazine HeadwallRepneNnierFitElmtDynamic Finite Element ESKIMO TestNonlinear Slabs Igloo Storage MagazineExplosive Blast NnierSoils

20. AISTRACT (Continuo on reveeae side It nocoearyE and Identify by bloCk Rumbet)

This report describes the results of dynamic response analyses of magazineheadwalls in three tests, namely, ESKIMO 1, 11, and '4V. The finite elementmodels of the headwalls were subjected to blast loadings selected on the basisof measured data and theoretical investigations. The responses of the headw.allswere obtained using the INSLAB code, a nonlinear, dynamic finite element computerprogram. The behavior of the headwall material was described by a bilinear

(continued on other side)

D JA~~ 47 NV~IOSLT UNCLASSIFIED

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UNCLASSIFIED%gCURITY CLA-SIPICATION OF THIS PA*e(Wh" OData Ird), ..

20. ABSTRACT (continue-)moment-curvative relationship, and the supporting soil was simulated b', a seriesof nonlinear springs and linear dampers. The results of the calculations werecompared with available test data. In general, the predicted behavior of theheadwalls agreed very well with their observed behavior. The present analysisof the south headwall In ESKIMO I, using the refined finite element mesh, showedbetter agreement with the tesZ results than those from the previous analysis,which used a coarse mesh. The results for the east headwall, ESKIMO 'tI, showedthat the computed permanent displacement contours are quite similar in shapeto those measured. The results for the northeast headwall, ESKIMO. Ii, indicatedthat the concrete beams around the doorway were effective in reducing themaximum displacement of the headwall and that the biparting and sliding typeof door was superior to the double-leaf and hinged type for resisting blastloads. The computed motionsof the northeast headwall, ESKIMOAiV, comparedvery well with the corresponding test data.

(PAGE8) tlUNCLASSIFIED

SIEUMIITY CLA$,sfiriATION Olt THIS PA&GE'Wlht~ Date 1"t

R-7556-1 -4182!

PREFACE

F: This technical report is submitted by Agbabian Associates as part

of the work required under Contract No. DAAB09-75-C-0025 with the Department

Sof Defense Explosives Safety Board. Project Manager for Agbabian Associates

and Principal Investigator for the preparation of this report is D. P. Reddy.

i' Major contributions to the study have been made by D. Van Dillon, H. S. Ts'ao,

B. Barclay, and J. W. Workman of the Agbabian Associates staff. Technical

ý- monitor of the contract for the Department of Defense Explosives Safety Boardis Dr. T. A. Zaker.

i21

ii

i 7A k R-7556- 1-4182

SUMMARY

This report describes the retults of dynamic response analyses ofmagazine headwalls in Zhree tests, namely, ESKIMO I, II, and IV. The finiteelement models of the headwalls were subjected to blast loadings selected onthe basis of measured data and theoretical Investigations. The responses of

the headwalls were obtained using the INSLAB code, a nonlinear, dynamicfinite element computer program. The behavior of the headwall material wasdescribed by a bilinmar moment-curvature relationship, and the supporting soil

was simulated by a series of nonlinear springs and linear dampers. The resultsof the calculations were compared with available test data. In general, thepredicted behavior of the headwalls agreed very well with their observedbehavior. The present analysis of the south headwall in ESKIMO I, using the

refined finite element r".h, showed better a6ý-eement with the test resultsthan those from the previous analysis, which used a coarse mesh. The results

for the east headwall, ESKIMO II, showed that the computed permanent displau.-ment contours are quite similar in shape to those measured. The result4 forthe northeast headwall, ESKIMO II, indicated that the concrete beams aroundthe doorway were effect:ive in reducing the maxin'tm dtplacement of the headwall

' and that the biparting arid sliding type of door w)s superior to the double-leafand hinged type for resisting blast loads. The computea motions of the north-east headwall, ESKIMO IV, compared very well with the corresponding test data.

v-i"V

CONTENTS

Section Pg

I INTRODUCTION AND BACKGROUND .. .. ... ....... . .

1.1 Description of ESKIMO. I Test. .. ........ I

1.2 Description of ESKIMO It Test... . . . . 71.3 Description of ESKIMO III Test .. .. ........10

1.4. Description of ESKIMO IV Test .. .. .. . .12

1.5 Objectives and Scope .. .. .... .......... 16]

2 PRESSURE LOADING ON HEADWALLS . . . . . . . . . . 17

2.1 Pressure Histories for ESKIMO I Test ... 172.2 Pressure Histo~ries for ESKIMO 11 Test ... 20

2.3 Pressure Loading History for ESKIMO IV Test 22

3 STRURUCTURAL MODEL OF HEADWALL AND DOOR SYSTEM 31

3.1 Structural Model, ESKIMO I Test........31

3.2 Structural Models of Headwalls In ESKIMO 11 583.3 Structural Model of Igloo B (Northeast)

k. Headwall, ESKIMO IV. .. .. .... ............. 64

4 INSTRUMENTATION FOR ESKIMO IV............71

4.1 Pressure Gages ... ....... ................. 71 I4.2 Accelerometers. .. ....... . ...... ......... 75

4.3 Linear Motion Transducers .. .. ..... .......75

5 DYNAMIC RESPONSE OF HEADWALLS IN ESKIMO TESTS .79

5.1 Introduction. .. ....... ..... ............. 79

5.2 Response of South Heatiwall, ESKIMO 1 795.3 Response of East Headwall, ESKIMO 11 895.4 Response of Northeast Headwall, ESKIMO 11 935.5 Response of Northeast Headwall, ESKIMO IV 99

Vii

i k R-7556-1-4182

CONTENTS (CONTINUED)

Section Page

6 CONCLUSIONS AND RECOMMENDATIONS ........... ... 181

6.1 Conclusions ...... ................ .... 181

6.2 Recommendations ..... .............. .... 183

7 REFERENCES ........ ................... .... 185

Appendix

A INCLUSION OF NONLINEAR SPRINGS IN INSLAB CODE . . 137

B PROCEDURE FOR CALCULATING YIELD MOMENTS FOR AREINFORCED-CONCRETE SECTION ... ........... .... 195

C PROCEDURE FOR COMPUTING EQUIVALENT MODULI FORA REINFORCED CONCRETE SECTION ... .......... ... 199

ILLUSTRATIONS

Figure

1-1 Layout of Test Structures for ESKIMO I ..... 3

1-2 Steel-Arch, Earth-Mounded Igloo Storage ..... 4

1-3 Layout of Test Structures for ESKIMt II MagazineSeparation Test ........... ................. 8

1-4 Layout of Test Structures for ESKIMO III MagazineSeparation Test . . . . . . . . . . . . . . . . . 13

1-5 Layout of Test Structures for ESKIMO IV MagazineSeparation Test ..... ................. .... 15

2-1 Reflected Overpressure on South Igloo, ESKIMO I 18

2-2 Headwall Blest-Pressure Loading Zones,ESKIMO I . . . . . . . . . . . . . . . . . . . . 19

2-3 Proposed Pressure Pistories for Nor:heast andEast Igloos, ESKIMu !I .... ............. ... 21

viii

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R-7556-1 -4l82r


Fiur

2-4 Placement of Pressure Gages, Igloo B (NortheastIgloo) of ESKIMO iV ................ 23

2-5 Comparison of Pressure Histories for a VerticalArray of Gages, Igloo B of ESKIMO IV ..... ... 25

S2-6 Comparison of Pressure Histories to Test!z Uniformity of Pressure tLoading across Widcth of

SHeadwall, Igloo B of ESKIMO :V ......... . 26

2-7 Free-F!e*d Ground Level and Reflected H(ouvi.jlPressure Pulses for Analysis of Igloo B,F"IMO IV ........... ..... ....... ......... 27

2-8 Comparison of Pressure Histories for a VerticalArray of Gages with the Proposed Loading Pulsefor Response Analysis of Igloo B, ESKIMO IV . . . 28

2-9 Comparison of Headwall Pressure Pulse forAnalysis of Igloo B (ESKIMO IV) with EstimatedReflected Pulse and Measured Free-Field GroundLevel Pulse ...... ................... .... 29

3-I Coarse Finite Element tlode, of South Headwall,ESKIMO I ..... ......... ................... . 32

3-2 Refined Finite Element Model of South Headwall,ESKIMO I ................. .................... 33

3-3 Door Details for South igloo, ESKIMO I 36

3-4 Details of Headwall Construction for South Igloc.ESKIMO I ......... .................... .... 37

3-5 Dynamic Stiffness of Soil ...... ............ 41

3-6 Test Problems to Determine a Suitable Model toRepresent Soil ............. ................. 44

3-7 Case A: Displacement-Time Histories of theHeadwall ......... .................... . .... 45

3-8 Case B: Displacement-Time Histories of theHeadwall ............... .................... 46

ix

k R-7556-1 -4182

CONTENTS (CON, INUED)

Fi gure Pg

3-9 Cse B: Velocity-Time Histories of the Headwall 47

3-10 Case C: Displacement-Time Histories of theHeadwall ........ .................... .... 48

3-11 Case C: Velocity-Time Histories of the Headwall 49

.3-12 AxijI Stiffness of Steel Arch ............. .... 53

3-13 Movement of Headwall of North Acceptor Igloo,ESKIMO I ........... ................... .... 56

3-14 Headwall of North Igloo, ESKIMO I ......... 57

3-15 Igloo C (Northeast) Hea%!wall, ESKIMO II ...... 59

3-16 Finite Element Mesh of Igloo B (Northeast)

Headwall, ESKIMO II1 ................... .... 61

3-17 Configuration of Steel Door for Igloo B

(Northeast), ESKIMO It .. ............ 63

;-18 Finite Element Model of Northeast Headwall,ESKIMO IV ............... .................... 65

3-19 Configuration of Steel Door for Igloo B(Northeast) Headwall, ESKIMO IV ........... ... 67

.- 20 Regions of Different Material Properties forIgloo 8 (Northeast) Headwall, FSKIMO IV . .. 68

4-1 Placement of Pressure Gages onNortheast (B) Igloo, ESKIMO IV .. ......... ... 73

4-2 Placement of Pressure Gages c. Ea-t (D) andWest (E) Igloos, ESKIMO IV ... ........... ... 74

4-3 Pl3cement of Accelerometers on Headwallof Northeast Igloo, ESKIMO IV ........... 76

4-4 Placement of LVDT Transducers on Headwallof Northeast Igloo, ESKIMO IV ... .......... ... 78

x

R-7556- 1-4182


Figure Pg

5-1 Computed Motion of South and West Igloos atNode 1 .......... ..................... .... 107

5-2 Computed Motion of South and West Igloos atNode 19 ....... ..................... .... 108

5-3 Computed Motion of South and West Igloos atNode 46 .... . ... ... ...... ..... .......... 109

5-4 Computed Motion of South and West Igloos atNode 49 . . . .......... . . .... . . ................. 110

5-5 Computed Motion of Scuth and West Igloos atNode 50 ....... .............................. 1 1

5-6 Computed Motion of South and Wnst Igloos atNode 73 ....... ... ....... ... ..................... 1,2

5-7 Computed Motion of South and Wost Igloos atNode 76 .. ... . . . . . . . . . . . . . . . . . 113

5-8 Computed Motion of South and West Igloos atNode 77 ....... ..................... .... 114

I 5-9 Computed Motion of South and West Igloos atNode 100 ........ .................... .... 115

5-10 Computed Displacemeits along Edges of Headwallsof South and West Igloos .... ............ .... 116

5-11 Computed Displacements along ' .h Line ofHeadwalls of South and West Igloos ........ .... 117

5-12 Computed Displacement at Ground Level of SeveralLocations on South and West Igloos ....... .... 118

5-13 Computed Motion from Prior CalculationCorresponding to Node 1 .... ............. .... 119

5-1h Computed Motion from Prior CalculationCorresponding to Node 19 .... ............ ... 120

S5-15 Computed Motion from Prior Calculation

Corresponding to Node 77 ..... ............ .121j

xI

A k R-7556-1 -4182


Figure Pag~e

5-16 Computed Motion from Prior CalculalionCorresponding to Node 46. .. .. ....... .......... 122

5-17 Computed Motion from Prior CalculationCorresponding to Node 49. .. .. ....... . ......... 123

5-18 Computed Motion from Prior CalculationCorresponding to Node 76. .. ............ ......... 124

5-19 Computed Motion from Prior CalculationCorresponding to Node 73. .. ..... ... ........... 125

5-20 Computed Motion from Prior CalculationCorresponding to Node 103 .. .. ............ ....... 126

5-21 Movement of Headwall of South Acceptor Igloo .. 127

5-22 Movement of Headwall of West Acceptor Igloo . . . 127

5-23 :omputed Displacements (in hundredths of a foot)

ESKIMO I, 0.22 Sec after Arrival of the BlastWave .. ........... . .................... .. ..... 128

5-24 Computed Displacements (in hundredths of a foot)with a Rigid Body Displacement of 0.25 Ft Added

in for the Sake of Comparison with the WestIgloo, ESKIMO I .. .. ............ ................. 129

5-25 Computed Displacements (in hundredths of a foot)

of the Headwalls of the South and West Igloos,ESKIMO 1, 0.22 Sec after Arrival of the Blast .. 130

5-26 Computed Motion of East Headwall (ESKIMO 11' atINode 1 .. .. ............. ................. ....... 131

5-27 Computed Motion of East Headwall (ESKIMO 11) atNode 9 .. ... . .... ....... . ...... ..... . ....... 132

5-28 Computed Motion of East Headwall (ESKIMO 11) atNode 19. .. ......... . ................ ........... 133

5-29 Computed Motion of East Headwall (ESKIMO 11) atNode 21. .. ............. . ................ ....... 134

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Ak~ R-7556-1 -4182

CONTENTS (CONTINUEDJ'

Figure Page

5-30 Computed Motion of East Headwall (ESKIMO il) atNode 46 .. .. ............ ......................... 135

5-31 Computed Motion of East Headwall (ESKIMO 1H) atNode 49. .. .. .. ..... ... ... ..... ..... ...... 136

5-32. Computed Motion of East Headwall (ESKIMO 11) atNode 50 .. .. ............ ......................... 137

5-33 Computed Motion of East Headwall (ESKIMO 11) atNode 73. .. .. .. ..... ... ..... ... ..... ...... 138

5 -34 Computed Motion of East Headwall (ESKIMO 11) atNode 76 .. .. .......... ..... *.............. . ......139

5-35 Computed Motion of East Headwall (ESKIMO 11) atINode 77 .. .. .......... ................... .......140

5-36 Computed Motion of East Headwall (ESKIMO 11) atNode 103. ...... .. ...... ......................... 141

5-37 Permanent Displacement Contours of East Headwall,ESKIMO 11I.. .. ................ ................... 142

5-38 Computed Displacement Contours of East Headwall

at t -145 msec. .. .......... ................... 143

5-39. Comr. .d Displacement Contours of East HeadwallIat t - 157 msec...................................144

5-40 Computed Motion~ of Northeast Igloo (ESKIMO 11) atNode 9 .. .. .... ... ..... ... ..... ... .........45

5-41 Computed Motion of Northeast Igloo (ESKIMO 11) atNode16 .. .. .......... ................... .......146

5-42 Computed Motion of Northeast Igloo (ESKIMO 11) atNODE 22 .. .. .......... ................... .......147

5-43 Computed Motion of Northeast Igloo (ESKIMO 11) atNode 39. .. .. .. ........ .. ... ... ..... ...... 148

5-44 Computed Motion of Northeast Igloo (ESKIMO 11) atNode 42 .. .. .......... ...................... 149

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ilk R-7 556-1-4182

CONTENTrS (CONTINUED)

FLIuES page

5-45 C;3mputed Motion of Fortheast Igloo (ESKIMO 11) atNode 45 .. ..... . .... ....... . ...... ........... 150

5-46 Computed Motion of Northeast Igloo (ESKIMO 11) atNode 60. .. .. ............ ....................... 151

5-47 Computed Motion of Northeast Igloo (ESKIMO 11) atNode 72. .. .. .......... ......................... 152

5-48 Computed Motion of Northeast Igloo (ESKIMO 11) atNode 75 .. .. ... . .... ....... . ...... ........... 153

5-49 Computed Motion of Northeast Igloo (ESKIMO 11) atNode 77.. .. ... . .... ....... . ...... .......... 154

5-50 Computed Mo-zion of Northeast Igloo (E!ýKIMO 11) at

Node 79 .. .. ... . .... ....... . ...... ........... 155I5-51 Computed Motion of Northeast Igloo (ESKIMO 1)a

5-52 Compted otio of orthast gloo(ES IMO1) atNode 801. ... . ................ ................... 156

5-52 Computed Motion of Northeast Igloo (ESKIMO I1) atNode 101 ... .. ............... . ..................157

5-53 Computed Motion of Northeast Igloo (ESKIMO 11) atI

rNod0 108 .. .. ............ ....................... 159r5-55 Computed Motion of Northeast Igloo (ESKIMO 11) atNode 115 .. .. .............. ..................... 160

5-56 Permanent Movements of Northeast Headwall ofESKIMO 11 as Measured (in hundredths of feet) . 161

5-57 Computed Permanent Displacements of NortheastHeadwall of ESKIMO III (in hundredths of feet' ~ 162

5-58 Computed Motion of Northeast Igloo (ESKIMO IV) atNode 21 .. .. ... . ...... ..... . ...... ........... 163

5-59 Computed Motion of Northeast Igloo (ESKIMO IV) atNode 24. .. .. ............ ....................... 164

xiv

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CCNTENTS (CONTINUED)

Figure

5-6o Computed Motion of Northeast Igloo (ESKIMO IV) atNode 61.. ............ ...........................165

5-61 Computed Motion of Northeast Igloo (ESKIMO IV) atNode 64 .. ........ ...............................166

5-62 Computed Motion of Northeast Igloo (ESKIMO IV) atNode 69 .. .. .............. ............ ....... 167

5-63 Computed Motion of Northeast Igloo (ESKIMO IV) atNode 91.. ............ ....... ...................168

5-6b Computed Motka of Northeast Igloo (ESKIMO IV) atNode 94 .. ........ ...............................169

5-65 Computed Motion of Northeast Igloo (ESKIMO IV) atNode 97 .. ........ ...............................170

5-66 Computed Motion of Northeast Igloo (ESKIMO IV) atNode 99. .. .... ........ ........ ............171

5-67 Computed Motion of Northeast Igloo (ESKIMO IV) atNode 119. .......... .............................172

5-68 Computed motion of Northeast Igloo (ESKIMO IV) atNode 12'. .............. .........................173

5-69 Computed Motion of Northeast Igloo (ESKIMO IV) atNode 124. .......... .............................174

5-70 Measured Permanent Displacement Contours ofNortheast Headwall of ESKIMO IV (in hundredthsof feet) .. .............................. . . . 175

5-71 Computed Displacement Contours of NortheastHeadwall of ESKIMO IV at 158 msec (in hundredthsof feet). ............ ...........................176

5-72 Measured Acceleration Time Histories of NortheastHeadwall of ESKIMO IV .. ........ ................. 177

5-73 Measured Displacement Time Histories of NortheastHeadwall in ESKIMO IV .. .......... ............... 179

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TABLES

Table Page

1-1 Details of Igloos in ESKIMO ItI.. .................. 9

1-2 Details of Igloos in ESKIMO III .. .. ..............11

3-1 Comparison of Coarse and Refined Finite ElementMeshes. .. ........ ................. ............. 34

3-2 Soil Stiffness from Test in North Igloo........40

3-3 Properties of Headwall and Wingwall Sections ofIgloo B (Northeast), ESKIMO 11. .. ................64

3-4- Material Properties for Igloo B (Northeast)Headwall, ESKIMO IV. .. ......... . ................69

4-1 Schedule of Gages for measurement of Air Blast,

ESKIMO IV .. .. ........ ................. . ........72

4-2 Schedule of Accelerometers for Northeasi Igloo,ESKIMO IV .. .. ...... ................... . ........77

5-1 Motion of South Headwall (ESKIMO 1) above Centerof Door .. .. ...... ................. . ............ 83

II5-2 Peak Velocities of Upper Corner of 'oor .. .. ......83

5-3 Peak Deflection of Center of Doorway. .. ..........84

5-4 Peak Acceleration of Base of Headwall .. .. ........85

5-5 Motion of East Headwall (ESKIMO 11) above Centerof Doorway. .. ...... ................... . ........92

5-6 Computed Maximum and Permanent Displacement ofNortheast Headwall, ESKIMn 1 I.. .. ................95

5-7 Comparison of Computed Maximum Displacements forESKIMO 11I.. .. .......... ................. .......96

5-8 Motion of Northeast Headwall, ESKIMO 11, aboveCenter of Doorway. .. ......... . ..................98

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A kR- 7556 -1 -4 18 2 14

CONTENTS (CONCLUDED)

Table Page

5-9 Comparison of Maximum Displacements of NortheastHeadwalls of ESKIMO 11 and ESKIMO IV Igloos ... 101

5-1-O Comparison of Maximum and Permanent Displacementsof No~rtheast Igloo, ESKIMO IV. .. .. ..... .......104

II5-11 Comparison of Maximum Acceleration of Northeast

Igloo, ESKIMO IV .. .. ..... ....... ............. 106

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SECTION 1

INTRODUCTION AND BACKGROUND

This report covers a part of a general program sponsored by the

Department of Defense Explosives Safety Board (DDESB) to determine safe inter-.

magazine separation distances for various orientations of magazines for storing

chemical explosives. The main objective of the program is to determine the

minimum intermagazine separation distances so that an explosion in one magazine

(donor) will not cause an explosion in an adjacent magazine (acceptor). This

report describes a study to predict analytically the behavior of magazine

headwalls and to compare analytical and test data.

