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Laboratory statnamic testing

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Title:
Laboratory statnamic testing
Physical Description:
Book
Language:
English
Creator:
Stokes, Michael Jeffrey
Publisher:
University of South Florida
Place of Publication:
Tampa, Fla.
Publication Date:

Subjects

Subjects / Keywords:
pyrotechnics
damping coefficient
influence zone
model testing
Frustum Confining Vessel
rapid load test
Dissertations, Academic -- Civil Engineering -- Masters -- USF   ( lcsh )
Genre:
government publication (state, provincial, terriorial, dependent)   ( marcgt )
bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )

Notes

Summary:
ABSTRACT: Despite advancements in the analysis of statnamic load testing data, there exists uncertainty with underlying procedural assumptions. Two such assumptions are that the system mass and soil-related damping coefficient remain constant throughout the loading event. These assumptions are the culprit of aberrant predictions of the static capacity at small displacements when the overall displacement is large. An exploration of the assumptions may validate prior existing test results as well as solidify the current analysis process. However, an exploration could also reveal an overestimation or underestimation of portions of the predicted static load responses. The testing program outlined herein consists of a two-phase sequential agenda devoted toward the preparation and familiarization of a new laboratory statnamic device. The first phase involves the development of user guidelines for accurately targeting a desired statnamic test, and the second incorporates the guidelines into a preliminary testing regime specifically targeted at determining a suspected strain-dependant statnamic damping coefficient. The steps taken in this thesis are intended to launch future research endeavors toward obtaining a better understanding of the statnamic damping coefficient.
Thesis:
Thesis (M.S.C.E.)--University of South Florida, 2004.
Bibliography:
Includes bibliographical references.
System Details:
System requirements: World Wide Web browser and PDF reader.
System Details:
Mode of access: World Wide Web.
Statement of Responsibility:
by Michael Jeffrey Stokes.
General Note:
Title from PDF of title page.
General Note:
Document formatted into pages; contains 211 pages.

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University of South Florida Library
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University of South Florida
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Resource Identifier:
aleph - 001469425
oclc - 55731623
notis - AJR1179
usfldc doi - E14-SFE0000326
usfldc handle - e14.326
System ID:
SFS0025021:00001


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Laboratory statnamic testing
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ABSTRACT: Despite advancements in the analysis of statnamic load testing data, there exists uncertainty with underlying procedural assumptions. Two such assumptions are that the system mass and soil-related damping coefficient remain constant throughout the loading event. These assumptions are the culprit of aberrant predictions of the static capacity at small displacements when the overall displacement is large. An exploration of the assumptions may validate prior existing test results as well as solidify the current analysis process. However, an exploration could also reveal an overestimation or underestimation of portions of the predicted static load responses. The testing program outlined herein consists of a two-phase sequential agenda devoted toward the preparation and familiarization of a new laboratory statnamic device. The first phase involves the development of user guidelines for accurately targeting a desired statnamic test, and the second incorporates the guidelines into a preliminary testing regime specifically targeted at determining a suspected strain-dependant statnamic damping coefficient. The steps taken in this thesis are intended to launch future research endeavors toward obtaining a better understanding of the statnamic damping coefficient.
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Frustum Confining Vessel.
rapid load test.
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L abora tory Statnamic Testing by Michae l J eff rey Stokes A thesis submitt ed in par tial fulfillment of the re quirements for the deg ree of Master of Science in Civi l Eng ineer ing Depa rtment of Civil and Environmental Eng ineer ing College of Eng ineer ing University of South Florida Major Profe ssor: Austin Gray Mullins, P h.D. Rajan Sen, Ph.D. Ashraf Ay oub, Ph.D. Da te of Ap pr ov a l: Marc h 18, 2004 Key words: ra pid load test, Frustum Confining Vessel, model testing influence zone, damping coef ficient, py rotec hnics Copy rig ht 2004, Michael J. S tokes