Preliminary tests had indicated that specifications'for minimumseparation distances betwveen magrzines were excessively conservative for some

orientations. Increasing land costs and siting problems made it desirable to

justify reducing the rear-to-front separation distance. Ea. ier tests had

Sindicated that earth-covered, steel-arch igloo magazines can be safely spaced

side by side at a distance in feet of 1.25 W in which W is the weight in

pounds of the high explosives in storage. On the other hand, very few test

data had been developed for determining the minimum safe distances for other

magazine orientations.

Starting in 1971, the DDESB sponsored a series of large-scale maga-

zinc explosion experiments, called the ESKIMtO series, for the purpose of estab-

j lishing minimum separation distances for earth-covered, steel-arch magazines.

To date, four tests designated as ESKIMO I, ESKIMO II, ESKIMO III, AND

ESKIMO IV have been conducted. These tests are described briefly in the

following sections.

1.1 DESCRIPTION OF ESKIMO I TEST

ESKIMO I was a large-scale magazine explosion experiment conducted

on 8 December 1971 at the Randsburg Wash Test Range of the Naval Weapons Center,

China Lake, California. Four earth-covered, steel-arch magazines were exposed

to the explosion of the contents of a similar magazine. The donor magazine

R-7556-1 -4182

contained 200,000 lb of high explosives. The four acceptor igloos faced the

donor and were located at various distancei ranging from 73 ft to 161 ft, asshown in F'gure 1-1. The distances 73 ft and 161 ft correspond to 1.25 W1/

1/3~and 2.75 W, respectively, whete W is the weight in pounds of the explo-sive in the donor magazine. Two concrete block structures simulating one

particular type of Air Force aboveground mAgazine were also placed in the

area at distances of 117 ft (2 W1 / 3 ) from the donor igloo, as shown inFigure 1-1.

t The four acceptor steel-arch Igloos were built in accordance with

the standard drawing shown in Figure 1-2. Each of the igloos was 25 ft wide

by 14 ft high, with the length limited to 20 ft. Steel wing walls were used

in the test in lieu of concrete. The igloos were covered by a 90*-compacted

r earth surchargp to a depth of 2 ft at the top of the arch.

The primary objective of this test was to establish a safe, practi-

cable minimum-separation distance between steel-arch magazines for face-on

exposures. Another major objective of the test was to determine the fraqmentand debris hazard from mass detonatioo of explosive-filled projectiles in an

earth-covered magazine.

The damage to structures varied from minor headwall damage at the

south igloo to complete destruction of the concrete block structures. The Istatus of the acceptor charges after the test indicated a range from no

explosion or burning in the south igloo to complete explosion or detonation

of all charges in the east igloo.

Permanent deflections of the order of several inches, accompanied

by yield-line formation, have been noted in some of the surviving headwalls.

On the other hand, photographic evidence indicates that the steel plate doors

in r.'_ igloos were driven in with considerable velocity before coming to rest,

while remaining partially attached to frames. In the forward exposure, com-

plete failure of the hinges occurred, and the doors were driven violently

against the rear wall of that magazine (20-ft depth, wall to wall).

2

j

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(1171)

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Refarence 1 includes a detailed description and the conclusions of

the E!,KIMC I test. Test results indicated that formerly applicable separation

distences could be significantly reduced.

Agbabian Associates (AA) performed dynamic response analyses of theheadwalls in the ESKIMO I test, using a finite element model of the headwall!(Ref. 2). The analyses were performed with the INSLAB code, a nonlinear firite

element computer program (Ref. 3). The objective of the analyses was to

understand the behavior of the reinforced concrete headwalls subjected to

blast loading and to use this knowledge in reducing reliance on full-scale

proof testing.

1.2 DESCRIPTION OF ESKIMO II TEST

.The ESKIMO II test was coinducted on 22 May 1973 at the RandsburgWash Test Range of the Naval Weapons Center, China Lake, California. Five

earth-covered, steel-arch magazines were exposed face-on all at the same

distance from the explosion source, as shown In Figure 1-3. The igloos to the

north, south, and west were those remaining from the ESKIMO I test. However,S the igloos to the south and west were fitted with'new door designs. All the

Smagazine structures were earth-covered, semicircular corrugated steel arches

I except the northeast igloo, which was constructed with a new type of noncir-

Scular steel arch. Table 1-1 shows details of all igloos in the ESKIMO II test.

The explosion source consisted of 72 tritonal-filled, 750-lb bombs

in two triangular stacks, in base-to-base contact. This source, containing

- 27,000 lb of explosives, had an expected TNT equivalent weight of approximately

S24,000 lb. The source was designed to produce an impulse load of 1100 psi msec

S on the headwalls of the test magazines located at 147 ft from the source. ThisS was the value of impulse estimated to art on the lowest third of an acceptor

. igloo from explosion of an earth-covered magazine filled to capacity (i.e.,

S500,000 lb net explosive weight permitted in one igloo by the current standards)Sw1/3

at a rear-to-front separation distance of 2.0 W , or 159 ft, where W is

the weight (lb) of charge in the magazine filled to capacity. Subsequently,

however, free-field measurements made to the rear of the ESKIMO III donor

magazine, and loadings observed in ESKIMO IV, have indicated an impulse load

7

R-7556-1 -4182

rn147'

20 20NO ESIM

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20'' DO

72 M117 BOMBS IGLOO

147' - k - 147'

]STRUCTURES FROMV®ROMESKIMO I

------------- ---_--. NEW STRUCTURES

FIGURE 1-3. LAYOUT OF TEST STRUCTURES FOR ESKIMO IIMAGAZINE SEPARATION TEST

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of about 1200 psi msec from only 350,000 lb detonated in an igloo at this

scaled distance. In ESKIMO IV, this level of loading was produced 147 ft

from a bare TNT hemisphere weighing 37,000 lb.

Piezoelectric and strain-gage pressure transducers were positioned

in and near the headwalls of the test magazines. Accelerometers and linear

motion transducers were mounted on the doors and headwalls of the structures.

Self-recording mechanical pressure gages were placed at distant stations.

Door motions were observed by a high-speed camera in the interior of each

of the magazines.

Because the near-field blast loading exceeded that planned, the

igloo structures were subjected to an overtest. Despite this overtest, the

large, single-leaf sliding door on Igloo D (south) withstood the blast loading

without breakup or severe distortions. Likewise, the Stradley-type headwall

used for Igloo B (northeast) incurred only an acceptable degree of damage.

The test reaffirmed the need for achieving a balance in the strength of

headwalls and doors.

Reference 4 includes a detailed description of the ESKI•0 II test.

1.3 DESCRIPTION OF ESKIMO III TEST

The ESKIMO III test was conducted on 12 June-.1-574 at the Randsburg

Wash Test Range of the Naval Weapons Center, China Lake, California. Five

earth-covered, steel-arch magazines were exposed in the test to the explosion

of the contents of a similar magazine, as shown in Figure 1-4. Igloos B,

D, and E were those remaining from the ESKIMO II test. Igloo A and the donor

magazine were new structures. Igloo A structure substituted a less expensive,

;ight-gage, deep-corrugated arch in place of heavy structural plate; other-

wise, it was identical to the standard steel-arch igloo. This igloo would

furnish % test of the opinion that the earth cover is the most important

factor in preventing explosion communication. In addition, this igloo was

intended to provide a direct qualification test of thr lightweight igloo.

The donor magazine was built to the same specifications as Igloo A. Table 1-2

shows details of all igloos in the ESKIMO III test.

10

R-7556-1-4182

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R-7556 -1 -4182

The explosion source consisted of 350,000 lb of tritonal in

750-lb bcmbs in the donor igloo shown in Figure 1-4.

Incident peak pressure was measured at the ground surface in front

of each acceptor igloo. Reflected peak pressure was measured from face-on

blast gages set in each headwall. A row of surface gages measured the

incident peak pressure over the earth on the oval arch igloo and on the light-

gage circular arch magazine. Acceleration and displacement measurements were

made on the arches of these igloos so that should they fail, the rapidity of

failure could be used to estimate whether there would have been a risk of

explosion communication to the contents. Detailed damage surveys and permanent

displacement measurements were made after the test.

The main objective of the ESKIMO III test was to expose an earth-

covered, noncircular, corrugated steel arch magazine (Igloo B) and a new

circular, light-gage, deep-corrugated steel arch magazine (Igloo A) to explo-

sion of an adjacent magazine at the minimum side-to-side spacing now permitted

by standards. In addition, magazine headwall and door structures were tested

at several other distances and orientations of interest.

A preliminary inspection of the structures after the test snowed

that the doors of Igloos A, B, D, and E were all blown open. The headwall of

Igloo E experienced the most severe damage, and permanent inward displacements

were as much as 1.5 ft. Except for local damage near one edge of the door

opening, the headwall of Igloo D experienced generally slight damage. The

remaining headwalls showed only minor damage. Additional details on the test

are provided in Reference 5.

1.4 DESCRIPTION OF ESKIMO IV TEST

The ESKIMO IV test was conducted on 10 Septembe' 1975, also at the

Randsburg Wash Test Range, Naval Weapons Center, China Lake, Cal.ifornia. Its

principal objective was to demonstrate the resistance of a newly designed

headwall-and-door combination to explosive blast loading from detonation of

the contents of another magazine.

12

J:1

R-7556-1 -4182

"-IZ

A (NEW) \.

114,

260 i 4,R (NEW)

EEXISTING

E! LD

FIGURE 1-4. LAYOUT OF TEST STRUCTURES FOR ESKIMO IIIMAGAZINE SEPARATION TEST

13

A k R-7556-1-4182

The ESKIMO IV test array consisted of three magazine structures

each facing the explosion source 147 ft away, as shown in Figure 1-5. The

primary target structure was Igloo B to the northeast, consisting of a single-

leaf s~iding door, horizontally spanned, mounted on a modified headwall of the

standard Stradlay magazine.

Igloo D (east) was rebuilt with the two-leaf, hinged, steel-plate

door and the headwall of the standard circular steel arch magazine. Exposed

to the same level of loading as the primary target, it served as a controlstructure to demonstrate directly the relative strength of the primary target

(Igloo B).

Igloo E to the west was rebuilt with the headwall if the standardcircular steel arch magazine, but fitted with a single-leaf sliding door.This combination was r-5ted inconclusively in ESKIMO II, but the test had

Indicated a serious Imbalance in strength between the door and headwall.

The test utilized a nearly ideal explosion source to generate blast

loadings. It afforded the opportunity for more extensive source diagnostics

and dynamic response measurements on the target structures than in previous

tests of the ESKIMO series. This in turn would enable an extensive correla-

tion between measured and calculated responses.

The explosion source consisted of 8-ib rectangular blocks of TNT

stacked in the form of a hemisphere, containing a total of 37,000 lb of TNT.

The explosives were left exposed, rather than surrounded by an earth cover

or barriers.

Pressure gages were installed in the headwalls and in the ground

nearby to measure blast pressure3 on the'headwalls. Accelerometers and jinear

displacement transducers (LVDTs) were used to measure structure-response time

histories of the headwalls. Self-recording pressure gages were installed tomeasure pressure loading at the far-field stations. Deta'ls on the locations

of the pressure gages, accelerometers, and LVDTs are discussed in Section 4.

14

R-7556-1-41 82

H\00

EXPLOSIVE

SOURCE C

[.E ._-_.. . .._ _

L J

I F

NOTE: IGLOOS A, C, AND F WERE

OLD STRUCTURES FROM THE PREVIOUS

ESKIMO TESTS THAT WERE NOT

CONSIDERED IN ESKIMO IV.

FIGURE 1-5. LAYOUT OF TEST STRUCTURES FOR ESKIMO IV MAGAZINE SEPARATION TEST

15

R-7556-1 -4182

Preliminary results (Ref. 6) showed that the doors of Igloos D

and E were blown in. The headwall of Igloo E sustained extensive damage.

The headwalls cof Igloos 8 and D and the door of Igloo B sustained little or

no damage.

1.5 OBJECTIVES AND SCOPE

The overall objective of the present study was to develop confi-

dence in analytical techniques for predicting the dynamic response of concrete

headwalls and steel-door structures to air-blast overpressures rerulting

from explosion of the contents of an adjacent magazine. To achieve the objec-

tive, the analytically predicted responses of the headwalls were compared

with experimental data from thm ESKIMO tests. The following tasks were

defined;

Task I

Calculate the response of the headwall and door of the south igloo

in the ESKIMO I test, using a finite element model win improved resolution.

I Task 2Calculate the response of the headwalls and doors of the east (C) and

northeast (B) igloos in the ESKIMO 11 test.

Task 3

Predict response of the strengthened Stradley-type headwall and

single-leaf sliding door of the northeast (B) igloo in the ESKIMO IV test.*

*Because of tight schedules, this task could not be completed before the test.Nevertheless, the analysis was performed before any results from the testbecame available.

16

A kR-7556-1 -4182

SECTION 2J

PRESSURE LOADING ON HEADWALLS

This section presents air-blast pressure histories used in the

dynamic response calculations of headwall and door systems. Provisions

for measurino air-blast overpressure data on headwalls were made in the plans

for all shots in the ESKIMO test series. However, the measured data were

generally meager and of low quality. Therefore, data from other tests and from

theoretical considerations were used to design the pressure histories for

the analytical calculations of the ESKIMO tests.

2.1 PRESSURE HISTORIES FOR ESKIMO I TEST

The pressure time histories for the south igloo in ESKIMO I used in

the present study were the same as the corresponding histories calculated in

the previous study (Ref. 2). These histories are shown in Figure 2-1. The

three pressure histories represent loading for the three zones of the headwall,

as shown in Figure 2-2, and differ only during the unloading phase of the

pressure history. The differences reflect the influence of unloading signals

propagating downward from the top of the headwall. The use of just threeI

different zones was considered adequate for the finite element calculations.All the pressure histories incorporate a mill'second (msec) rise-time rampfront for compatibility with the integration time step.

Additional discussions on the calculation of the pressure histories

for ESKIMO I may be found in Reference 2.

17

A R-7556-i -4182

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19

R-7556-1-4182

2.2 PRESSURE HISTORIES FOR ESKIMO II TEST.

Although redundant air-blast instrumentation was provided at allfive of the test igloos In ESKIMO II, obtaining reliable detailed descriptions

of the blast loads applied to the magazine headwalls was difficult. Records

from most of the gages were reported to be "difficult to read and consideredunreliable." Peak-incident (side-on) and reflected overpressures measured

at the east and northeast igloos were consistent with other experimental data

and with the thsory of gas dynamics for shock reflection. On the basis of

the measured values and this consistency, a peak-loading pulse pressure of260 psi was selected for the ESKIMO 11 calculations.

For the five test igloos the measured impulse varied by a factor of

.wo from the lowest to the highest value. The nearly twofold variation in

measured inpulse may, in part, oe due to the lack of rotational symmetry of

the charge and surrounding revetment. The impulse for the east and westigloos is well below that for the other igloos. However, significant (20%

to 30%) north-south and east-west variations in impulse are present. Theimpulse selected for the headwall loading pulse (1720 psi msec) is considered

representative for the east and northeast igloos.

No positive-phase duration data were reported for the pressure

histories measured at the headwalls. Pressure histories were not available

for examination to establish durations. Scaling of previous magazine-safety

test data, general high-explosives and nuclear-test data, and computationaldata suggested durations of 15 to 35 msec. Consideration of typical pressure

history pulse shapes, the selected peak pressure, and the desired impulse led

to the selection of a 30-msec duration. The resulting pulse developed for

loading the east and northeast igloos of ESKIMO II is shown in Figure 2-3.

The three-zone description of the pressure loading of the headwall

was retained for ESKIMO II. The pressure histories for Zones I and 2, which

experience earlier unloading, are shown in Figure 2-3 superimposed on the

pressure history for Zone 3 derived from measured peak pressure and impulse.

20

'AkR-7556-1l.41182

300C

250-

+ +i

I I

p max p

200-ZONE 3 30 MSEC 260 PSI 1720 PSI MSEC

ZONE 2 30 MSfUC 260 PSI 1432 PSI MSEC

ZONE 1 30 MSEC 260 PSI 1100 PSI MSEC

1150

F 100

ONE 3

ZONE 2

50

010 20 30TIME, NSEC AA 7580

FIGURE 2-3. PROPOSED PRESSURE HISTORIES FOR NORTHEAST ANDEAST IGLOOS, ESKIMIO HI

21

A k R-7556-1 -4182

Adjustments in the pressure load history proposed for calculating -

response of the ESKIMO 11 east and northeast igloos may be made if more reliable

estimates of positive-phase duration are obtained or if more accurate estimates

of the impulse are obtained.

2.3 PRESSURE LOADING 41ISTORY FOR ESKIMO IV TEST

Eight pressure gages were placed, as shown in Figure 2-4, on the

headwall of Igloo 8 (northeast igloo) in ESKIMO IV. This concentration of

instrumentation was intended to measure the variation of pressure over the

height of the headwall and to determine the uniformity of the pressure across

the face. In addition, side-on pressure at ground lev,-l was measured at

three ranges to establish the free-foeld blast pressure corresponding to the

reflected overpressure loading on the headwall. Review of the "quick-look"

data indicated that useful records were obtained from seven of the eightI

stations on th~e headwall and from all the free-field ground levei stations.

At the 147-ft range, the free-field ground level station recordeda peak pressure of 62 psi. Empirical data for high-explosive detonations in

air indicate that the peak reflected overpressure at the same range shouldbe 290 psi (Ref. 7), whereas classical estimates of reflected shock strength

for ideal gases indicate a peak reflected pressure of 265 psi. Raw reflectedIr pressure peaks taken from the "quick-look" records range from 195 to 295 psi.

Pressure histories from Stations P16, P48, and P513 appeared to be

influenced by movement or leakage of the door. The record from Station P48

suggests failure of the gage about 5 msec after blast arrival. The record

from Station P7B shows a prominent oscillatory signal of about a 3-msec period,

which distorts the early portion of the record. Development of pressure

loading for the headwall of Igloo B (northeast) was therefore based primarily

on the records from Stations P28, P38, P6B, and P88, and on the classical

treatment and empirical data for chemical explosions and shock waves in air.

22

Ak R-7556-1--J4 182

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R-7556-1-4182

Comoarison of traces from Stations P23, P68, and P88, as shown in

Figure 2-5, fails to support the assumption of systematic variation of the

pressure history over the height of the headwall. Duration of the meaningful

pressure loading on the headwall appears to be 14 msec. This is the duration

adopted for pulses to be used in computing headwall response.

Precursors are apparent in all three pulses. The delay between

eailest arrival and what is considered the main blast-pressure signal is

approximately 1 msec. C=Iarison of signals frown Stations P3B and P68 is

show'n in Figure 2-6. Although differences in peak pressure and precursor

timing and amplitude are apparent, the signals show good agreement. Pressuredifferences durinq the decay phase are of the same order as the differences

between signals from the lower, middle, and upper stations shown in Figure 2-5.

On the basis of the ccmp.irisons of "quick-look" data for Stations P2B,

P36, P6B, and P88, and the analytical and empirical data for chemical explo-I

sions in air, a single pressure history was developed for the headwall response

calculation. The pulse is shown in Figure 2-7 with a smoothed version of the

frea-field ground level (side-on) pressure history measured at the same range.

The peak pressure, 280 psi, is consistent with the analytical, empirical, and!

experimental data. The duration, 14 msec, is congistent with the ESKIMO IVdata, but is considerably shorter than that predicted from the analytical andempirical data. The impulse, 1180 psi msec, is consistent with both the

ESKIMO IV data as shown in Figure 2-8 and with empirical data. The scaled

empirical data (Ref. 7) indicate that the reflected pressure pulse correspond-

ing to a 62-psi incident overpressure pulse from a 37,000-lb hemispherical

TNT charge should have a peak pressure of 290 psi, a positive-nhase duration

of 34 msec, and an impulse of 1160 psi msec. Pulses closely resembling the

represent3tive reflected pulse shown in Figure 2-7 can be made to satisfy

these requirements by adding a low amplitude tail. For example, the pulseshown in Figure 2-9 has a peak pressure of 290 psi, a duration of 31.7 msec,

and an impulse of 1170 psi msec. Its close tesemblance to the proposed short-

duration pulse is obvious. The use of the short-duration pulse is considered

satisfactory and may be preferred for reasons of economy in calculating

headwall response.

24

tI R-7556-1-4182

R

P8B

P28

"P2B

300 P68

..200-

CII

0 0 P28

La P8B

00

-2 0 2 8 10 12 14 16 18 20

TIME, MSEC

FIGURE 2-5. COMPARISON OF PRESSURE HISTORIES FOR A VERTICALARRAY OF GAGES, IGLOO B OF ESKIMO IV

25

A k R-7556- 1-4182

P38 _P68

300- P68

200-

• 100-'A , P38

-10•

-2 0 2 4 6 8 10 12 14 16 18 'TIME, MSEC

FIGURE 2-6. COMPARISON OF PRESSURE HISTORIES TO TEST UNIFORMITY OF PRESSURELOADING ACROSS WIDTH OF ilEADWALL, IGLOO 8 OF ESKIMO IV

26

T + + i I + I . . . . . . . . ' I - i + ,` , . . . . . . .. .. . . . . . . " , , , ... . . .. . . . . . . . . .. . . . . . .

R-7556-1 -4182

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27I

A R-7556-1-4182

P86

P68H P213

P2B

300 P68

v 200- PROPOSED LOADING PULSE

S100-

C,. 0 P8B

-100 f-2 0 2 4 6 8 10 12 14 16 18 20

TIME, MSEC

FIGURE 2-8. COMPARISON OF PRESSURE HISTORIES FOR A VERTICAL ARRAY OF GAGES WiTH TH!PROPOSED LOADING PULSE FOR RESPONSE ANALYSIS OF IGLOO u, LSKIMO IV

28

R-7556-1-4182

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Aik R-7556-1 - 4 182

SECTION 3

STRUCTURAL MODEL OF HEADWALLAND DOOR SY'OTEM

This section describes the finite element models of the headwalls

in ESKIMO tests to be used in performing the dynamic analyses described in

Section 5. The models are to be used in conjunction with the INSLAB computer

program. Section 3.1 describes the finite element model of the south headwall

in the ESKIMO I test. Also included in this section are the modeling tech-

* niques for considering the effects of soil supporting the headwall, concrete

floor slab, and steel arch on the response of the headwall. Section 3.2presents the finite element models for the east and northeast headwalls in the

ESKIMO II test. Section 3.3 discusses the finite element of the northeast

headwall in the ESKIMO IV test.

3.1 STRUCTURAL MODEL, ESKIMO I TEST

3.1.1 :INITE ELEMENT MESH

Fig. 3-1 shows a coarse finite element mesh of the south headwall

ir, :.heESKIMO I test which was used in the previous study to compute analyti-

cally the dynamic response of the headwall (Ref. 2). A refined finite element

model of the same headwall used in the present study is shown in Figure 3-2.

The previous model was necessarily coarse because the existing INSLAB code

(Ref. 8) placed severe limits on the size of the model. To refine the model,the INSLAB code was modified to solve larger problems (Ref. 2). Table 3-1presents a cofmTt'nson , he coarse and refined finite element meshes of the

south headwa i in ESai MO I.

The face of the magazine consists of a concrete headwall and two

steel wingwalls. As di', ;ed in Reference 2, the finite element model did not

include the wingwalls, )se effect on the headwalls it considered negligible.

Preceding page blank

31

A k R-7556-1-41b2

y NODE NUMBER

I ELEMENT NUMBER

z6

i1

133

i 2142= 1._ 16/ 3 17 23 35 3

S/52/ 2. 7 2 8 29

.. __.. /

D3IST AN CE I

3F 38 39 40 49 SI

3,2

44 45 46 47 48 511

-ISO- -ISO. -120. -0-0.-30. -0.

DISTANCE, IN.

FIGURE 3-1. COARSE FINITE ELEMENT MODEL OF SOUTH HEADWALL, ESKIMO I

32

-~n 7 - . - .7

iNODE NUMBER R-7556-1-4182

I 2 4 5 6 1,1LOI 1 9 1 A. nit •t• , 18•

4 1 0 53 54 i1

t p P57 5s 59 20 6 2 63 64

2i 5 Its 27 6 9 70 71 72

73 74 75 76 77 71 7 9 40

41 32 43 44 47 48

3 0 50 1 2 53 64 9 6s

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a 90 aO 22 9 •3 94 9iS 96

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S~DISTANCE, IN.

S~~FIGURE 3-2. REFINEC) FINITE ELEMqENT MODEL OF SOUTH HEADWALL, ESKIMO I

233

R-7556-1 -4182

TABLE 3-1. COMPARISON OF COARSE AND REFINEDFINITE ELEMENT MESHES

Coarse Mesh Used Refined Model of Change,item to Be Compared in Previous Study Present Study

1. Total nodes 66 120 + 80

2. Total elements 51 96 + 90

3. Half bandwidth ofstiffness matrix 33 33 0

4. Total elementsrepresentingthe door 8 18 +125

5. Total discreteelements representingsoil 43 71 + 65

6. fotal discreteelements representingconcrete floor 0 18

7. Nodes for whichresponse histories tobe obtained 10 19 + 90

8. Estimated fundamentalfrequency of thelargest element 1000 Hz 2250 Hz +125

34

h6j

R-7556-1-4182

3.1.1.1 Properties of Door

The south-igloo headwall in ESKIMO I was fitted with double-leaf

hinged steel doors. The door was constructed from a 31o-in. plate supportedby 3-in. channels and 3/8-in. plate stiffeners, as shown in Figure 3-3. A

No. 16-gage steel plate was spot-welded on the inside of the door. The doorI is modeled as an orthotropic plate of un;form thickness possessing the charac-

terisLics of the real door. The equivalent properties of the steel door as

computed in Reference 2 are summarized below:

Property Symbol Numerical Value

Equivalent plate thickness h 2.04 in.

Modulus of elasticity E 32.4 x 106 pi

Modulus of elasticity E 27.8 x 10 psi

Equivalent density 1 0.0812 lb/in. 3

Yield moment M 10.52 kip-in./in.xx

Yield moment M 12.83 kip-in./in.yy

Plastic modulus E 0.1 of elastic modulusp

3.1.2.2 Properties of Headwall Section

A typical section of the headwall, showing the details of the rein-

forcement, is shown in Figure 3-4. To account for the rapid application of

loading, the dynamic yield stress, f, for the reinforcing steel is taken

as 52 ksi, as suggested in Reference 9. Similarly, the dynamic strength of

concrete in compression, f, is taken as 3900 psi, a 30% increase from the

static strength of 3000 psi. Young's moduli for steel and concretp are

S assumed to be 30 x 106 psi and 3 x 106 psi, respectively.

35

yI

3/8- 1II

13" X 3/8" BAR

NO. 16 Ga-- j

3C 6

-w x

(a) Elevation of the door (c) Cross-section B-Balong y-axis

3 " 6 /NO. 16 Ga

3 E6

3/8" V'0' \3 X 318" BAR

(b) Cross-section A-A along x-axis

FIGURE 3-3. DOOR DETAILS FOR SOUTH IGLOO, ESKIMO I

36 I

R-7556- 1-4182

!x

N.4NO.6 T* 12"1

- j-y-z 1.75" 4.375"

1- *T SOIL1"

ARCH1 L (b) Section AA: cross-section SF" - 4-- perpendicular to y-axls Y

15I NO. 4 AT 12" y

PtNO. 6 AT 12" .12

L' NO. 4 NO. 40 * 12"

(a) Reinforced concrete section

2.2 5•"- - 5-1---

(c) Section BB: cross-section Sperpendicular to x axis

FIGURE 3-4. SKETCHES OF HEADWJALL SECTIONS TO COMPUTE MATERIAL

PROPERTIES (SOUTH IGLOO, ESKIMO I)

37

ilk R-7556-1 -4182

Based on Figure 3-4 and the assumed material properties of

reinforced concrete, the yield moments for ooth cross sections S and Sx yaire calculated. It is found that both cross sections are underreinforced;

therefore, the yield moments are governed by the tensile strength of steel.

The procedures for computing these moments are presented in Appendix B.

For Section Sx

M+ - 121.2 kip-in./ft when the headwall is concave inwardyyM - 159.0 kip-in./ft when the headwall is concave outwardYY

For Section Sy

M+ = 110.7 kip-in./ft when the headwall is concave inwardxx

M" - 69.2 kip-in./ft when the headwall is concave outwardxx

The headwall section is modeled as a homogeneous, orthotropic plate

of uniform thickness possessing the same dynamic characteristics as the actual

reinforced concrete headwall. The equivalent properties of the headwall

sectiorn are given below:

Property Symbol Numerical Value

Equivalent plate thickness h 12 in.

Modulus of elasticity E 3 x 105 psi

Modulus of elasticity E 2 x 105 psiy

3Equivalent density 150 lb/ft

The values of E and E are obtained using the procedure described inx y

Appendix C.

38

ii~iL R-7556-1 -4182

3.- 2 STIFFNESS OF SOIL

The ESKIMO tests (Refs. 1, 4, 5) showed that the compacted soils

behind the headwall and covering the steel arch influence the behavior of the

headwall significantly because of the interaction of soil and headwall. In

the longitudinal direction, the earth cover merges smoothly with the ground

behind the rear wall. Therefore, any support provided by the soil per unit

area of the headwall is similar to an infinitely long compressible column.

The response of the soil is expected to be highly nonlinear because the

permanent displacements of the headwall are of the order of several inches

(Refs. 1, 4, 5).

Actual test data regarding the strength of the compacted soil over

the north igloo of the ESKIMO I test array are available (Ref. 10). In the

test, two opposing rams were driven by a hydraulic jack horizontally outward

against the earth fill through circuiar openings cut in the right and left

sides of the corrugated steel arch. Load deflection curves were rlotted for

the soil over the igloo at the initial stage of the loading and the final

stage (5 min after the application of lobds). The spring constants of the

soil based on these curves are shown in Table 3-2. It is noted that in the

testing, the soil was allowed to settle for one minute before additional

loading was applied. For the quantities of explosives normally stored in

magazines, blast-pulse durations at distances of interest are of the order

of tens of milliseconds. As a consequence, the corresponding stiffness isvery hiah. To arrive at a reasonable dynamic stiffness of the soil, a

column of soil subjected to step loading of magnitude P was investigated.

The deflection S at ti-e t is

PLAE

39

R-7556-1 -4182

TABLE 3-2. SOIL STIFFNESS FROM TEST IN NORTH IGLOO

___ ___ ___ ___ K, lbin.3

Stage Location P -0 to 60 psil P -60 to 270 Psii P - 270 Psi

Iiil Right 700 350 230

Left 666 245 133

Right 600 330 190Final

Left 580 235 133

The stiffness is defined as

K P FAE

whereI A - The cross-sectional area of the soil columnw

E - PC

C - Wave velocity in the soil medium, 4000 ft/sec

p- Mass density of the soil, 0.00018 lb-sec 2 /n.4

L - Ct

Because of the reflections of the pre~ssure wave a3t the ends of the

soil column, different expressions for the deflections were derived and are

illustrated in Figures 3-5a to 3-5c. The resulting stiffness withi respect to

time is shown in Figure 3-5d.

The dynamic stiffness calculations are based on a one-dimensional

wave propagation model. Neither soil friction nor wave dispersion was con-

sidered; therefore, the true valups should be a little higher than the test data.

In addition, there was ample tir'e during the test for soil to settle; whereas

in the dynamic stiffness calculation, there is very little time for soil to

40

A ~R-7556-1 -4182

K L

AA- t

A

- L/C < t < 2L/C

S6 "•÷LT"

(b)

P

SPL PL PL'

W E + WE A

L' " E+P(L + L'')Si ---IAE

(c)

3000

2000 -

1728 ) 1723 \1728zi7z

.J

U,,

S1000 - 864 8ý4

U,-

0 I I0 5 10 15 20 Z5 30

TIME. MSEC

(d)

FIGURE 3-5. DYNAMIC STIFFNESS OF SOIL

41

R-7556-1-4182

settle. The mroulus of elasticity for soil under high pressure conditicns

is much smaller tnan that under low pressure conditions, as can be seen in

Table 3-2, which shows lower static stiffnesses at hiqh pressure levels.

It is doubtful that the effect of loading magnitude is important, especially

when the peak pressure occurs for only a 3-msec duration.

The lowest dynamic stiffness, otcurring at 10 msec, 30 msec,50 msec, etc., is 864 lb/in. 3 (Fig. 3-5d), which is slightly higner than the

static stiffness shown in Table 3-2 (700 and 666 lb/in.3 for right and leftlocations, respectively) in the initial stage. Since the major exolosive

loadings used in this study were applied to the headwall within the first

few milliseconds, the stiffness is subject to rapid change during this

period. A value of 1300 lb/in.3 is considered to be the best estimate on

the soil stiffness.

3.1.3 MODEL REPRESENTATION FOR SOIL AND HEADWALL INTERACTIONI

In most analyses involving structures supported on soil, a common

practice is to represent the soil by spring-mass or spring-dashpot systems

(Ref. 11). This approach is valid if the motions are small so that the soil

response is linearly elastic. Since the soil behind the headwall behaves io

a highly nonlinear fashion, the conventional approach of representing soil

by spring-mass or spring-dashpot systems may not be useful. In addition,the presence of springs would not allow the headwall to undergo permanent

deflection. For this reason, viscous damping elements, or dashpots, wereused in the previous study (Ref. 2). Massless dashpots with damping

coefficient equal to -C per unit area of headwall were used, where is

the mass density and C is the wave velocity of the soil. The computeddisplacements from the study generally exceeded the measured values from th3test. The use of dashpots alone was considered to be a factor in producing

excessie ddisplacements.

42

R-7556-1 -4i182

In order t3 determine the best possible model to represent the soil,

the three test cases shown in Figure 3-6 were considered. A section of the

headwall was sliced along the vertical plane. The base of the headmall was

embedded in the ground. The top of the arch line var;nIs from 13 ft at the

center tr zero at the ends of the headwall. A value of 5 ft was arbitrarily

selectt6 •;e rear of the wall, from the top of the steel arch ro the top

of the :-_adwal 1, was supported by earth fill.

In Case A, the earth fill was represented by a series cf elestic

springs attached to the nodes on the headwall, as shown in Figure 3-6.

A certain percentage of the mass of soil was concentrated at each of these

rnodes, as discussed in Reference 2. The stiffness of the springs was equal to

1300 lb/in. per unit area of the headwall section. In Case B, the earth

fill was modeled by a series of linear dampers attached to the nodes on the

headwall section. Tho coefficient of the dampers was taken equal to -C.

In Case C, t:he soil medium behindl the headwall was modeled by lineardampers and nonlinear springs in series attached to the nodes on the headwall

section. The coefficients of the linear dampers were equal to -C. The

nonlinear springs were one-way springs that can resist notion only in one

diiection. i.e., in compression. The stiffness of the springs in cor'pression

was equal to 1300 Wb/in. per unit area of the headwall section.

All three models were subjected to the same blast-pressure loading

experienced by the south igloo in ESKIMO I. Dynamic responses of the models

in three cases were obtained using TRI/SAC code (Ref. 12), a general finite-

element computer program capable of solving linear and nonlinear problems.

Cases A and B were solved with the linear step-by-step option of TRI/SAC

(Ref. 12), whereas Case C was solved with the nonlinear step-by-step option.

The response time histories at selected locations are shown in

Figures 3-7 through 3-11. In Case A, displacement responses oscillate at high

frequencies and eventually attenuate to zero (Fig. 3-7). This type of behavior

of the headwall is in contrast to the observed behavior in the ESKIMO I test,

43

R-7556- 1-4182

4c

- En

4L-z

a 0i

ujT-

34, r i

-TI

T7

1

~zII

I" a

inuz

CM .1 %SM I I

T :-I

LijJ

4',c

ft% PO 0 I1~:TE~ : 4-;

44 4

R-7556-1 -4182

so SO*

j IA

CA

u1

T to

1! 34 L6J~

_ _ _ _ _ _ _ _ _ _ _* 31 I

45~

R-7556-1-4182

do

IL

; 0

L!I

03 a

a C-4

i1 \ (A

500~~ ~ 500 '0 0 ai0 Io

~, I

• .•

L ZLi

46.

SJ E

/ I

a. ,3' ZfliO PZ8" E; 61 r 01 OT"?L c•a .N3I];3'•,S :

: 146

R-7556-I-41 82

I.

1 7

I L'

F;t4

!

r

-i vi

L 0 3,

CIO

AL!-G"3A -

_ _ __I_"_ _ _ _ _ __"_ _ _ _ _ '• I' tl \" ! -

in , U 0il

Si ,!I

' I47

4•7

Ak R-7556-1-41 82

i L

0 , . . (al r

tot. 3313 0 2-

a.!

UO

I =Z

,i a t' Oi" O t ieO s o s 1 " O" O~ o o • ' • a

LjA

ttv

a I,,.,

/ -

L a?

48

A-= R-7556-t-4182

!gig

I

Go, alI! *

a

La

,1 .2•

IF I

U Inni-

,. O: ll 0 G

49. •

I, i . ,..Il•"3 '• C'.

urg li ~ 00'- I

"• • 00 II •0"I~t O0"I 0 " i O0Jo 0'

•136•h

R-7556- 1-4182

where largo permanent displacements of headwalls were noted. The headwall in

Case S (Fig. 3-8) does not exhibit any oscillations initially aiid then

stabilizes at a displacement level slightly smaller, than the maximum value.

The displacement and velocity time histories for Case C are shown in

Figures 3-10 and 3-11, respectively. The behavior of the headwall in

Case C is similar to Case 8 except that the final displacements in Case C

are well below the maximum values.

In the ESKIMO I test, a gap of several inches between the headwall

and the earth fill was noted (Ref. 1). This indicated that the permanent

displacements of the headwalls were significantly smaller than the maximum

values reached during the test. The soil model of Case C (Fig. 3-6) appears

to best represent the qualitative behavior of the earth fill in the

ESK(IMO tests. Howevir, the magnitude of the displacements obtained in

Case C indicates that reduced numerical values of coefficients for the springs

and dampers must be used. In the absence of any relevant measurements, the

only guidelines for choosing these coefficients is their performance in small

test problems. It was found that, in such a test problem, a spring constant

of 40 lbin, per unit area and a damping coefficient of 0.75 lb-sec/in, per

unit area produced headwall displacements that were of the order of magnitudeI

This combination of linear damper and nonlinear one-.',ay spring was

used to represent the interaction of soil with the finite element mesh of

the south headwall (Fig. 3-2). The constants for the spring and dashpot at

a node were based on the total tributary area of soil to be concentrated at

that node. The existing INSLAS code did not provide for nonlinear springs.

Therefore, the program was modified to accept nonlinear one-way springs.

Theoretical details on the incorporation of these springs, along with som~e

test cases, are presented in Appendix A.

50

ilk~ R-7556-1 -4182

3.1.4 E7FECTS OF CONCRETE FLOOR SLAB

The floor of the south igloo in ESKIMO I is a concrete slab 6-in.

thick, which thickens to 12 in. near the headwall. The reinforcement consists

of No. 4 ba;% spaced 12 in. apart, 3 in. below the top surface of the slab.

Linear spring elements and concentrated masses are used to model the effects

of the floor. The spring constant per unit area of the floor slab, determined

in response to a static-compressive stress, is

a 12,500 lb/in. 3zL

This value was obtained assuming Young's modulus of concrete to be

Eu 3 x 106 lb/in.2

c

and the length of the igloo to be 20 ft. The stiffness of the floor in

response to a dynamic load would be larger than the value given above.

However, the fact that the rear wall of the igloo is not anchored perfectly

would result in a slightly lower stiffness value. Assuming that the -,arious

unknowns compensate for each other, the static stiffness was used in modeling

the effect of the floor.

The value of the mass of the floor slab participating in the mass/

spring representation was chosen to preserve the fundamental frequency of

longitudinal vibration of the floor. The resultirg value is equal to the

mass of a strip of floor slab 8.2-ft wide.

II

511

R-7556-l -4182

3.1.5 EFFECTS OF STEEL ARCH

The main function of the steel arch in a magazine is to protect the

contents of the magazine from t;.e weather and from the earth fill over the

magazine. The only structural requirement for the arch is to support the

earth fill around the arch. The material used in the arch for the south

;gloo headwall (ESKIMO I) is No. 1-gage corrugated steel. The corrugation

increases the bending and circumferential stiffness of the arch, but reduces

its longitudinal, or axial, stiffness.