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i Tabl e of Contents L i s t o f T a b l e s .......................................................... iii L i s t o f F i g u r e s ......................................................... iv A b s t r a c t ............................................................. x vi 1 0 I n t r o d u c t i o n ......................................................... 1 2 0 L i t e r a t u r e R e v i e w ..................................................... 4 2 1 C o n c e p t o f S t a t n a m i c ............................................ 5 2 2 D e v i c e C o m p o n e n t s ............................................. 5 2 2 1 P i s t o n ................................................ 6 2.2.2 Silencer a nd Reac tion Masses . . . . . . . . . . . . . . . 6 2 2 3 C a t c h i n g M e c h a n i s m s .................................... 7 2 3 I n t e r n a l B a l l i s t i c s o f S t a t n a m i c .................................... 9 2. 4 E vo lut ion of Sta tna mic Te sti ng a nd An a ly sis . . . . . . . . . . . . 12 2 4 1 T h e E a r l y Y e a r s........................................ 12 2.4.2 The F irst I nterna tional Statnamic Seminar . . . . . . . . . 14 2.4.3 The Sec ond I nterna tional Statnamic Seminar . . . . . . . . 16 2.4.4 Additional Analy sis Procedure s . . . . . . . . . . . . . 21 2 4 5 S o f t w a r e D e v e l o p m e n t .................................. 22 3 0 L a b o r a t o r y E q u i p m e n t ................................................ 36 3 1 L a b o r a t o r y S t a t n a m i c D e v i c e ..................................... 36 3 1 1 P i s t o n ............................................... 37 3.1.2 Silencer a nd Reac tion Masses . . . . . . . . . . . . . . 38 3 1 3 C a t c h i n g M e c h a n i s m ................................... 38 3 2 M i n i m e M o d i f i c a t i o n s .......................................... 39 3. 2. 1 I nte g ra te d St a tic L oa d T e st F ra me . . . . . . . . . . . . 39 3 2 2 C a t c h i n g F r a m e B o l t H o l e s ............................... 39 3 2 3 L i f t P i n s .............................................. 40 3. 2. 4 Re a c tio n M a ss P ic k E y e s a nd Al ig nme nt D ow e ls . . . . . . 40 3 2 5 C a t c h S y s t e m.......................................... 41 3 3 F r u s t u m C o n f i n i n g V e s s e l ....................................... 43 3 3 1 P o s t G r o u t o f D r i l l e d S h a f t s .............................. 43 3.3.2 I nfluenc e of Water Table on D rilled Shaft Construction . . . . 44

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ii 4 0 T e s t P r o g r a m ....................................................... 56 4 1 I n s t r u m e n t a t i o n ............................................... 56 4 2 C a l i b r a t i o n T e s t i n g............................................. 58 4 2 1 T e s t M a t r i x ........................................... 58 4 2 2 M a s s C o n f i g u r a t i o n ..................................... 59 4 2 3 I n i t i a l V o l u m e ......................................... 60 4 2 4 V e n t D i s t a n c e ......................................... 61 4 2 5 F u e l R a n g e s ........................................... 61 4.2.6 Test Matrix L imitations : J ump Heig ht . . . . . . . . . . . 63 4.3 Preliminary Pursuit of the Statnamic Damping Coeffic ient . . . . . . 64 4.3.1 Static-Statnamic Comparisons . . . . . . . . . . . . . . 64 4 3 2 F r u s t u m T e s t i n g ....................................... 65 5 0 R e s u l t s ............................................................ 73 5 1 C a l i b r a t i o n T e s t R e s u l t s ......................................... 73 5 1 1 M a s s C o n f i g u r a t i o n ..................................... 74 5 1 2 I n i t i a l V o l u m e ......................................... 75 5 1 3 V e n t D i s t a n c e ......................................... 77 5.1.4 Fue l Rang es and the Shape F actor . . . . . . . . . . . . 78 5 1 5 O p e r a t o r G r a p h s ....................................... 80 5. 2 St a tna mic Da mpi ng Coe ff ic ie nt R e su lts . . . . . . . . . . . . . . 85 5 2 1 F r u s t u m T e s t i n g R e s u l t s ................................. 85 5 2 2 F r u s t u m F r u s t r a t i o n s .................................... 87 6 0 C o n c l u s i o n s a n d R e c o m m e n d a t i o n s .................................... 111 R e f e r e n c e s ........................................................... 117 A p p e n d i c e s ........................................................... 119 A p p e n d i x A : F a m i l y o f C u r v e s ..................................... 120 A 1 3 M a s s C o n f i g u r a t i o n s .................................. 120 A 2 4 M a s s C o n f i g u r a t i o n s .................................. 124 A 3 5 M a s s C o n f i g u r a t i o n s .................................. 131 A 4 6 M a s s C o n f i g u r a t i o n s .................................. 149 A 5 7 M a s s C o n f i g u r a t i o n s .................................. 152 A 6 9 M a s s C o n f i g u r a t i o n s .................................. 157 A 7 1 1 M a s s C o n f i g u r a t i o n s ................................. 162 A p p e n d i x B : P r o c e d u r e s .......................................... 176 B.1 F rustum Prepara tion and Pressurization . . . . . . . . . . 176 B 2 D r i l l e d S h a f t C o n s t r u c t i o n ............................... 178 B 3 S t a t i c L o a d T e s t ........................................ 181 B.4 Statnamic L oad Te st and Calibration Testing . . . . . . . . 182 Ap p en d i x C : S t at n am i c M i n i T es t er Dr aw i n gs . . . . . . . . . . . . 194