To study the longitudinal stiffness of the arch, one corrucation of

the arch is considered. Since this is symmetrical at the centerline of the

folý only one half of the fv-hd is necessary. The curved fold is approximated

by a straight segment AB, as ,.hown in Figure 3-12. Uoider the action of a

horizontal load P at end A of the segment, the horizontal displacement of

A results due to bending and axial compression of the member AB. The

component of deflection due to bending can be calculatcd as

PL 3 sin 2 eIb Ib 12EI cos3 e

and the component due to axia: compression is given by

PL cos 6a AE

where El and AE are, respectively, the bending and axial stiffnesses of

the arch. Therefore the total horizontal displacement of A is

PL 3 sin2 e PL cos e

12EI cos 3L AE

52

R-7556-1-4182

LINE OF APPLICATIONOF AXIAL LOAD

E0

L L

P

m 2

I--D

PD

A

FIGURE 3-12. AXIAL STIFFNESS OF STEEL ARCH

53

R-7556-1-4182

For a unit width of the arch, the following values are used to

compute

2A - 0.2758 in.

E - 30 x 106 psi

I - 0.001743 in. 4

L - 3 in.

h - 0.2758 in.

9 - 33.70

The horizontal displacement 5 is computed as

6 - (2.32 x 10-5 in./lb) P

If the corrugated arch were to be treated as if it were constricted

of an equivalent uncorrugated material, the relation between load and deflec-

tion would be

PLAE

e

where Ee is the equivalent elastic modulus of the uncorrugated -ateria:.

This relation can be used to determine the ec.-valent moculis. -aking .se

of the above relation between load and ae=lec:ion. The resil! 's

E - 4.60 x 105 psie

The buckling stress of tne e•jivalent unccrruqa:ez arc- is ::-:.:ez

forn the relation

Ehe

a !3ý1 -

54

R-7556-1 -4182

where a is the radius of the arch (a -156 in.), h is the thickness of the

arch, and is Poisson's ratio of the arch material (assumed v - 0.25).

The buckling stress is computed to be 495 psi. Although this is the theo-

retical buckling stress for the equivalent uncorrugated arch, buckling

experiments on cylindrical shells show that the stress at which the shells

buckle is seldom better than 30% of the theoretical value (Ref. 13). Thus,

the buckling stress of the arch is estimated to be 150 psi.

Nodal point 31 of the finite element grid of Figure 3-2 is a

typical nodal point located on the arch. The length of the arch that is

attributed to tnis node is about 24 in. Therefore, the force acting on this

n-de due to buckling of the arch is 990 lb. At no time can the fo.'ce of the

arch on Node 31 exceed this value. This node is also influenced by in area

of about 143 in.2 of soil backfill. Using Node 28 (see Fig. 3-1) of the

previous calculation of ESKIMO 1, south igloo, as a guide, the expected

peak displacement and velocity of Node 31 are 5 in. and 150 in./sec',

respectively. The soil is represented with springs having a stiffness of

40 lbin, per unit area, and dampers having a viscosity of 0.75 lb-sec/in.

per unit area. These values result in a peak force of 28,600 lb due to

elasticity of the soil, and an additional peak force of 16,100 lb due todamping. By comparison, the contribution of the arch is expected to be

negligible.

A study of the permanent deformations and damage patterns of headwalls

in the ESKIMO tests indicate that the steel arch appears to strongly influence

the behavior of the headwalls during the tests. As an example, Figure 3-13

is a contour diagram of the deformation of a headwall after the ESK~IMO I

test. The deformation contours generally approximate the shape of the steel

arch, which was semicircular. Figure 3-14 shows a front photographic view

of the same headwall after the test. The crack pattern experienced by the

headwall again approximates the shape of the steel arch. It is believed

that this phenomenon occurs because the arch separates the supported and

unsupoorted areas of the headwall. in particular, the unsupported area of

55

-3' -31 -Z2 -32 .4

- 36

-

0

-11 4

FIGURE ~ ~ ~~~+3 31. MVMN1FHAWL FNOT CETRILO SIOi

A plsvleshw0oeen1wy,~r h oo

mAgzn;amnsvuesosmvmn tor.04-e unit ar in hunreth offeet

+1356

A'ICD d R-7556-1-41 62C'P available to DDC dn•.s nf',t

P" !Ofl legiblo ea o'

i

FIUR 3-. "EAWAL OFNRT.GOO SKM. Noecrc

:~* ,'*.. I

*.1

SFIGURE 3-14. HEADW4ALL OF NORTH IGLOO, ESKIIIO I. Note crack

pattern approximating shape of steel arch.

57

Copy avcilable to DDC does not

pen]. fI. ly legible o•pxoducn b.

R-7556- 1-4182

the headwall is semicircular, and hence it is not surprising that the permanent

deformation and damage patterns of the headwall resemble the shape of the arch.

In addition, the sharpness of the steel arch causes high stresses in the head-Iwall, causing local failure along the arch line.

3.2 STRUCTURAL MODELS OF HEADWALLS IN ESKIMO II

Two different headwalls in the ESKIMO II test have been analyzed.

These are the Igloo C (east) and Igloo B (northeast) headwalls. The structural

models of these headwalls are described in the following subsections.

3.2.1 IGLOO C (EAST) HEADWALLAs described in Section 1.2, the east headwall in the ESKIMO II test

is identical in every respect to the igloos used in ESKIMO I. Therefore, the

finite element model of the east headwall in ESKIMO II is identical to the

model of the south headwall in ESKIMO I (Fig. 3-2) described in Section 3.1.

3.2.2 IGLOO B (NORTHEAST) HEADWALL

Figure 3-15 shows -. plan and an elevation of the Igloo B (northeast)

headwall in the ESKIMO II test. The wingwalls are of reinforced concrete

construction and are monolithic with the headwall. Therefore, the finite

element model of the headwall shown in Figure 3-16 includes the portion of

the wingwall up to the counterfort in order to consider the effect of thewingwall on the response of the headwall. As Jescribed before, an oval-shaped

steel arch is used behind the headwall to support the soil. The opening in

the headwall for the door is strengthened with concrete beams, as shown in

Figure 3-15. On top of the horizontal beam, there is an overhang that extends3 ft from the headwall. Since there is very little reinforcement provided

along the vertical direction, the overhang is not considered to function as a

structural member. Therefore, although the mass of the overhang is includedin the finite element model, the stiffness is not. In designing the finite

element mesh shown in Figure 3-16, the beams are represented by separatte

53

R-7556-1 -4182

I IL % C-W Ai9M1L

ine f lO V31VUI±3WAS I

cia

Oj~/Jo -L J

LI 71 CL

C11C

_ 0

-6- .

05

R-7556-1 -416~2

inpa ArV3WA

- -) ±osv v~I~.3wws I-IA :1

L-a

WIW

_Ij

~?liC.

R-7556-1-4.182

9 it Iwole

10 0

p.0to,

u.J

LLZ

Cc:C

Sr

14 0 x 49cc U- -- ----- - ----- -- ---

400

61.

i iAkilk R-7556-1-4182

elements so that the actual beam properties can be assigned to only the

elements representing the beams. This avoids the averaging of properties

that becomes necessary when the same element represents the beam and a

portion of headwall. The arch line is placed as closely as possible on the

edges of the finite elements. In order to minimize the use of triangular

elements, the arch line Is permitted to run across the Elements 11, 12, 22,

33, and 44, as shown in Figure 3-16. The finite element shown in Figure 3-16

consists of a total of 107 plate elements and 127 nodes.

The biparting and sliding steel door of the northeast igloo consi5s

of a 5/8-in. plate and a 1/ 4 -in. plate sandwiching five 5110 steel sections

arranged vertically as shown in Figure 3-17. Following the procedures

described in Reference 2, the mnterial properties of the elements representing

the steel door are computed. These values are summarized below:

IProperty Symbol Numerical Value

Equivalent plate thickness h 4.14 in

Modulus of elasticity E 30 x 10 ksi

Equivalent density 0 0.0773 1b/in.3

Yield moment M 68.6 kip-in./in.xx

Yield moment Myy 9Z.9 kip-in./in.

Plastic modulus E 0.1 of elastic modulus

Poisson's ratio V 0.25

The headwall and wingwall are modeled as homogeneous plates of

uniform thickness possessing the same dynamic characteristics as the actual

reinforced-concrete sections. The yield moments for these plates are cor-puted

using the procedures described in Appendix B. The yield moments and equivalent

properties of the headwall and wingwall sections are sho-in in Table 3-3.

6Z

R-7556- 1-4182

1/4" P,

5/8" It

IJ

II

(a) Elevation (b) Longstudina! section

51-05/8" It j e

-" 51-3" -1

(c) Cross section

FIGURE 3-17. CONFIGURATION OF STEEL DCOR FOR IGLOO B (NORTHEAST . ESBimC 1i

63

R-7556-1-4182

TABLE 3-3. PROPERTIES OF HEADWALL AND WINGWALL SECTIONSOF IGLOO B (NORTHEAST), ESKIMO 1I

Value for Value forProperty Hiiadwall Section Wingwall Section

Equivalent plate thickness, h 12 In. 12 in.

Modulus of elasticity. E 4.6 X 105 psi 2"67 x 105 psi

Equivalent density, a 150 lb/ft3 150 lb/ft 3

Yield moment, M 290 kip-in./ft 101 kip-in./ft

Yield moment, MXX -231 kin-in./ft -79 kip-in./ft

Yield moment, M- 196 kip-in./ft 1-2 kip-in./ft

Yield moment, M -160 kip-in./ft -81 kip-in./ft

AA8012

The supporting system of the headwall consists of the backfill on

top of the steel arch, the concrete floor slab, and the soil below the 'loor

slab. These supports are represented in the form of sarings and darrpers as

described in Sections 3.1.3 ano 3.1.4.

3.3 STRUCTURAL MODEL OF IGLOO B (NORTHEAST) HEADWALL, ESKIMO IV

Figure 3-18 shcxvs the finite element model of the heaz.ali of t:e

northeast igloo in the ESKIMO IV test. An oval-shaped steel arch su:cor.s

the soil for this igloo. The door opening in tle heac..all is s.ren:t.e-ez

with concrete beams. The vertical oeam extends to tne to o0f tne neao..aV.

As in the case of the northeast nead.-all in tre ESKIMO II "es:. --e -'oce' :.

this headwall represented the bea.-s by separate ele'ents. An el"ort ..as -aze,

as far aw possiole. to place :ne arch line on the edges cf t-e 4;-ýte e'e-e-:s.

4owever, in order to -rini-.:e the use of tr;angular eie-en:s. t"e a-:- *'-e

was pernitted to run across Ele-ents 22. 33. 43. and 53. as sn.-r in

F;gure 3-IS. The finite ele-ent -tv-sh 4or t;s nea,..a1i s :. .t- i "-a:

Ak?

1 2 3 4 S 6 7 a g

II to L-toISi•

to It 13 14 is t6 17 16

to 20 21 "3 24 26 27

229 30 3 3t 33 34 35 36it to L9 t A &a .So0

37 30 33 40 41 42 43. 44 45

43 47 46 49 so 51 52 54

55 7 6 57 57 59 60 6t 62 63

w 54 65 66 67 65 69 70 71 72

73 74 75 75 77 70 79 00. 6tA...,..1.

52 03 64 as *6 87 so a9 90inj m, L02 - •OR tO I ne o? hM nit no It

21 92 93 94 Us g6 97 gO 9 g

lO00 ot t - 103 104 105 106 107 /100

tog Ito 1i1 112 113 114 115 it6 11'

its L 19 tL• t '21 122 123 124 125 126

FIGURE 3-13. FINITE ELEMENT MODEL OF NORTHEAST HEADWALL, ESKIMO IV

65

R-7556-1-40 82

the locations of the accelerometers and the LVDT transducers (see Sec. 4) gen-

erally correspond to sc.ne nodes in the mesh. This facilitates a direct compari-

son of the test and calculated results. The finite element mesh of the head-

wall shown in Figure 3-18 consists of a total of 126 elements and 150 nodes.

The single-leaf sliding steel door of this headwall consists of a3/8-in, plate and a 1/4-in. plate, strengthened by four 6WF25 wide flange

sections and two 6 C 13 channels, all running horizontally. Two 6 C 13 channels

also run vertically along the two ends. This arrangement is shown in Figure 3-19.

Fo;lowing the procedures described in Reference 2, the material properties of

the elements representing the steel door were computed. These vadues are

summarized below:

Property Symbol Numerical VaIue

Equivalent plate thickness h 4.49 in.

Modulus of elasticity E 30 x 103 ksi

Equivalent density 9 0.05>• lb/in. 3

Yield ,momen t M 107.0 kip-in./in.

Yield moment M 14.07. kip-in./in.

Plastic modulus E 0.1 of elastic modulusP

Poisson's ratio v 0.25

To account for the variation of section )roperties, a total of nine

different materials is used to describe the model, as shown in Figure 3-20.Material No. 1 refers to the pruperties of the steel door, as discussed above.

Due to the different ar.angtmnenL of the reinforcing steel, the headwall section

is assigned four dilfferent materials with Nos. 2, 3, 8, and 9, as shown in

Figure 3-20. Material Nos. 5, 6, and 7 are used to represent the beams.

Material , is assigned t- the footing of the headwafl. The materialproperties assignedi to each material number is shown in Table 3-4. The yielc

moments of all soncrtte sections are computed using the procedures described

in 4ppendix B.

I' JtI

P-"556- 1-4182

P ~6[•

10'

3/8" P, 6 WF25

I_ _ _ _ _ U----'(a)~~~~~ ~~~ Clvto (b og Udi eto

(a) Elevation (b) Longitudinal section

1/4, It\

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(c) Cross section

FiGURE 3-19. .ONFjGURATION OF STEEL DOOR FOR IGLOO B (NORTHEAST) HEADWALL,ESKIMO IV

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The supporting system of the headwall consists of the ackfJi l on

top of the steel arcn, the concrete floor Slab, ano the soil beow t"e floor

slab. The representation of these supports in the form of springs and

dampers is described in Sections 3.1.3 and 3.1.4.

70

iS R-7556-1-l 182

SECTION 4

INSTRUMENTATION FOR ESKIMO IV

This section describes Agbabian Associates' recormendations on tte

instrumentation.of the igloos in the ESKIMO IV test: types of transducers :nat

were to be used. their locations on the headwalls and doors. and t.e rarces 04

variables over which the transducers were to be calibrated. The recommenda-

tions reflected a desire to obtain sufficient measurements of the northeast

,ieadwalI, since this is the only headwall of ESKIMO IV that was anairzea

using the INSLAB code.

4.1 PRESSURE GAGES

The Kistler gages were used to measiira pressure-time histories on

headwalls in the ESKIMO IV test. These quartz crystal piezoelectric trans-

ducers were selected because of their excellent past performance in similar

events. Table 4-1 shows estimated peak pressures and the ratings of

pressure gages that were scheduled to be used in ESKIMO IV. Table 4-1 also

shows similar information for the Ballistic Research Laboratory (BRL) self-

recording mechanical gages, placed in pairs, to measure far-field pressures

along radial lines in th": northwest, west, and south directions.

Figure 4-I shows the recommended arrangement of pressure gages on

the northeast ioloo (Igloo B). The primary objective of this recommendation

was to determine the variation of pressure loading on the wall in vertical and

horizontal directions. Because of the symmetry of the loading with respect to

the centerline of the headwall, all gages except one were placed on the right

half of the headwall. The gage on the left half of the headwall was intended

to detect any significant deviations in the symmetry of the loading. The

arrangement shown in the figure commits 8 pressure gages for the northeast

igloo. Figure 4-2 shows the recommended arrangement of the pressure gages

on the remaining two igloos.

71

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SKR-7556-1-4182

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0PRESSURE GAGE

FIGURE 4-2. PLACEMENT OF PRESSURE GAGES ON EAST (D)AND WEST (E) IGLOOS, ESKIMO IV

74

u k R-7556-i-41 82

4.2 ACCELEROMETERS

Accelerometers (Model 114 by Setra Systems Inc.) were used to

measure acceleration-time histories at various locations on headwalls in

the ESKi(IO IV test. These gages yield good response from zero hertz to

several hundred hertz, and the damping of the seismic eiement is essentially

independent of the changes in ambient temperature. Table 4-2 shows estimated

peak accelerations and ratings of the accelerometers used in ESKIMO IV.

Recoemmnded placement of the accelerometers on the headwall of the

northeast (B) igloo is shown in Figure 4-3. Because of the assumed sym•setry of

the loading and the structure, the transducers were placed only on one side

of the centerline of the igloo. The recommended locations for the gages

generally coincided with the nodes of the finite element mesh that was

used to analyze the headwall. As shown in the figure, a total of 12 acceler-

ometers was placed on this headwall and no accelerometers were placed on the

headwalls of the east (D) and west (E) igloos.

The impulse response of the accelerometers was checked ou• prior to

the test with a drop-table calibration device. This portable device was

carried to the site for one-the-spot checkout of the accelerometers.

4.3 LINEAR MOTION TRANSDUCERS

Long-stroke displacement transducers of the LVDT type were used in

ESKIMO IV to measure movement of the concrete headwall. The female part of

the transducer was attached to a universal joint mounted on a rail section

(mass) that was suspended from the corrugated metal roof of the igloo by

chains. The male or rod portion was supported by universal joints, with one

universal joint securely attached to the headwall at the desired point of

measurement. An effort was made to reference as many transducers as practical

to the same mass.

75

A kR-7556-1-4182

CENTER~~AU LIEINE'3* t31 a10

f DOOR FRMEACCELEROMETER NO.

10,3 4 5

S'S

AA 7501

0 ACCELEROMETER

FIGURE 4-3. PLACEMENT OF ACCELEROMETERS ON HEADWALL OF NORTHEAST

IGLOO, ESKIMO IV

76

R-7556-1-4182

TA9LE .-2. SCHEDULE OF ACCELEROMETERS FORNORTHEAST IGLOO, ESKIMO IV

Estimated Desiredmex i mwM Accelerometer

Acceleration, Rating,Position _ 9g

Door 630 1000

Headwall -- away from door 150 300

Headwall -- near door 200 300

Figure 4-4 shows reconmended placement of the displacement trans-

ducers (LVDT) on the headwall of the northeast igloo. Again, the locations

shown for LVDiTs generailly coincided with the nodes of the finite element mesh.

Nine LVDTs were placed on the northeast igloo, as shown in the figure, and

6 LVOTs were placed or, the remaining two igloos.

77

A k R-7556-1-4182

CuNTkI LINI OF IGLOO

I

ARCH LIN I

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3m-ge' DOOR FRMIE

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5,

AA 7500

0 LVOT

FIGURE 4-4. PLACEMENT OF LVDT TRANSDUCERS ON HEADWALL OF NORTHEAST

IGLOO, ESKIMO IV

78

R-7556-1- 4 82

SECTION 5

DYNAMIC RESPONSE OF HEADWALLS IN ESKIMO TESTS

5.1 INTRODUCTION

This section describes the results of dynamic analyses of fourdifferent headwalls in t ne ESKIOO tests. T e he eadwalls considered arethe south (and west) headwall In the ESKIMO I test, the east and northeast

headwalls in the ESKIMO II test, and the northeast headwall in the ESKIMO IV

K test. The analyses were performed subjecting the finite element model of the

headwall and door systems to blast loads. The finite element models are

discussed in Section 3 and the pressure loadings applicable to each model

are given in Section 2. The dynamic response of the models was obtained

with the modified INSLAB code (Ref. 3), a nonlinear, dynamic finite element

program. The results of these analyses are compared with the available test

resilts from the ESKIMO tests.

Because Section 5 requires some 70 figures to present the anelysisresults, they have been grouped at the end of the section text. Figure 5-1

et seq. begins on page 106.

5.2 RESPONSE OF SOUTH HEADWALL, ESKIMO I

The results of the ESKIMO I calculation using the refined fiiite

element model of the south headwall (Fig. 3-2, Sec. 3) are presented in

this section. The finite element model of the headwall was subjected to

the pressure loadings shown in Figure 2-1 (Sec. 2). The results of the

calculation are also applicable to the west headwall, since the south and

west headwalls have identical geometries and were exposed to the same loading.

These results are shown as time-history plots of the headwall motion and

contour plots of the displacement of the headwall. Coý,iparisons are made

between these results and the results of the prior calculation of Reference 2.

In addition, where experimental measurements are available, comparisons are

made between the calculation and the actual response of the south and west

igloos of ESKIMO I.

79

R-7556-1-4182

5.2.1 TIME-HISTORY DATA

Figures 5-1 through 5-9 show displacement, velocity, and accelera-

tion histories computed at several locations on the south and west headwalls

and doors of the ESKIMO I event. In addition, Figures 5-10 through 5-12 show

displacement histories at several other locations. Typically, these response

histories exhibit a steady climb to peak displacement, followed by a recovery

of displacement such that the magnitude of the final displacement is less

than half the magnitude of the peak displacement. Furthermore, the frequency

content of the displacement histories is extremely low compared to the input

pressure histories. The rise times of the displacement histiries are often

30 or 40 nisec, whereas the rise time of the input pressure history is I msec.

This is because the fundamental frequency of the headwall is very low

compared tc the predominant frequencies in the input loading.

The tendency for final displacements to be smaller than the peak

displacements is due primarily to the use of nonlinear spring elements In

modeling the soil backfill behind the headwall. A second factor is the use

of linear springu to model the concrete floor slab. In contrast, the

calculations of Refarenc3 2 used only damping elements to model both the

backfill and the founiation. This latter formulation resulted in final

displacements that were nearly equal to the peak d~splacements.

Figure 5-1 shows the motion of Node 1, wh;ch corresponds to the

top center of the headwalls of the south and west Igloos of ESKIMO I. The

peak positive displacementit Is 0.3 In., whereas the final displacement is

negative and Is equal' to 0.7 in. This indicates the presence of a gap about

fln this 'tpcrt the positive displacement of a headwall represents movementaway from the source, or into the igloo; and the negative displacementrepresents movement towards the source, or out of the igloo.

80

i: ~ ~

ji~~hJLR-7556-1-MI182.I-in. wide between the headwall and the compressed backfill after the shock.

Figure 5-13 (from Ref. 2), which shows the motion of the corresponding point

of the prior calculation, predicts no such gap. However, gaps between the

headwall and the soil have been observed during posttest inspection of tie

acceptor magazines. This indicates that the present method of modeling the

soil is a step in the right direction. The displacement histories of other

nodes on the backfill portions of the headwalls are shown in Figure 5-10.

Figure 5-2 shows the response history of Node 19, located on thetop of the arch line of the south and west headwalls. The response of the

corresponding point of the prior calculation is shown i.i Figure 5-14 (from

Ref. 2). The displacement histories begin in very similar fashion, reaching

displacements of several inches after 40 msec. At that time the present Y A

calculation begins to recover displacement, whereas the prior calculation

continues to show increased displacement. A gap of about 2.75 in. develops

in the current calculation. A large difference in final position of the

headwall Is shown in the two calculations. The current calculation shows

a final displacement of about 0.3 in., whereas the prior calculation shows

a 6-in. final dLkplacement. A similar situation exists with Figure 5-1. :

Figure 5-li shows the displacement histories of several other locations,

alor~g the arch line.

Figures 5-5 and 5-8 show the responses of points located within

the arch line on the south and west headwalls. While less strongly influenced

by the soil backfill than points located on or outside the arch line, these

points also show considerable recovery from peek displacement, However,

the ratios of final displacement to peak displacement are greater in these

cases than in those more directly dependenZ -in soil behavior. Figure 5-15

(from Ref. 2) shows the response for the prior calculation of the po t -

corresponding to that of Figure 5-8. The displzcement histories bet.. a1

the two c~ases disagrie in the ratio of final d!splacement to peak displace-

ment, and in the magnitude of the pePk displacement. The two cases are in

good agreement on the peak velocity and the peak acceleration, although the

A durations are dlifferenc.

81

. ...

- .- ,-f-.-,¶r'~-.~ TIC'Y

A k R-7 556-1-4182

Figures 5-3, 5-4, and 5-7 show the responses .)f points on the

boundary between the headwall and the steel door. In the present calculation,

the door Is connected to the headwall only along its top and side edges. It

is free along Its bottom and center edges. As a result, the door exerts aAIi great deal of influence on the headwall along the contact boundary. Sincethe connection along this boundary is accomplished by hinges, all of thisinfluence is transmitted to the headwall in the form of shear force. The

resultIng displacements are considerably larger, therefore, than displace-

ments of the headviall not along the boundary. For example, the displacement

of Node 49 (Fig. 5-4) exceeds that of the adjacent point, Node 50 (Fig. 5-5).Similarly, the displacement of Node 76 (Fig. 5-7) exceeds that of Node 77(Fig. 5-8). Figures 5-16, 5-17, and 5-18 (from Ref. 2) show points of the

prior calculation that correspond, respectively, to Figures 5-3, 5-4, and5-7 of the current calculation. In the previous calculation, the door was

modeled as having shear support along the bottom boundary as well as along

the top and side. As a result, the door played a slightly less important

*role In the displacements of the prior r~alculat ion. The peak displacements

of the present calculation are comparable to those of the prior calculation;

and, in the case of Niode 46 (F*-g- 5-3), the peak displacement greatly

exceeds that of the corresponding point in the prior calculation. However,

Experimental data from the south iiloo, for a location corresponding

to Node 46, is availaile. A comparison between the measured data and the

computed response is given in Table 5-1. Although the average acceleration

is in good agreement, the duration and the velocities are not. The trend of

the comparison sug~ests that, locally, the door may have broken free of its

support during loading. Had this been able to occur in the finite element

model, the unloading of Node 46 would have been initiated much earlier,

resulting in lower velocities. This would have been accomplished without

significantly altering the iverage acceleration. It would be desirable in

future calculations to possess the capability of modeling breakable hinges.

82

R-7556- 1-4182

TABLE 5-1. MOTION OF SOUTH HEADWALL (ESKIMO 1)

ABOVE CENTER OF DOOR

Measured Value Present CaIc. Prior Calc.Item for South Igloo (Node 46) (Node 33)

Maximum Velocity, fps 27.9 44.2 20

Average Velocity frominitial Motion to PeakDisplacement, fps 13.3 29.0 11.7

Tim. Interval fromInitial Motion CoPeak Velocity, msec 14.4 25.6 11.2

Average Acceleration *from Initial Motionto Peak Velocity, g 60 53.6 64.8

In addition to the gage data for the south headwall above thi center

of the door, experimental data exist also in the form of motion picture film.

From these films it was possible to estimate, although not with great -

precision, the velocity of the upper corners of the doorways of the south

and west igloos. Although it was also possible to measure displacements,

flying debris in the igloos obscured the view of the door prior to maximum

displacement. The peak velocities of the corner points are presented in

Table 5-2.

TABLE 5-2. PEAK VELOCITIES OF UPPER CORNER OF DOOR

Source Peak Velocity, fps

South Igloo (Measured) 33

West Igloo (Measured) 19

Current Calculation (Node 49) 19.2

tPrior Calculation (Node 31) 16.6

83

A k R-7556-i -4182

Figures 5-6 and 5-9 shov, che motion of points on the interior of

the steel door. The displacements are very large. However, the displacement

values shown in the figures are probably typical of the order of magnitude

of the actual door displacements. Figure 5-19 (from Ref. 2) shows the motion

of the point in the prior calculation corresponding to that of Figure 5-6.

Actual measu.rements from the motion picture film of the west igloo are

available, although visibilit~y was obscured prior to maximum displacement.

The maximum deflections of the center of the door, as determined by the

three independent means, are listed in Table 5-3.

TABLE 5-3. PEAK DEFLECTION OF CENTER OF DOORWAY

Sourc~e .Displacement, in.

West lglo (Measured) 30*

Present Calculation (Node 73) 20.6

Prior Calculation (Node 49) 10.1.

*The motion picture record terminated prior to maximumdisplacement. The value shown is the largest observedIdisplacement prior to termination of the record.

Figure 5-12 shows the displacement histories of several points at

ground level on the headwall. Figure 5-20 (fromt Ref. 2) is comparable to

Figure 5-12a. From this comparison it is evident that there is a great

difference between the two calculations in modeling the foundation. The

foundation of the present calculation is much more rigid than the founda-

tion of the prior calculation. Accelerometers located on the floors of both

the south and the west igloos provide experimental base motion data. The

results are presented in Table 5-4.

84

ilk R-7556-1-4182

TABLE 5-4. PEAK ACCELERATION OF BASE OF HEADWALL

Source Peak Acceleration, gSouth Igloo (Measured) 6.3

West Igloo (Measured) 5.5Present Calculation (Node 104) 19.8t Present Calculation (Node 108) 12.9

Prior Calculation (Node 52) 66.2

5.2.2 STATIC HEADWALL MEASUREMENT

The static headwall measurements involved setting up survey monuments

3 ft in front of the igloo headwalls. The distances from the monuments to

the headwal!s were measured at selected points before the test. These dis-

tances were again measured after the test. The net changes in position

represented the permanent displacement of the headwalls. A gap of approxi-

mately 0.2 ft was found between the back of the south headwall and the earth

cover at the top left corner, and a similar space 0.1-ft wide was found atthe top right corner. Thl.. demonstrates that the static measurements are not

the maximum displacements but are the permanent movements of the headwall.

These permanent displacements of the headwalls are shown in Figures 5-21

and 5-22 (Ref. 1). All the measurements are subject to +0.05 ft of error

becausa pretest measurements showed that the walls deviated from a true

vertical plane by that amount. The measured displacement patterns indicate

that the headwalls appear to have responded in different ways. More pronounced

yielding on the steel arch was found in tnie south igloo. In the west igloo,

there was clear indication that the steel arch acted as a reaction line

resisting headwall movement. The difference in the observed data, therefore,

implies that material properties in the two igloos are not the same. As was

mentioned before, the fin'te element models used to predict the -esponses of

the south and west igloos are identical. The assumed material properties of

the model would therefore seem to represent characteristics that are a

compromise between the actual properties of the south iglco and those of

the west igloo.

85

R-7556-l-- 4182#4

Fig.re 5-23 shows a contour plot of the computed displacements at A

0.22 sec of the current ESKIMO I calculation. As can be seen from theresponse curves (Fis. '-I through 5-12), motion of the headwall has

essentially stopped by that time. This figure can be interpreted, therefore,

as a P;ot ef the computed permanent displacements. The deformed shape of

the hiadwall appears to be very similar to that of the west igloo, although

the ,magnitudes of the displacements differ considerably. It appears as ifthe west igloo experienced a rigid body displacement not experienced in the

calculation. The backfill and the foundation of the finite element modelwere too stiff to permit substantial deformation. If a rigid body displace-

ment of 0.15 ft is added to every point of Figure 5-23, the contour plot

of Figure 5-24 results. This plot is in much better agreement with Figure 5-22

than is Figure 5-23. The rigid body displacement does not change the stress

field in the headwall. The largest discrepancy between Figures 5-24 and 5-22

is the magnitude of the displacements above the door. The calculation shows

them to be substantially higher than the measured values. This may be due

to the inability of hinges to fail in the finite element model.

There seems to be no means of adjusting Figure 5-23 such that itcompares well with the deformat~ion of the south headwall, shown in Figulre 5-21.

It is surprising that the south and the west igloos, being of essentially the

,.ame construction and subject to similar load conditions, should exhibit such

dissimilar deformation. Figure 5-21 indicates that the most pronounced

feature of the deformation of the south headwall seems to be the folding

about a vertical axis. In the case of the west headwall, there seems to

have been a tendency toward folding about a horizontal axis. The difference

between the computed deformations of the finite element analysis and those

of the vest headwall appears to be smaller than the difference between the

deformations of the south and west headwalls. This implies that the stiffness

properties of the igloos, particularly of the soil backfill, are variable.

Furthermore, these variable properties exert considerable influence on the

deformaition of the headwalls.

86

ilk R-7556-1-4182

The final displacements of the current calculation are considerably

smaller than the peik displacements. It has already been noted that strong

evidence exists to indicate that the same is true of the actual head -lls.

For the sake of comparison with the final deformations, Figure 5-25 shows

the displacement contours of the headwall of the finite element model at

F 0.042 see, a time at which much of the headwall was in the vicinity of peak

iisplacement. The comparison indicates that the final displacement contours

do not provide an accurate measure of the severity of loading that occL.'red

during the blast. Time-dependent measurements are essential for determining

peak stresses during such an experiment.

"5.2.3 CONCLUSIONS

The finite element caTculation dis. -sed in this section is a

modification of a previous calculation of the response of the south and

west heaowalls of the ESKIMZ I event. The modifications included increasing

the number of elements, representing the soil backfill and the foundation by

different models, changing the boundary condition along the bottom edye of

the door, and increasing the flexibility of the concrete. Several differencesbetween the present calculation and the earlier calculation have been pointedout. The most notable difference is the tendency, in the present calculation,

for final displacements to be significantly smaller than peak displacements.The differences between the calculations appear to result primarily fromthe changes in the type of model (for example, using nonlinear springG for

the backfill) rather than from the increase in the number of elements. It

appears that the finite element grids are fine enouq.h, i.)d that further

improvements in correlation between calculation and experiment are to be

obtained thre-ugh improving the means of modeling the influence of the vf.rious

components.

87

I ... . .i ° . . • ' .. . ' : . .r : • - .. .•. .. . .. : - .., •• * • • ... .•... . . . .... . ..

-g W TF

ilk -R-7556-1-4182

Comparison of the calculated results with the experimental results

indicates that improved correlation might be obtainable by modeling breakable

hinges along the top and side boundaries of the door. This would limit the

influence of the door on the headwall, and perhaps lower the headwall dis-

placements adjacent to the doorway. In order to kncoi-porate such a hinge

element into future calculations, ;t will be necessary to know the ultimate

strength of the doo-/headwall connection.

A second area of modification of the finite element model is the

stiffness of the soil backfill and the foundation. The permanent displace-

ments of the headwalls indicate that these components should be modeled as

softer. As pointed out in Section 4, assignind values to the soil parameters

wms largely a matter of intuition, plus trial and error. Experimental

measurements establishing the nature of participation of the soil in the

response of the headwall are needed. This oarticipation is evidently quite

complex, thus rendering static laboratory tests of soil properties inadequate.

In fact, the only experimental means of determining che participation of the

hackfill seems to be the ESKIMO series itself. It must be noted that further

reduction of the stiffness of the backfill will result in the steel arch

applying a significant influence on the headwall. Thus future calculations

may have to include the effects of the arch.

The comparison of final di~placements of the south and west headwalls

indicated a variability in the stiffness of various components of the igloos.

This variability increases the confusion over the role of the backfill, the

ach, .. d the foundation in the headwall response. It suggests that there

may always be a significant degree of uncertainty conc..rning the parameters

used in modeling a headwall test.

88

R-7556-1-4182

5.3 RESPONSE OF EAST HEADWALL, ESKIMhO II

The finite element model for the east headwall of ESKIMO II is the

same as that used for the south headwall of ESKIMO I, since the two headwalls

are of identical construction. Ther,*fore, the model shown in Figure 3-2

(Sec. 3) was subjected to the pressure loading applicable to the ESKIMO II

test. The pressure loading histories are shoin in Figure 2-3 (Sec. 2). The

results from the dynamic response calculation are presented as time-history

plots of the headwall motion and contour plots of the displacement of the

headwall. Comparisons are made between the calculation and the available

experimental measurements on the east headwall in ESKIMO If.

5.3.1 RESPONSE TIME HISTORIES

Since the model used in this study is the same as the one used for

the south headwall of ESKIMO I except for the pressure loading, the responsetime histories are shown at the same nodes as in Section 5.2 in order tocompare the results due to different loading environments. These responses

are plotted in Figures 5-16 through 5-36.

The geoeral shapes of these tihne histories are similar to the

corresoonding ones for.the south headwall in ESKIMO I except that the

magnitudes of the present time histories are, in most cases, greater. It

is seen from Figure 5-26, for example, that the displacement of Node 1 risesinitially to a positive peak of 0.8 in., then reverses the motion to reach

a negative peak of 2.5 in. The positive peak is 25% greater than the corre-

sponding peak at the same node for the south headwall ,n ESKIM0 I, whereas

L the negative peak is 40% greater.

The motions at nodes located outside the steel .arch, where the

headwaul is supported by soil, are only slightly greater than those in

ESKIMO I. However, the peak pressure in ESKIMO Ii is roughly three times

greater :han that in ESKIMO I. Within the arch, the headwall motions in the

present case are much greater. For example, at Node 50 th- rsximum dis-

placement is about two and a half times greater than the corresponding value

89

SR-7556- 1-4182

in ESKIMO I; and at the center of the door (Node 73), the maximum displacement

is about three timus greater. This phenomenon may be due to the fact that the

headwall and the door within the arch are unsupported and yield sooner than

the region outside the arch. After yielding, additional loading causes

disproportionately large displacements.

Figure 5-33a shows that the maximum displacement of the center of

the door is about 86 in., which is greater than the width of the door (60 in.).

Since the INSLAB computer program is based on the theory of small displacements,

the above displacement value may be subjected to significant error. However,

the large displacements predicted by the program simply reinforce the fact that

the door would be bent out of shape under the loading experienced by the headwall.

As noted above, the response calculation of the east headwall showed

that the steel door would be blown open under the pressure loading assumed

for the ESKIMO II test. After the door is blown open, a redistribution of

the pressure on the headwall will take place, resulting in a net reduction

of the total load on the headwall. However, the calculation assumed that

the pressure was acting uniformly on the headwall and the door throughout

the calculation. Therefore, the calculation considered higher loading than

was the actual case and the computed headwall motions woilfd be significantly

different after the door is blown open. The computation for the response of

the east headwall, ESKIMO II, was terminated at about 165 msec; whereas for

the ESKIMO I calculation this ,,nt was at abnut 240 msec. Because of this,

the permanent displacements of the headwall are not clearly identified formost nodes in Figures 5-26 through 5-36. In any event, for the reason

mentioned above, the computed permanent displacements are expected to be

in significant error.

90

F Jl~j1 R-7556 -1 -4182

5.3.2 COMPARISON OF COMPUTED RESULTS WITH TEST DATA

In the ESKIMO 11 test, linear motion transducers were positioned

above the center of the doorways of the five igloos. For the east igloo,

this location corresponds to Node 46 of the finite element model (Fig. 3-2).

A comparison between the test data and the computed motions for this loca-

tion is shown in Table 5-5. The computed duration and velocities are much

higher than the measured values. However, as in the case of the south igloo

Fin ESKIMO 1, the average acceleration is in good agreement. As suggested in

Reference 4, the measured data at this location are very sensitive to thetype of doorstop devices used for In~hibiting the movement of the door top,

relative to the headwall. Also, as discussed before, the computed motions

may be greater because the separation of the door from the headwall was not

considered in the analysis.

Two accelerometers, one on each door leaf, were mounted on the

east igloo (ESKIMO 11). However, these gages failed to perform properly

and therefore no useful data were obtained, as observed in Reference 4.

The static measurements intended to record the permanent headwall

deformations were perforried as described in Reference 4. Figure 5-37 shows

these deformations on one half of the headwall and door system for the east

igloo, ESKIMO 11.

Since the measurements are made on the whole headwall but only

one half of the headwall is used in the finite element model, there are two

measured values for each node of the model except those at the centerline

of the headwall. The contours in Figure 5-37 are based on the average of

the two measured values where applicable. All the values are in hundredths

of a foot, and the positive value indicates deformation into the igloo.

91

R-7556-I -4182

TABLE 5-5. MOTION OF EAST HEADWALL (ESKIMO II)ABOVE CENTER OF DOORWAY

ComputedMeasured Value

Item Value (Node 46)

Maximum velocity,ft/sec 33.3 102

Average velocityfrom initial motionto peak, ft/sec' 31.5 72

Time from initiationof motion to maximum

velocity, msec 6.75 20

Average accelerationfrom initial motion tomaximum velocity, g 153 155

92

............. ,

R-7556-1 -4182

As was discussed in Section 5.3, the east headwall, ESKIMO II, hadnot reached steady state at the end of the calculation. Therefore, it isdifficult to compare quantitatively the calculated results with measuredresults. However, all the nodes indicate that the accelerations and velocities

become siwl1 near the end of the computation. The displacement contours at

two instants of time late in the calculat!,n (t - 145 msec and t - 157.5 msec)

are shown in Figures 5-30 and 5-39. In both figures the maximum displacementsare at the top center of the door, with an order of magnitude of 1.3 ft.

Although this is much higher than the measured value, the general deformedpatterns are quite similar to the measurements (Fig. 5-37). In addition,

the contours in Figure 5-37 do not extend to the doorway, because the doorwas blown off during the test. The computed displacement contours, however,extend routinely Into the doorway.

5.4 RESPONSE OF NORTHEAST HEADWALL, ESKIMO II

This section presents the results from the dynamic analysis of

the northeast headwal! In ESKIMO I. The results from the dynamic responseS calculation are preserted as time-history piots of the headwall motion and

contour plots of the displacement of the headwall. Also presented arecomparisons of experimental data with the results from the calculation. The

finite element model of the headwall is shown in Figure 3-16 (Sec. 3). Thismodel Is subjected to the blast pressure loadings shown in Figure 2-3(Sec. 2). These same loadings are applicable to the east headwall, since 4the two headwalls were at the same distance from the source. j


Figures 5-40 through 5-55 show d;splacement, velocity, and accelera-

tion time histories computed at several nodes in the finite element modelof the northeast headwall and door system of ESKIMO 1! As in the case ofthe south headwall, ESKIMO I, the displacement histories for this caseexhibit lower frequencies compared to the input loading. The rise times of

93

R-7556-1 -4182

the displacement h1stories are longer than 20 msec, whereas the rise time of ýthe input pressure history is I msec. As observed in Section 5.2.1, this

phenonenon is attributed to the low fundamental frequency of the headwall andI, door sys zem.

Table 5-6 2hows tne computed maximum and permanent displacements at

several nodes. It is clear from this table that the maximum displacements of

the nodes inside the arch line are much greater than the corresponding values

of the nodes outside the archline. However, no such correlation exists for

the permanent displacements. The observation implies that the soil behindthe headwall is very effective in resisting the dynamic forces on the wall,

but does not greatly influence the residual displacements of the wall.

Although the cast headwall is subjected to the same loading as the

northeast headwall, the geometries of these two headwalls are different.

Therefore, the relative responses of the headwalls will be compared in order

to get an irsight into their relative strengths and their performances in

the test. Because of the differences in the finite element models of the

headwalls, a node in one model may not correspond exactly to a node in the

other. Each comparison is therefore made between two nodes located in the

samte general area. .

For the northeast headwall, Node 9 Is located at the crown of the

sponding node for the east headwall, Node 19, has the maximum displacement

of 8.2 in. Similar comparison Is seen in Table 5-7 for other locations on

or inside the arch. Although the area of the northeast headwall supported

by the backfill soil is much smaller than that of the east headwall, the

additional stiffness due to the presence of the concrete beams around the

doorway of the northeast headwall appears to have reduced the maximum

displacements of the headwall significantly.

94 I;

4 di~ALR-7556-i -4182

TABLE 5-6. COMPUTED MAXIMUM AND PERMANENT DISPLACEMFrNTOF NORTHEAST HEADWALL, ESKIMO 11

Maximum PermanentDisplacement, Displacement, Location

Node No. in. in. _ _ _ _

9 4.7 0.3 On the arch line

16 1.9 -0.4 Outside th* arch

22 4.1 0.2 On the arch lime

39 7.3 1.5 Inside tne arch,I on door frame42 6.0 1.1 Inside the arch,

on door frame45 2.6 0.7 On the arch line:I6o 1.4 0.8 Outside the arch72 17.0 7.5 Inside the arch,

on center of door

75 4,7 1.3 Inside the arch,on door frame

7'4.o 1.1 Inside the arch

79 2.8 1.1 On the arch line81 1.3 0'8 Outside the &arch

101 0.9 0.3 On the arch line105 16.5 8.0 Inside the arch,

on door frame108 0.4 0.1 Inside the arch,

on door frame

150.1 0.0 Outside the arch

95

(~. II~hR-7556-1 -4182

TABLE 5-7. COMPARISON OF COMPUTED MAXIMUMDISPLACEMENTS FOR ESKIMO 11

East Headwall Northeast Headwall

Mtaximum Maximum

Noe Displacement, Noe Displacement, GnrlLctoNoein. Noein. Gnr)Lcto

19 8.2 9 4.7 Crown of the arch]

46 45.0 9 . Top center of door

49 20.0 42 6.0 Top corner of door

73 86.o 72 17.0 Center of door

76 21.0 75 . 4.7 Center edge of door77 15.0 .77 4.0 Insi~de arch, alongI

horiz~ontal centerl ine

of door

103 0.3 108 0.4 jBottom corner of door

96

R-7556-1 -4182

Perhaps the most obvious difference between the two headwall

responses is seen in the steel door area. The maximum displacements in

the door area for the northeast headwall are much smaller than those for

the east headwall (Table 5-7). At the center of the door, for example, the

maximum displacement for the northeast igloo is 17 in. as against 86 in.for the east headwall. As described in Section 1, the door system for the

northeast igloo is of the biparting and sliding type, whereas the door

system for the east igloo is of the double leaf and hinged type. The results

of the calculations, therefore, suggest that the biparting and sliding type

is superior to the double leaf and hinged type for resisting the blast loads.

r 5.4.2 COMPARISON OF COMPUTED RESULTS WITH TEST DATA

As explained in Section 5.3.2, linear motion transducers were

rplaced above the center of the doorways of all the igloos in the ESKIMO 11

test. For the northeast igloo this position corresponds to Node 39 of the

finite element model (Fig. 3-16, Sec. 3). A comparison betw~een the test

data and the computed motions for this location is shown in Table 5-3.Among the four items compared, the times from initiation of motion to maximum4

velocity are in good agreement between the computed and measured values. The

remaining items show that the computed values are abouc two times greater.( As mentioned before, the motion of this point is very sensitive to the type

of door-stop device used for inhibiting the movement of the door relative

to the headwall. Also, the computed motions may be greater because the

separation of the door from the headwall was not considered in the analysis.

Two accelerometers were mounted, one on each door leaf. The gage

on the left door leaf failed to perform, while the gage on the right door

leaf recorded a peak acceleration value of 1200g. The computed value at

the corresponding location (Node 72) is seen from Figure 5-47 to be 1300g.r

97

R-7556-1-4182

TABLE 5-8. MOTION OF NORTHEAST HEADWALL, ESKIMO 11,ABOVE CENTER OF DOORWAY

ComputedMeasured Value

Item Value (Node 39)

Maximum veiocity,ft/sec 14.3 32

Average velocityfrom initial motiontc peak, ft/sec 10.4 21

Time from initiationof motion to maximum

I

velocity, msec 17 19

Average accelerationfrom initial motion tomaximum velocity, g 26 52

98

~-77

A k R-75156-1 -4182

The permanent deformations of the northeast headwall are given in

Reference 4, and are shown plotted in Figure 5-56. The contours in the

figure are based on the average of the twc1 measurements at symmiietrical

Ipoints on the headwall. Figure 5-57 shows the computed displacementcontours of the headwall at 109 msec. Since the motions become essentially

- steady state at this time, the displacements of the headwall at this instant

are equal to the permanent displacements of the headwall.

Figures 5-56 and 5-57 show that the maximum deformations occur

around the doorway. The contours seem to follow the patterns of the steel

arch and the floor slab. In general, the measured values are slightly

higher than the computed values. In both figures, the movements tend to be

S smaller toward the top and the bottom of the headwall. At the top of the

I shoaw all, the computeddisplacementns are negative, whereas the measurements

sho smll osiivevales. Ingeneral, tewingwall experiences smaller

t displacements. At the far end of the wingwall, some displacements are4

negaive Ths my b du tothefact that the headwall is supported by

the soil outside the arch and is subject to rotation about the support.

S 5.5 RESPONSE OF NORTHEAST HEADWALL, ESKIMO IV

The response calculation of the northeast headwall, ESKIMO IV, was

S to have been performed before the test was conducted on 10 September 1975,

E so that the analytical results could be used to predict the behavior of the

S headwall and door system in the test. Because of tight schedules, the above

calculation could not be completed before the test; but the calculation was

S performed before any results from the test were available. This assured

that the calculation was performed independently of the test and was not

subject to any bias that could have resulted from reviewing the test results

before performing the calculation.

R-75.56-1 -4132

As of the writing of this report, the data fromt the ESKIMO IV test

are available only in prelininary form. Therefore, the test results reflect

raw data that may be subject to future corrections. This fact should be

j kept in mind when comparing the analytical results with the test data.


Figures 5-58 through 5-69 show displacemnent. velocity, -nd accelera-

tion time histories computed at several locations on the northeast headwall

norheat hadwll f te EKIM 11event, for which the motion time historiesare shown in Figures 5-40 through 5-55. Since the structural configurationof the no-theast headwall, ESKIMO IV, clusely resembles the northeast headwallof the SSKlMO 11 test, a comparison of the responses of both northeast

Themoton imehistories shown in Figures 5-58 through 5-69 reflect

calulaion wih adurtio of186 msec. The displacem~ent time histories at

most locations show a single peak at about 25 msec and become steady state

after about 100 miec. These time histories are quite similar to those for

The input blast pressure for ESKIMO IV is slightly higher than that for

ESKIMO 11, but the resulting peak-displacements of the headwall are slightly

lower in ESKIMO IV, as shown in Table 5-9. Therefore, it can be concluded

that the northeast headwall structure in ESKIMO IV is stronger than that in

ESKIMO 11 for resisting blast loadings.

The response time histories corresponding to the steel door at

Nodes 61, 64, 91, 94, 121, and 124 are shown respectively in Figures 5-060,

5-61, 5-63,, 5-64, 5-68, and 5-69. For the r'ortheast igloo -ý ESKIMO 11,

the ocak displacements along the edges of the door are only slightly higher;

but those at the center of the door are significantly higher than the values

shown in Table 5-9 for ESKIMO IV. The primary reason for these differences

100

R-7556-i -4182

TABLE 5-9. COMPARISON OF tIAXIMUM DISPLACEMENTS OF NORTHEASTHEADWALLS OF ESKIMO II AND ESKIMO IV IGLOOS

ESKIMO II ESKIMO IV

- Maximum MaximumDisplacement, Displacement,

Node in. Mode in. General Location

9 4.7 21 3.1 Crown of the arch

22 4.1 24 3.6 On the arch line nearthe crown

39 7.3 61 6.0 Top center of the door

42 6.0 64 5.4 Top corner of the door

45 2.7 69 2.7 On the arch line, at thelevel of the door top

72 17.0 91 5.2 Center of the door

75 4.7 94 3.7 Right center edge of thedoor

• 77 4.0 97 3.3 Inside thc arch, at the

level of the door center

79 2.8 93 2.6 On the arch line, at thelevel of the door center

105 16.5 121 5.- Bottom center of the door

108 0.4 124 0.3 Bottom corner of the door

101

_____ ____ _____ - - - ~ . -. ........ '

R-7556-1 -4182

is the c*oor configurations. In ESKIMO IV, the door is of a single-leaf

sliding type, wheruas the door in ESKIMO II is of a biparting sliding type.

The sirngle-leaf type has a much greater stiffness to resist deflection at thecancer of the door than dos the double-leaf type. Therefore, other things

being equal, the double-leaf door experiences higher deflectior than the

single-leaf one.

5.5.2 COMPARISON OF COMPUTED RESULTS WITH TEST DATA

As In the case of the other Eskimo tests, posttsst measurem~ents

were made on the headwalls of the ESKIMO IV test (Ref. 6), in order to

obtain permanent displacements of the headwalls. Figure 5-70 shows the

permanent displacement contour lines of the northeast headwall based on the

average of -wo measured values due to the symmetry of the headwall at the

vertical centerline. The computed displacement contours at time t a 158 msec

are shown in Figure 5-71. As noted before, the computed displacements becomne

steady state after about 100 msec and therefore the displacements of the

headwall at 158 msec represent the permanent disp!acements. A comparison

of the computed and measured contours shows that the computed displacementsgenerally are smaller than those measured. However, the differences are notgreat and are not significant because the magnitudes of the pern-anent displace-

ments are small. The contours do not indicate any strong influence of the

arch on the headwall responte.

Figures 4-3 and 4-4 (Sec. 4) show the locations of the accelero-

meters and the linear motion transducers mounted on the northeast headwall

and door for ESKIMO IV. The measwred acceleration and displacement thie

historits for the northeast headwall are shown respectively in Figures 5-72and 5-73. These records are reproduced from the preliminary report (Ref. 6)

on the ESKIMO IV test. As such, these records have not been corrected for

drifts and other random errors. This fact should be kept in mind in the

following aiscussion involving the ineasured time histories.

102

!*

• - --

E R-7556-1 -4182

The me.asured displacement time histories at several locations on

the headwall aný door are shown in Figure 5-73. The displacements shown are

in inch units and Pre plotted as functions of tlme expressed in mse¢ units.

Next to each time history the node in the finite element mesh of the headwall

(Fig. 3-18, Sec. 3) to which the time history corresponds, is ,shown. Of the

eight measured displacement time histories, direct comparison with the

calculated histories is possible at only four locations. These are at Nodes 21,

64, 94, and 97 and the corresponding time histories are shown respectively in

Figures 5-58, 5-61, 5-64, and 5-65. A comparison of the calculated andS measured d~splacement at the four locations shows that shapes of the pulses

S are in good agreement. Table 5-10 shows a comparison of the maximum displace-

ments and permanent displacements. The agreement between the computed and

measured permanent displacements is very good. The computed maximum dis-

placements are somewhat higher than those measured. Nevertheless, the

differences between the computed and measured values are small in comparison

with those found for the headwalls in the ESKIMO I and II tests.

The measured acceleration time histories at several locations on

the headwall and door are shown in Figure 5-72. The accelerations are given

in the units of g (gravity constv.it) and the time is expressed in msec units.

Next to each record the corresponding node in the finite elemeýit mesh

(Fig. 3-18, Sec. 3) is shown. Out of a total of eleven records, the computed

pulses are available only at seven locations. These are at Nodes 21, 61, 64,

91, 94, 97, and 99 and the corresponding acceleration pulses are given

respectively ir Figures 5-S8. 5-60, 5-61, and 5-63 through 5-66. The

measured pulses are shown up to a maximum of 50 msec, while the duration

of the computed time histories is 186 msec. The general shapes of the

computed pulses are different from those measured. The measured records

show small motions after about 25 msec. In contrast, the computed accelera-

tion records show strong motions even after 150 msec. This is attributed

to the fact that in the actual test, cracking and crushing of concrete

dissipates large amounts of energy. Although the INSLA8 code accounts for

103

, k R-7556-1 -4182

TABLE 5-10. COMPARISON OF MAXIMUM ANO PERMANENT DISPLACEMENTSOF NORTHEAST IGLOO, ESKIMO IV

Max'imum Permanent

Displacements, Displacements,Locv,1 i on in. in.

Nods Gage 1.0. Measured Computed Measured Computed

94 L-1-B 3.0 3.7 0.8 0.9

97 L-2-B 3.2 3.3 i.0 1.0

64 L-5-B 3.6 5.3 1.0 0.8

21 L-9-B 1.9 3.1 0.3

*The transducer seemed to have failed after recording about 50 msec

of mot.ion.

104

R-7556-1 -4182

the energy dissipation tnrtugh the yielding of concrete, it is not intended

to consider the crushing of concrete. Therefore, th6 energy dissipation

model in the calculation may underestimate the acttual energy loss. A

comparison of the crwmputed and measured maximum accelerations at various

locations on the headwall and door is shown In Table 5-11. The agreement

between the measured and computed values is good and the differences *e

small in comparison with similar differences in the ESKIMO I and II tes1-.

In ESKIMO IV, unlike In the previous ESKIMO tests, the headwalls

were heavily Instrumented to measure pressure, accelerat!on, and displacement

time histories on the headwall and door systems. As described in Section 4,

the northeast headwall was instrumented with seven pressure gages, twelve

accelerometers, end nine linear motion transducers. This provided for theS first time an ,.9portunity to compare the computed and measured time histories

of accelerationis and displacements at several locations on the headwall.

The information contairied in the measured records can be used to adjust the

parameters of scil models in any future calculations to improve the

analytical prediction capabilities.

105

7W .k -_ .

R-7556-1 -4182

TABLE 5-11. COMPARISON OF MAXIMUM ACCELERATION OFNORTHEAST IGLOO, ESKIMO IV

Location Maximum Accelerations, g

Node Gage I.D. Computed Meas,'red

21 A-IO-B 258 225

61 A-6-B 280 208

64 A-7-B 196 238

91 A-1-B 1550 1250*

94 A-2-B 236 395

97 A-3-B 272 151

99 A-5-B 264 241

*Estimated value, since the gage exceedel the rating limit

106

ýF v

R- 7556 -1-4182 ~

_____________(a) Displacement

3~

US (b) Velocity

Iis

0.g0 0.04 0.03 0.12 0.1 0.20 0.04 0.11 0 J2

.10

R-7556-1-4182

(a) Displacement

I4

U' :(b) Velocity

-

fo. . 0 7 080 C.12 0.6 0.40 0. -20.6 0

T! (c) Acceleration

W64AAAA

-'V

?to . .C

FIGURE 5-2. COMPUTED MOTION OF SOUTH AND WEST IGLOOS AT NODE 19(Refined ESKIMO-I calculation)

108

SiI j

R-7556-1 -4182

(a) Displacement-

I.!

I 6

.0.(b) Velocity

(c) Acceleration

!' ~~~ -V v , V v -

11-"

a. c 00 3.01 •.•t U 0.0 3•Z4 J. 2 3 12L; [,,. 'rT,. U411

FIGURE 5-3. COMPUTED MOTION OF SOUTH AND WEST IGLOOS AT NODE 46(Refined ESKIMO-I calculation)

l0g

A k R-7556-1 -4182

L (a) Displacement

,. 0 0 .0 4 a. 0 6 0 .1 t 0 . 1 6 0, 1 0 0 4 Z 4 1 0 i .s l o .- 3tM. tic

U

II-

(b) Velocity

4• i

iii

-.00 0.04 O .t 0.10 0.•14 0 ".0 0.24 2- .O l 0.30

'111 ....A Ilt••' (c) Acceleration

01 ' 0 0 .0 4 0 .3 6 0 .4 l 0 .! S 0 .2 0 0 .0 6 2 . • 1 0 .0 0FIGURE 5-4. COMPUTED MOTION OF SOUTH AND WEST IGLOOS AT NODE 49(Refined ESKIMO-I calculation)110

R-7556-1 -4182 I

If

;1 *131

(a) Displacement

I!!

I.o. 6.04 .0. 0.12 .0.4 0 a .a 4 0 0 J2

"F I

I (b) Velocityio

Tt.g sic-

ii

V. I

(Reine "-(c) Acceleration

L Ii1k .A_____I , ¢

ji30a O 3i.4 0~ll 46 l 0 l. tl 3 .?6 l 0 2 .44 31 46l 3 1

?ll, Mc

FIGURE 5-5. COMPUTED MOTION OF SOUTH AND WEST IGLOOS AT NODE 50I(Refined ESKIMO-I calculation)

ill

A k R-7556-1 -4182

z

(a) Displacement

.f 71 -5 01"e o 3f I!

aJ

( (c) Ac c i t .tion

?IN. sIc

! ,

(RfndEKM- (c)lAccatiotn)

i.

I:

I! t

'.G 0.0l~4 0.06 0.0• O.dIe lO O'.aa az . l az, ,

?Ilq. SIC

(Re(ne) SKIM-Ilercuttion

11

Ij

R-7556-1 -4182

U (a) Displacement

'i' -S 4 - -t 01 - 8 .1 93I!.

W.0 04 0.66 6.19 0. 40 6 0.2 1 Is 0

fine. 66 A

- (b) Velocityio

0.0 0.04 0.0 V.:2 .16 0,20 0.7a4 a i. a.3vtq. 1J

",I

'1 (C) Acceleration

FIGURE 5-7. COMPUTED MOTION OF SOUTH AND WEST IGLOOS AT NODE 76(Refined ESKIMO-I calculation) j

113

I 4 A .... . . .."

!i .. I' IM1- A:-=iV . ... .

R-7556-1 -4182

'-'--' (a) Displacement

I!,I

1." se .0 eta if-to Ca s 0.31

(b) Velocity

Lf I.lif

(c) Acceleration

'I.06 C.o4 0.6 CS12 0.14 cf.4" 0.24 3." 4.32

FIGURE 5-8. COMPUTED MOTION OF SOUTH AND WEST IGLOOS AT NODE 77(Reftned ESKIMO-I calculation)

114

R-7556-1 -4182

•*• l• ~(a) Displacement "'

a ( A

115

I* UL!

U•.0 'O ,O .1 O.il Ol .Z .1 01

I L iP a iplcmn

U

lRefne ESIM -I acu ton

I _______

i3

R-7556-1 -4182S

4ii

St

(a) Node 9

Si i

S/

'W4. v

4• 01(C Node 63

m0.

FIGURE 5-10. COMPUTED DISPLACEMENTS ALONG EDGES OF S'EADW/ALLS OF SOUTH ANDWEST IGLOOS (Refined ESKII\I calculation)

116

* LJWg1

(b) Nde 3

&

AkJ-R-7556-1-4182

1'(a) Node 21

U ___ __ __ __

ETB,.o . ., .... oo i I. , I

LUi

(b) Node 32

,Two.ISo

h; FIGURE 5-11. COMPUTED DISPLACEMENTS ALONG ARC" LINE OF HEADW/ALLS OF SOUTHA-ND WEST IGLOOS (Refined ESKIO-I calculation)

[ 117

r A -• ----.. .. . . . .. .. .

A R-7556-1 -4182

L,

/1 (b) Node 104

U

6. 0 04 .0 0 1 S E 6.14 3.23 0 3 4 4 3 a .t a i

I: * (c) Node 108

a

L *

sF1

00 2-24 als a , .2 6 3 .3 3.,36 ,j .9 3 it

FIGURE 5-12. COMPUTED DISPLACEMENT AT GROUND LEVEL OF SEVERAL LOCATIONSON SOUTH AND WEST IGLO3S (Refined ESKIMO-I calculation)

118

R-7556-1 -4182

3A

•,_- _ NI!

iI (a) Displacement

0.114 Cgs O.0 1 e 0.10 t 0.1 'k4 Q011

Ii(b) Velocity

a 4IXI

(c) Acceleration

0,O1 0'.01 0.04 @0, I .05 " .IO 1,1 0 lt 0.14 0.1t1

FIGURE 5-13. CJMPUTE-J MOTION FROM PRIOR CALCULATION CORRESPONDING TO NODE I

119

R-7556-1 -4182

I, (a) Displacement

0 il', 0 1 1 0 .a

!Y1111.,W

I _____(b) AVelcityo

"0-60 a,-. 0,04 !6 l ,1 it] 0.t V.1 1,14

410 las all #

120

23

I A A

0.0 0.10 010 f lo a.12 0.:4 9.141

i4~t- .c Aceliaco

FIGURE 5-14. COMPUTED MOTION FROM PRIOR CALCUJLATION CORRESPONDING TO NODE 19

120

I ,.. .. ..- '. ." '.i. ; •'L." -L. •.ii

ilk__ _ _ _ R- 7556- -14182

il! 1(a) Displacement -

010 0.2 a.1 Q1

I, / !

/ /

I' /

3/

S:I(b) Velocity

0, i. 11504 O. ON0 0 0.a 0Vi2 0,14 0.!

4;-L (c) AccelerationJ I•

S.00 0,41l 0",04 a-as Fas af. a O a 77,1 37Y *.to

i FIGURE 5-15. COMPUTED MOTION FROM PRIOR CALCULATION CORRESPONDING TO NODE 77

121

R-7556-1-418201

isiii (a) Displacement

(b ;2I cit111

"fne

' I/

+ I I

iI N 0.02 0.04. 0.06 0.02 0.20 0.t2 0.t4 0.16

I 5,b. V otIy

122

6O.00 6.02 0.04 " .0 0. 021 0. 26 0.lO 0 " .t 4 0.l 26.1?rai. UL

022

A k0-- 1R -7556-1-4182

I' I

iii I I (a) Displacement

-1IL

r ~ ~ ~ ~ ~ I /3 .9ao

-o-o0o aJ!a 0.04 C* iso* ~ t

FIUR 5-17. COPTDMTO RMPR ACLTO OREPNIGT OE4'123

ilk R-7556-1-L4182

(a) Displacement

0.at 0.04 0.06 a.0" 2.12 0.12 13.14 0'.16

1 '67

ii (b) Velocity

(c) Acceleration

FIGURE 5-18. COMPUTED MOTION FROM PRIOR CALCULATION CORRESPONDING TO NODE 76

124.

jlkR-7556-1-018241

4.

IL

. (a) Displacement

i.•o

20 • f= 2 2,,2Z 0 0 4 0 .0 3.0 6 0 .0 ,.50 0 . t4 0 .16

(b) Velocity

!iUI

t 1

m•Sl~l'i' i, /k J~v . ,•l'g /,.(c) Acceleration

*i ! .,9

0 .02 0.04 a-06s 3.0 0 2.10 '2 a !&4 70.

3 1t41. ic

FIGURE 5-19. COMPUTED MOTION FROM PRIOR CALCULATION COR•RESPONDING TO NODE 73

125

S2

ilk_ _ _ _ _ R-7556-1-41 82

• • /"

I1. (a) Displacement

-iig ti

I. (b) Velocity

tI

s. T fine[, S"•

"-" \41' (c) Acceleration

SV

'a-ccl I',0 0.04 a."I 3 N .1 0 2.:z 0.1 6 0-:6l;q

FIGURE 5-20. COMPUTED MOTION FROM PRIOR CALCULATION CORRESPONDING TO NODE 103

12

R-7556-1 -4182

024 *23 11 .0 14 .2 -p

Nof

, 110

010 oil .14

-181

03 - p -ost-01

92 #3 I#160 0#1#23 .? 03 I#to IRCU10 0

FIGURE 5-22. MOVEMENT OF HEADWALL OF WSOTH ACCEPTOR IGLOO(ESKIMO 1)

1274

101

AkR-7556- -41 82

-o5. -4.2 -22 0.8

7 -i

92.4 *.

-0.1 0-~ .

40.5 202, , , 0.8, A E RI

L I

____________0.1 0.-0.1 0.0

FIGURE 5-23. COMPUTED DISPLACEMENTS (IN HUNDREDTHS OF A FOOT) OF THE HEADWALLSOF THE SOUTH AND WEST IGLOOS, ESKIMO I, 0.22 SEC AFTER ARRIVAL

OF THE BLAST WAVE

128

9.'.28 5010 ~10.8 1.

17415413.9 15.4

II0 N 19 .015.81

-1\ 16.04

FIGURE 5-24. COMPUTED DISPLACEMENTS (IN HUNDREDTHS OF A FOOT) WITH A RIGIDBODY DISPLACEMENT OF 0.15 FT ADDED IN FOR THE SAKE OFCOMPARISON WITH THE WEST IGLOO, ESKIMO I

129

10.

00.

10.5 -0.1-01

FIGURE 5-25. COMPUTED DISPLACEMENTS (IN HUNDREDTHS OF A FOOT) OF THE HEADWALLSOF THE SOUTH AND WEST 16,.OOS, ESKIMO 1. 0.042 SEC AFTER ARRIVALOF THE BLAST

130

R-7556-l-4182

(a) Displacement

1" W-. 1 g to Wn Te, C" 1SI I

-: •(b) Veloci ty

31 j

em( eg) Acceleration

it

Irlo. sic

FIGURE 5-z6. COMPUTED MOTION OF EAST HEADWALL (ESKIMO 11) AT NOCE 1

131

1t ,-7556- 1-182

S3 I

(a) Displacement

1' 3

? Tom. IK

a ..

3A

I (b) Velocity

(c) Acceleration

V._ V^

11

TIo$. sac

FIGURE 5-27. COMPUITED MOTION OF EAST HEADVIALL (ESKIMO 1I) AT NODE 9

132

-,i ,.,,,.,,,,ilk R-7556-1 -4182

(a) Displacement

1: IL _ _

a." F0.4 " .m o.1 .6 6.- 1 Zito ,, . C to 6.3

Ting. KIC

(b) Velocity

03

3 ,lil. slC

-133

..

_. S (c) Acer.1erat ion

I

I"oI.O me. 04 o, t m.iP gi.O o i aO O ZO 0.3Z

?tII, SEC

FIGURE 5-28. COMAPUTED MOTION O," EAST HEADWALL (ESKIMO It) AT N+OD:E 19

133

. .. ... 7 7

R-7556- 1-4182

I;I

" " i

" .. * (a) Displacement

S.o " gag. If.1 8. 8.14 a.23" 0.ns llIl9, 59C

I' __(b) Velocity

W' .46 C4.3 UN f.or gl 3.100 6.24 0.11 j-j•3.

To$..i

(c) Accelerat ion

FiGURE 5-29. COMPUTED MOTION OF EAST HEADWALL (ESKIMO 11) AT NODE 21

134

R-7556-1-4182

S"/-i4i

X* (a) Displacement

Ss o. ,.

(b) Velocity

T1ii __ _ _ _ __ _ _ _ _ __ _ _ _ __ _ _ _ _ __ _ _ _ _

0.60 0.44 0.0 5.62 6.46 0.n 0.84 90*0 4.1

. ,im, mc

00

TIM•. SiC

FIGURE 5-30. COMPUTED MOTIO1014O EAST HEADWALL (ESKIMO 11) AT nODE 46

135

R-7556-1-4182

; 3;

| ~(a) Di splacement

* ~/\Tim. C

iFi'

S'i N e e• mN eJa' Vie0 i.29o r84 41.81 o-M

"(c) Acceleration

3 I

FIGURE 5-31. COMPUTED MOTION OF EAST HEADW•ALL (ESKIMO 11) AT NODE 49

136

0.66 3W I? ge 6.8 644 6.33 0.3ThU SI

R-7556-1-4182

i __(a) Displacement

!I

9 ,or .. ... Zo V I I i e . 68 C" 11,11

(b) Veiocity

S• Tif. UC

(c) Acceleration

t.t.St

?Ia6, UCt

FhIURE 5-32. COMPUTED MOTIOtN OF EAST HEADWALL (ESKIMO II) AT NODE 50

137

...... ...

R-7556-1-41 82

3

(a) Displacement

Told. wII.I

•.n (b) Velocity

of CO I*hOON I11| TIRE. "C

ij

13

-.,

! L _ .,.• .^..,,IA •o ,oo ,,,•,oN. . -v7*'

U

(b)Velcit

0 fo I10 o.l ~ tl f~l II 1 .

_____________________________________________

FGURE -3g .g OaPUTED gOTIO OFg EAST gHE AgWL EKM I rOE7

y~g* 1a8

R-7356-1-4182

(a) Displacement

[1.04 C.t 6. 6. nl 6 86 6 r.1 6 .16

TINS. SIC

(b) Velocity

S: (c) Acceleration

I.,

1 16

(c) Acclertio

fill VT v . $1

TINI. SIC

FIGURE 5-34. COMPUTED MOTION OF EAST HEADWALL (ESKIMO II) AT NODE 76

139

R-7 556-1-4182

14(a) Displacement

. • 1119. SIC

a..;..S|

S:i (b) Velocity

TIM. SIC

:•" ="t<'='=.,••,•(c) Acceleration

Till[ SIC

FIGURE 5-35. COMPUTED MOTION OF EAST HEADWJALL (ESKIMO 11) AT NODE 77

140

I AR-7556-1-4182

- (a) Displacement

+

'@.a M's Cuoi of-it 0e.o 6 6 C24 a.8 64nTIMg. sgc

t61

3

(b) Velocity

IrITINg. S9C

." .

L 2

w vv VYv-Y(c) Acceleration

.6 0.04 0-.0 W.1 i .16 0*0 0.24 0TINS. SIC

FIGURE 5-36. COMPUTED MOTION OF EAST HEADW.IALL (ESKIMO II) AT NODE 103

141

R-7556-.1-4182

y

4 3 9 0 5 15\574

1425

-20 1 1 i 13 1ý4 I

R-7556-1-4182

lit 000O OO O 0S 0OS 0ooo0 9

* li lt It5

0 o9ooo .

31 3 al l i t31 333 3 1 I late OI

5 oao e0 4 10 0Sit333 go1 0O

S• It! / 33 OOO O3e

333333a a 0

: Well ll l 06 I

*_98appealare I

S"li lt It31111fai l 0

0 3]5 in I

* !121 I 10

* Inns jlI I 0o~*o 1a . * I

• 32•1 0

a0

I JII-DOOR OPENINGO lti ll lt t t t t

l -33 J 0w* 00 I 0

it 000S

11 111 0 S* 1111 O I3 :0.w

FIGURE : O F S

0 1 0i 0 14300 0 OI 0

* . 1 oo0

9 0 O I 0 S

•ooI o =.'.

FIGURE 5-38. COMPUTED DISPLACEMENT CONTOURS OF EAST HEADWALL AT t * 145 MSEC

+•k R-7 556-1-4o182

tilo133 vva•e7 tt

e O03 1 00 a* 60000

O*ltttOt O

to 3

* *iuia 111+ e

313333 ill 67 t eo3* si$ss aiP 1

0 3333 II$* a~s 100 1 O S

333 3 3 3 3 .all

-11311 ll 1 0 5

* 0 f3 'a i 0 f* 33 q 1t 0 a* 3333 ti1•I 0 5

111l 11 fll l f tillit t I

* 1 00 0

* DOOR OPENING 0

ItS3 3 0 v

* O I 0 •

*[email protected],0

as goa I 0

' *0 0 i 0

SI 0o•

0 0: ," I SoSi, 0.6 0 i I

I S0 •

*0 0 0 |0

0o 0 0 IO

I O0000OO0SSSS008@Oee O oOgOOOO 0oOOOOOOOOOOOOO OOeOOOOOOOOOOSOOSee SSeees•

FIGURE 5-39. COMPUTED DISPLACEMENT CONTOURS OF EAST HEADWALL AT t = 157 MSEC

144

-1 R-7556-1-4182

"$1 Ot\" 0-

(a) AIscleraeent

vFGR540 Com 1.ED em TIeN OF ýýORTZS I-,OO (ESK.m 11) At'.

•14 • ij.t tt 04 d

_______ (c) Actlleratiy

I!

SI

FIGURE 5-4O. COMIPUTED) MOTION OF NORTHEAST IGLOO (ESKIMO II) AT •iOOE

14,5

SmaA

R-75561-l -182

I!i ~(a) Displacement

I,

is (b) VeIoci ty

(c). Acclertio

21

on of a S " S." .S S I I I I

FIGURE 5-41. COMPUTED MOTION OF %ORTHEAST IGLOC (ESKI!ý 11) AlT !iODE 1

146

IS~~R-7556-i-0, 82

3- U

II

SI1 (a) Displacement

aw so c $-a em 04 si s01n Z aIt si . mi

I-

II

I:

. S.(b) Velocity

a: ______

If

E. M (E) Accelert ion

!,4

'4

III

sit 34 S W I t 2 3 ~ 3 '4 2 .

R-7556-1-41 82

I! (a) Displacement

?z

I

(b) Velocity

0.06 0.02 0.04 0.06 0.as 0.10 0.12 0-14 *.16

IIU

-q Cc) Acceleration

.. 0.1 0.14

FIGURE 5-43. COMPUTE.- MOTION OF NORTHEAST IGLOO (ESKIMO 1I) AT NODE 39

148

-,7 , 7 m7- 7

ii k R-7556-1 -4182

I! (a)Displacement

ii.

•iTomI. Im

:; •Ig"==x (b) Vel oc i ty

•I! '•(c) Acceleration

• !

I!I

!FIGURE 5-44. COMPUTED ,"OTION , " ORTHEAST IGLOO (ESKI"1O !1I ATr %ODE£ 42

.149

R-7556-1-4182

3

#-a- re. eu i .". 0 .10 C to eii[ ~(b) Vesloceiety"

z

ItI

I...*I~g (b) Aceleratio

IISI

"em: (e. sA ce.lig lt-.i,*

I 150

.............

I A _ _ _ _R-7556-1 -4 182

(a) Displacement

8.4 90-W I

x a

7 U__ _ _ _ _ _Q__ _ _ _ _ _ _1_%.W . 6.4 SW 6.66 gig ig e Mi

FI'4,,RE 5-46. CmPUTED MO~~~TION. OFNRHAT IGOUEKC 1)A OE6

15

Lan.

R-7556-1-4182

1' (a) Displacement

•U 6 66 63 6.56 6.11 6~| .14 8.56

Tue. me

II

.3 _______________(c) Acceleration

a," a of as# on an * . . 1 oil 0 1.

FIGURE 5-47. COMPUTED MOTION OF NORTHEAST IGLOO (ESKIMO 11) AT NODE 72

152

vie4, j

R-7556-1-4182

II(a) Displacement

I

toI 14

FIUR 5e8 ED m OF NR e LOO (K14 0.ND

- ti.

I 4

(b) Velocity

33

I r

SUts I • 00 ' J 02 ;4 1 0 .,3 I @3 n10 SO CI 4 01n5

FIGURE 5-4•8. COM•PUTED NOTION OF NORTHEAST IGLOO (ESKIMO I1• AT NODE 75

1 ~3

R-7556-1 -4182

(a) Displacement

S1

wie weJ

i•i(b) Velocity

0.09 0.02 0 d Se06 0.00 6 .1 i 0.14 0

tim1. 1t

U

•[ (c) Accelerat ion

I

!N

I V

) Ve o cit

SFIGURE 5-49. COMPUTED MOTION OF NORTHEAST IGLOO (ESKIMO 11) AT NODE 77/

F 15

J . . .. . .. .I 1 . . . . l i , , . . . . . . . .. . . . .. . .. . . . . ..

ilk R-7556-1-4182

2J2i

S(a) Displacement

2 .

148 i"1fTI SIC

(b) Velocity

'e I

(c) Acceleration

L . Et

S?• • V vvVW- v

FIGURE 5-50. COMPUTED MOTIONJ OF NJORTHEAST IGLOO S,.IMO I AT :,CCE "

155

Ji~%hhR-7556-1 -4.182

2

()Dsp acemfen t

'km.(c Ace em I~ eeg St t1 oan

... g.si

FIIUE 551.COnPUTED MOT1014 OF ?IJOqREAST IGLOO JESKIMO II Ar 'iOE 3'

R-7556-1 -4182

S( a) D i sp lacemen t

II,1

TIM9o No:

1•=(b) VelocityIt

C-M Woo IQ ei ,4 4 o-oe,

aq

IiI

,.o

(c) Acceleration

vv• v - V v." L, ,i€

FIGURE 5-52. COMPUTED MOTIOn OF NORTHEAST IGLOO (ESKIMO I1) AT NODE 101

157

,.. IJ

Ak__________R-7556-1 -4182

a(a) Displacement

i-3I.6 4M ifs i s1 t

%.u~~~~~b Velocityes e*e i ** i

N23

-3(c) Vceloc aity

hi 7

I2 _ _ _ _ _V

W~ ~ ~~~1M a ,4 wm sI a aisC.

FIUE55. CMUE3OINO OTES GO SIGl"A ID C

15

R-7556-1 -4182

(a) Displacement

if"oS.. 3Ff - 4 4,t , 4b

a3 _ _ _ _ _ ?,IN.__W_

k b) Velocity

do a

- UEm em 00 e 0 0.6 j

Ak R-7556-1 -4.182

94

(a) Displacement

(b*eo il

-4"tie.S

g~~~~(c Accee g~m em em atOs. 6.

F i VRE -55. COWUED "TI-Cts~ Or!X-mA

3: , ' i

a6

R-.7556-1-4182

_kA 0-

-wj

FL.

VIA

000,

u.j

I . ' -_ _ _ _ _ _ _ _ _

Z

~~2AJ

R-7556-1-4182

I= LLI

* * - *

-~ L.6

a , L ' I Ij

p. p. p.fI. * p. 0

SO SO 1

- 2 2fj

162-

_ -7556-1 -4 182

'~II

I '(a) Di splaceument

-• (b)Velocity

E z ATIRE. ul.

AZC

7Ti0 0, S .

S 3 00 00 0 O-I @ '11 3 0 ".24 0".*1 0 UI

p. 2 IM[. SI€

FIGURe" 5-58. COMPUTED MO0TION OF NORTHEAST IGLOO (ESKIMO IV) AT ,"10DE 2.1

163

-=.-.. ..~-,r--,--'.. . . . ,• ,., • ... 9¶T Y :•:• •+, +:. .. " .. !•••W,,

R-7556-1 -4182

* '1xI

(a) Displacement

a!

IN.-w 41f I." if-it l oe 0f." 9-4d $"A a wTi. e. SEC

(b) Velocity

S

-3 -'- - --- -----------r..•• -4'50 0.6 4I. 08 @al if-it If f-oi.I . 1-t 933it

S

- _ _ _(c) Ac.celeration

0,.1;4 a.as 0.22 0'.16 0'.2 0o.21 0.20 0.32TingSECC

FIGURE 5-59. COMPUTED MOTION OF NORTHEAST IGLOO (ESKIMO IV) AT NODE 24

164

R-7556-l -4182

Tud Set

a i I* | - )ipa••n

Go 0 4 0.09 0.1 Is 6 o -20 a.24 0'2 U' •32

STIME. SEC

2

s

"F (b) Velocity

S 0I-54 s , a 1 - I.g |--' @6

a (c) Acceleration

TIM, S,

FIGURE 5-60. COMPUTED MOTION OF NORTHEAST IGLOO (ESKIM.O IV) AT N'ODE 61

• • 165

|7

Ak A-7SS6- -4182

i "" (a)e Displacement

2

(c)I ( A)- I era t on

-In

V. 0 d0 0. 8 u .1 d.1 0. 4 04 0(3t

Tilg, SIC

S 5A616

• | (b) Vceloc aty oi"I

166

R-77556-1 -4 1,82

F wI2

2

tI g

"* I

2

jam * a(b) Veloci t*y

1Tim 3 a

I

U.1 ~ ~ (b) ve'ciy

3 I

*.M9 sic J 24 63

S.3 (c) Accel era tion

U8

O .00 00 .6 .* 01 0 .20 0.4 0.32

FIGURE: 5-62. COMPUTED MOTION OF NORTHEAST IGLOO (ESKIMO IV) AT NODE 69

167

L 4

11-7556-1 -14182

iIt() ODisplacementi-

~. *~ *~ (b)velocity

vii

STile. ac

(c) Acceleration

0.o0 .o 0 " 0.0 .60e 02 7424 a.3T

Sisic


168

A

, 1 04 *411 9-1 41t 9 1

(c _____ _ era__io

169 .

'1 1

(c cclrao

| TrlM. StC

-16

It -7556-1 -, 182

S,, I

'-'II! '- (ai ISplacenment

| ~Tue. we=

g~~~~eb Veiotciieg tc :2

CI I (b eleraion

Si

II

000 0'.04 0.00 gig2 e*.ig . 0 , g a. e

k 1

-D IG ( IV) JeNoDE9

.170

-~I

I

S

0.0,.0 00 0.1* :1 0.30 0.24 0.,6 0.3

T ISIC


170

I k q-7556-1 -4182

2 17"

I I

il

IV as N t oo $as *1# 4 0 oN a o I 01• e

I ii

.- sA.

WT IV, tyy & W

a 00 0.04 ieo 0.1 d~ o'.20 e -*• 4 " o 0'.32 )

12171

Ij

"V I£3,

." 3 (c) Acceleratkon

S0.00 "0 " O s O 0, 0,4 OO *]

FIGURE 5-66. COMPUTED MOTION OF NORTHEAST IGLOO (ESKIM•O IV) AT NODE 99

A ik R- 7556-14 t82

(b velcit

I k A

3 TOM. m'

:V,.. . . I

-l

Ac --( e I A eration

,I 0.04 0'.04 0'.11 Sl I I . .0

TIIA, stc

FýGURE 5-6o7. COMPUTED MOTION OF NORTHEAST IGLOO (ESKIMO IV) AT NODE 119172

0]

muI

.

[A L___ .-"556-1T -•,18

01 T

is -' = * m

E I ,,-.------

. sic ot

(C) ?M I

I

'-g

1F

" 'IU FI A-8 OPTD/lTONO OTES GO (ES) M Acc )l ATi;On E1

"Ii

S173?.a

Ak 7556-' -b 182II

Va Iipacmn

3v2

10 ft *as * 040 1 as 6 me 40 a as 0w

Tom. -u

0.0 1.ili0 iI .1 .0 02 0 4.29 0

T14. i

FIUE56. cmUE OINO OTES GO EKM V TND 2

17

4I• R-7556-1 -4182

LLL1 161 51 3[50 St

IS7 • 4 9t 79

too tot t�oS 10 t014 is

to Is 2

-te toe 10 31 2 11 3 433

|•I L 39 4c st V7 i's 44 89

1 13 /f. ,0 S

17

FIR 0

73 17 l 11 123 104 I-1< I6 Ila e

-.. 9, 18 19 12 0 21 922 9 3 16 97 o 9

S175

e..ý

//I Ic fAC19

R-7556-1 -4182

011 4- a-i

IAI

00

3 24

573 2 .3 34 35 36

&do It

46 47 46 49 so 51 52 5

55 s6 57 511 59 50 61 62 6

73 74 75 76 77 is 79 600 8

10 10 02 103 104 105 11790

1213

FIGURE 5-71. COMPUTED DISPLACEMENT CONTOURS OF NORTHEAST HEADWALL CF ESKIMO IV

AT 158 MSEC (IN HUNDREDTHS OF FEET)

176

7_T

R-7556- 1-4182

A-01-5 ______ ______

I CORRESPONDS TO NODE 91"-300F (FIGURE 5-63)

1. 3as so

M~ CQARESPONOS TO NODE 94

I __________ _________ __________ __________ CORRESPONDS TO NODE 97(FIGURE 5-65)

UAU

___________ __________ ___________CORRESPONDS TO NODE,99

TIE VIEC AA800

~~~~~~~~~~~~~~(FIGURE 5-7266SRDACEEAINT) HSOISO ORHATH L

OF ESKIMO IV (Ref. 6

ý'.The motions at this gage exceeded its rating. Therefore, the recornot quite reliable.

17.7

R-7556-1-4182

00.•

- A __. ...- CORRESPONDS TO NODE 61(FIGURE 5-60)

•J

IIts

_____ I " I CORRESPONDS TO NODE 64, '- (FIGURE 5-61)

a. ,4Il • _ _______ _____|______ CORRESPONDS TO NODE. 35

e&qw

k.!...... CORRESPONDS TO NODE 21

_ __.CORRESPONDS TO NODE j1MI 8

"s' CORRESPONDS TC NODE 21(FIGURE 5-58)

t ORRESPONDS TO NODE 28

TIME, MSECAA8004

FIGURE 5-72. (CONTINUED)

1

t 178

t:~....................................... .

.- - - - - - - - -.-• - - - _ -' _ _ - 7-

R-7 556-1-41 82

ilkl

I.-Of

CORRESPONDS TO NODE 94

S•--• Im • -- -(FIGURE 5.64)

aCORRESPONDS TO NODE 97ho (FIGURE 5-65)

-______ ... CORRESPONDS TO NODE 98

-. .CORRESPONDS TO NODE 64(FIGURE 5-61)

S• .CORRESPONDS TO NODE 76

•' ~L-1,41.

t . I(j ____CORRESPONDS TO NODE 55

{CORRESPONDS TO NODE 31

I..-We

1+0 CORRESPONDS TO NODE .21(FIGURE 5-58)

TIME, NSECAA8002

FIGURE 5-73. MEASURED DISPLACEMENT TIME HISTORIES OF NORTHEAST HEADWALLIN ESKIMO IV (Ref. 6)

179

....

R-7556-1-4.182

SECTION 6

CONCLUSIONS AND RECO~MMENDATIONS

6.1 CONCLUSIONS

The present study consisted of dynamic analyses of magazine head-

walls subjected to blast loadings in the ESKIMC tests. All the analyses

were performed using the INSLAB code, a nonlinear finite element computer

program. The computed results were compared with available test data. The

following is a summary of conclusions of the study.

a. The modified INSLAB computer program is capable of analytically

predicting the behavior of the magazine headwalls used in the

ESKIMO tests.

b. The proposed nonlinear material model to represent the soil

behind the headwalls appears to be satisfactory.

C. The general behavior of the hea~iwalls predicted by the calcula-

tions agreed well with the actual behavior of the headwalls

In the tests.

d. The results from the present analysis of the south and west

headwalls in ESKIMO 1, using the refined finite element mesh,

show better agreement with the test results than those from

the previous analysis.

e. The analysis of the east headwall in thý2 ESKIMO 11 test shows

that (1) the computed maximum motions are much higher than

those measured, and (2) the computed permanent displacement

contours are similar in shape to those measured.

Preceding pape blankt 181

R-7556-1 -4182

Sf. The results of the analysis of the northeast headwall inthe ESKIMO II te.t show that:

1. The computed maximum velocity above the doorway is muchhigher than that measured using the linear motion

transducers.

2. The computed maximum acceleration of the door is in goodI agreement with that measured using the accelerometers.

3. The presence of the concrete beams around the doorway iseffective In reducing the maximum displacements of the

headwal l.

4. The biparting and sliding type of door is superior to thedouble-leaf and hinged type, for resisting the blast

loads.

g. The results of the aialysis of the northeast headwall in theESKIMO IV test indicated that:

1. The corrugated steel arch doesn't seem to. provide anysignificant resistance to the motion of the headwall.

2. The magnitudes.and general shapes of the computed dis-placement time histories are in good agrcement withthose measured by the linear motion transducers.

3. The computed acceleration time histories look somewhatdifferent from those measured using the accelerometers;however, the computed maximum accelerations are in good

agreement with those measured.

182

____________________________________A

i k R-7556-1 -4182

6.2 RECOMMENDATIONS

The analycical prediction capabilities exhibited by the presen:

study have been satisfactory. However, there are certain aspects to the

modeling of the headwall and door system that can improve the analyticalprediction capabilities. The following is a summary of recommendations for

improving the analytical prediction capabilities in order to reduce the

dependence on the expensive, full-scale testing program.

a. The present techniques for analyzing the headwcll systems are

not satisfactory when the doors are blown open. Therefore,the analytical methods should be improved to include the

concept of breakable hinges. This would per;ait the calaula-

k tion of true response of the headwall even after the doors

are blow open.

b. The parameters in the nonlinear soil models should be adjusted Ibased on the test date avi.,lable for the ESKIMO IV test. 7he

resulting models are expected to better represent the backfill

soils for improved analytical predictions.

c. Detailed anilysis of the test data for ESKIMO IV and comparison

of the data with the results of the present analysis should

be undertaken. This may include corrections to the data for

drifts, etc., and also statistical analyses of the test data.

d. Future tests should include a sufficient amount of instrumenta-tion to produce data necessary to study the stress distributionin the headwall sections. This would include placing strain

v'ages on reinforcing bars.

183

R-7556-1 -4182

SECTION 7

REFERENCES

1. Weals, F.H. rSwyTMO r Magazine Separation :e8e, NWC TP 5430. China Lake,

CA: Naval Weapons Center, April 1973.

2. Ts'ao, H.S., et a). Magazine HeadwacZi Response to Explosive BZ-aa:,R-7336-3284. El Segundo, CA: Agbablan Associates, January 1974.

3. User's Guide for INSLA4B Code, U-7556-1-4001. El Segundo, CA: Agbabian

Assrociates. September 1975.

4. Weals, F.H. ESY.TiMO I Magazine Separation Tet• t WC TP 5557. China Lake,CA: Naval Weapons Center, September 1974.

5. Weals, F.H. ESKIMO XII Magazine Sep.zation 2e',•, NWC TP 5771. China Lake,CA: Naval Weapons Center, February 1976.

6. Weals, F.H., and Wilson, C.H. RrelZimina, Rypepert, Z7SKMC i:. China Lake,

CA: Naval Weapons Center, 1976.

7. Baker, W.E. E'rý.Zo.iona in Air. Austin, TX: University of Texas Press,1973.

S. User,' Guide for .NSLAB Code, R-6820-1580. Los Angeles: Agbabian-Jacobsen

Associates, September 1970.

9. Strength of MAateriaZs and StruoturaZ EZ•,ente, Manual for Design ofStructures to Resist the Effects of Ato'nic Weapons, EM1110-345-414.U.S. Amy, Corps -;f Engineers, tMarch 1957.

S 10. "IGLOO Door Test -- Modulus of Soil Reaction," unpublikhed memorandum,.Washington, D.C.: Naval Weapons Center, Code 7036, October 1972.

_ 11. Richert, F.E., Jr., et al. V-,'rtion o.f Soils and Fo ur.=ion. EnglewoodCliffs, NJ: Prentice-Hall, 1970.

12. Uear'a Guide for "TRI/SAC Code, r'-7128-4-2314. El Segundo, CA: AgbabianAssociates, May 1972.

13. Wang, C.T. Applied EZaatim ty. New York: McGraw-Hill, 1953.

Preceding pap blank185

R-7556-1 -4182

APPENDIX A

INCLUSION OF NONLINEAR SPRINGS IN INSLAB CODE

The response of tht magazine headwall to blast loading is greatly

influenced by the earth fill behind the headwall. The effect of the soil can

best be Incorporated In the two-dimensional headwall model by using a com-

bination of damping elements and nonlinear (one-way) springs. Linear springs,

which are already present in the existing INSLAB code, are inadequate for

k modeling the influence of the soil because they exert both pressures and

tensile forces on the headwall and they tend toward a final displacement ofzero. The properties of the nonlinear springs and the details -' their incor-

poration in INSLAB are discussed herein.

SFigure A-1 shows the load/deflection characteristics of the non-

linear springs. Two different spring constants, kL and ku, appropriate

in the virgin loading zone (Zone 2) and the unloading/reloading zone (Zone 1)respectively, have been incorporated in such a way that after loading, equi-

librium corresponds to a nonvanishing displacement, 6 . This equilibrium

displacement Is a function of 6max' the largest compressive displacement of

the prior load history. Tensile spring forces are eliminated by using aspring constant of zero in "Zone 0,' in which the displacement is on the

tensile side of the equilibrium displacement.

Th. '?arying status of the nonlinear spring Latween Zones 0, 1,

and 2 requires reformulation of the global stiffness matrix Jiuring transitionfrom one zone to another. Furthermore, as shown in Table A-1, transition

between zones usually requires an adjustment to the load vector. This isbecause the stiffness matrix ;s capable of accomodatiný, only that portion ýf

= the incremental spring force that is proportional to the incremental displace-ment, A6. Note that for a linear spring in which there Is never any

transition between zones, there is no need for a load vector adjustment.

Preceding pate blank

[ 187

R-7556-1 -4182

_i1

NOTE: kt - SPRING CONSTANT IN LOADING

ku a AN ARBITRARY STIFFNESS VALUE IN UNLOADING(CONTROLS THE PERMANENT DISPLACEMENT OFTHE SPRING)

F(COMPRESSION)

IIFI ku L

k 1

(COMPRESSION)6 6o max

' - "- - ZONE 0- ZONE 1 - "-,, -' -- - -ZONE 2 -

FIGURE A-i. LOAD/DEFLECTION CHARACTERISTICS OF NONLINEAR SPRINGS

188

R-7556-1-4182

o - o ,,

II?AO

a"4, i a , t 4

r 0 -0 -S• -0 -0 a

LU-

t..

'0 -0

.u IL

I0 .0 : ... 1 0

40 '0 4• 4 0

-. 4 44 .

UAU

189

R-7556-l-0182

Successful incorporation of the spring force (Table A-1) in the

finite element model is dependent upon the ability to predict upcoming

changes in zone. This is particularly important in the case of rebonding

(transition from Zone 0 to Zone 1). In this case the spring constant changes

from 0 to k If this change in stiffness is iot anticipated, calculatinnU.

of the incremental displacement will proceed as if the spring constant

remains 0 throughout the time Interval. This will result in an excessivelylarge displacement into Zones 1 or 2. By the time the spring force correspond-Ing to this large displacement is included in the subsequent step, an incre-

ment of potential energy (spring deformation) has been erroneoutsly added to

the dynamic system. Cyclic repetition of this error causes unstable growth

of oscillatory motion.

Using a truncated Taylor series expanded about time t, the dis-

placement at the end of the tirre interval at can he estimated according to

the formula

x(t + at) X + Xat +X(at) 2 (A-1)

The accuracy of this estimate should improve with decreasing It. This fore-

casted future displacement is used to predict whether any changes in zone are

to be anticipated. If so, a stiffness reformulation occurs during the next

step, and the appropriate adjustment is incorporated in the load vector.

Figure A-2 shows the test problem that was used to check out the

performance of the nonlinear spring. Some sample results of this test problem

are shown in Figure A-3. Figure A-3a shows the time dependence of the load

function, P, used in Case 1. The displacement of the end of the beam for

this case is shown in Figure A-3b. The external load (- 2P) deflects the

beam until the nonlinear springs supply an equilibrating force. When the

external load is relaxed, the nonlinear spring relaxes also. However, due

to the high unloading spring constant, this relaxation of the spring occurs

190

R-7556-1-41 82 7

iiP

Iy

IizUx

LENGTH a 10 IN.WIDTH - 1 IN.DEPTH - 0.2 IN. SRN OSATE - 30 x 106 PSI SRN OSAT

7.4x1-4 LB-SEC2 600 LB/IN.

7.IN.4 ku -6000 LB/IN.

FIGURE A-2. TEST PROOLEfI USED TO CHECK OUT NONLINEAR SPRINGS

191

- - -7',-w flx~.v~y-wvv V

R-7556-1-4182

fA0 C

*0 71C

C

aha

*NI ~ ~ ~ V *I33VdSQ*I'N33V4~

C C,

.0 cm

oi 0

0 0.

192

- - - --- --- - --- --

Iilk R-7 556-1- 41821

with only a small recovery of displacement. When the external load has

relaxed to the extent that the elasticity of the beam overcomes it, the beam

debonds from the nonlinear spring and undergoes free vibration.

Figure A-La shows the time dependence of the load function used inCase 2, which waes designed to test ,'ebonding. The results are shown in

Figure A-4b. Debonding occurs at about 30 msec in this case, after which

free vibration begins. The free vibration continues until the reapplication

of external load at 45 msec. This external load and the inertia of thevibrating beam cause the beam to slam violently into the relaxed spring at

the displacement o (see Fig. A-1). Tcmporary equilibrium is found in thevicinity of this displacement until the external load grows large enough to

force the beam into Zone 2 of Figure A-1. At this point the stiffnessreduces to the virgin loading value, allowing further displacement until a

new equilibrium is reached.

The results of these two test cases indicated that the nonlinearspring is performing as intended. Both debonding and rebonding appear to be

working correctly. Furthermore, the nonzero equilibrium displacement follow-

ing a load cycle has been checked and found satisfactory. It is anticipatedI that these'properties, when used in conjunction with dampers and/or concen-trated masses, will prove satisfactory in modeling the effects of the soil

behind the headwall.

193

R-7556- ,• 182

S! IAPPENDIX 8

PROCEDURE FOR CALCULATING YIELD MOMENTSFOR A REINFORCED-CONCRETE SECTION

The yield moment of a reonforced-concrete cross section is defined a

as the moment that makes the steel in tension or the concrete in compressionreach its yle~d limit. The reinforcement .rovided in the headwall section

is governed by the former cese; therefore, only the derivation for the under-reinforcement case (steel-in-tension yield) is described below.

A typical cross section of a reinforced-concrete sec.:tion is shownin Figure B-1, and the strain diagram is shown in Figure 5-2, where A and ]A; are the areas of the steel reinforcemnnt in tension and compression,respectively. The strain level in tension steel is ct, in concrete is - c'

and in compression steel is c'. The strains are related by the following

formula:

t d -Kd I - K

C K

e' d' - Kd dE Kd •Kc

The stresses in steel are as follows:

a no 1- K stress in tension steels c K

t n stress in compression steel (B-2)

Es

where m E -, the ratio of modulus of elasticity of steel to concrete.c

4.cdg page hnk•, 195

R-7556-1 -J.182

z #cc

z a

UA ýcc

4.' qnj

"L6

196U~

R-7556- 1 -4182

Denoting th- area of steel as a fraction of the area of the concretesection, i.e. ,

A 5,sP"bd

Spl As$

S" b"•'-(8-3)bd

the equation of equilibrium becomes

a A +;A' + 4 cc Kbd - 0 (8-4)

This can be rewritten after some arrangement into the form

K2 d'K + 2(np + np') K - (2np + 2np' 0

Therefore the solution of K becomes

2np+ 2npd' L +(np + np')2 -(np + np') (8-5)

The yield moment for the underreinforcement case is

M "Cs As (d"') + A; (d' Kd

or

M - A jda (0-6)S 7

197j

i R-7556-1 -4182 -

whe re

Kd ' d' 3)•

p 'K (-7)

If the solution of Equation B-5 is such that K >- then the

stress in compression steel is

d' d'-K '- K*" = 2na d - 2 -- K (8-8)

s € K 1 --K as

The equation of equilibrium for this case becomes

1

a A + a' A' + aKbd - E el A' - (8-9)5 S 5 5 25

After some rearrangement, and the use of Equation B-3, K becomes

K np + (2n - 1)p' !-.-] + (np + (2n - 1)p'] 2

- [np + (2n - 1)p'] (8-10)

The form of Equation B-6 remains the same except that for this case, j is

defined as

(2n - 1) K - 2.,- d'

j d- I -) d ('- K (B-Pf)3 W1- K) p d 3)

1 98

R-7556-1 -4182

APPENDIX C

PROCEDURE FOR COMPUTING EQUIVALENT MDL-TOR A REINFORCED CONCRETE SECTION

to

yoIhI

xu

RE INFORCED CONCRETE STRUCTURE AA82L.0

Assume that the displacements in the reinforced concrete structure shown

S above are in the following form:

U(xIYIz) -- wx) z -- W'(x)z

v(X,y,z) *0j

w(x,yZ) -W(X)

and the strains:

* -- z W'l(x)zxx ax

zz eyy Exz Exy a ryz a

199

SiElk R-7556- 1-4182

Assuming that the vertical stress a 0

(X42G)c + x(C Ec ) 0zz xx yy

a n d - ~ c . ~ + G W (~

a U (X+2G)c xx+ Ez

M JX2 ) - X E Dý(x4(G ~xx (-2) CXX I 'xx

where

Now he omet M is given by

h/2M - bf xxzdz

-bOW" ,h/22

200

A--

R-7556-1-4182

kd :

d!

of ~ ~ ~ ~ ~ ~ -i (x) tai ltlbtoS

t(1-k)d

Ct" (1-k)dW'(x)

[ioment of the section is then given by

M A Asids AsjdE st

AJEA .(1,-k)d2W"(x) W '(x)

Also

D - A jE (1-k)d 2(1-v2)

Therefore the effective E for the concrete section is given by

2 2AsJE (1-k)d (1-v

201

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