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iii List of Tabl es Table 21 L ist of statnamic device s (Tra nsportation Resear ch B oard, 2003) . . . . . 6 T a b l e 2 2 F C V s c a l i n g f a c t o r s ............................................ 20 T a b l e 4 1 F o u n d a t i o n p r e l o a d s ............................................ 59 Table 42 Effe ct of spac ers on the initial volume and powe r stroke ( d ) ............ 60 Table 43 Effe ct of spac ers a nd fuel on the f uel density (%) . . . . . . . . . . 62 Table 51 Effe ct of incr easing space rs on the maximum forc e (kN ). . . . . . . . 76 Table 52 Effe ct of spac ers a nd fuel on the f uel density (%) . . . . . . . . . . . 78

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iv List of F igures Fig ure 11 (1) Radia lly incre asing zone of influence . . . . . . . . . . . . . . 2 Fig ure 12 (2) Ma x imum downward displace ment and shea r strain. . . . . . . . . 2 F ig ur e 13 ( 3) Th e zon e of inf lue nc e sh a rp ly dim ini sh e d a s th e pil e dis pla c e s r e l a t i v e t o t h e s o i l .............................................. 3 Fig ure 14 Presumed var iation of mass (M) with downwa rd displace ment (D). . . . 3 Fig ure 21 Kentledg e static load te st (PMC, 2004). . . . . . . . . . . . . . . 24 Fig ure 22 16 MN piston with picking lid and stee l plate attac hed. . . . . . . . . 24 F i g u r e 2 3 1 6 M N f u e l b a s k e t ............................................ 25 F i g u r e 2 4 1 6 M N v e n t p i n .............................................. 25 Fig ure 25 4 MN silencer (left) and 16 MN silence r with picking collar ( rig ht). . . . 26 F i g u r e 2 6 M u f f l e r o f t h e 1 6 M N s i l e n c e r ................................... 26 F ig ur e 27 4 MN (l e ft ) a nd 16 MN (r ig ht) re a c tio n ma sse s. . . . . . . . . . . . 27 Fig ure 28 16 MN multi-toothed catching rails (lef t) and ra tchet tee th (rig ht). . . . 27 F ig ur e 29 Co mpa ri so n o f s ta tna mic to a c omm on fi re a rm . . . . . . . . . . . 28 Fig ure 210 Pressure c urve f or a 3006 rifle loade d with 52 gr ains of I MR 4064 and a 150 g rain bullet (F abrique Scientific, I nc., 2001). . . . . . . . 29 Fig ure 211 Ty pical statnamic loa d pulse. . . . . . . . . . . . . . . . . . 29 Fig ure 212 Def inition of the shape fa ctor (SF ). . . . . . . . . . . . . . . . 30 Fig ure 213 UPM tim e window f or c deter mination (Transpor tation Resear ch B o a r d 2 0 0 3 ) ............................................... 30

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v Fig ure 214 Var iation in c betwee n times (1) and ( 2) (Tr ansportation Resea rch B o a r d 2 0 0 3 ) ............................................... 31 Fig ure 215 Statnamic fuel pe llets, partially consumed (le ft) and w hole (rig ht). . . . 31 F ig ur e 216 Va ry ing the a mou nt o f f ue l w ith the re a c tio n ma ss a nd ve nt distance c onstant (B erming ham, 1995). . . . . . . . . . . . . . 32 F ig ur e 217 Re a c tio n ma ss e qu a l to 2. 5% 5 %, 10 %, a nd 20 % o f e xpe c te d te st load with a consta nt amount of fuel a nd vent distance ( B e r m i n g h a m 1 9 9 5 ) ......................................... 32 F ig ur e 218 Ve nti ng fo r d if fe re nt v e nt d ist a nc e s w ith a c on sta nt a mou nt o f f ue l and re action mass (B erming ham, 1995). . . . . . . . . . . . . . 33 Fig ure 219 Fr ustum Confini ng Vessel with static load te st frame . . . . . . . . 33 Fig ure 220 Fr ustum pressurization scheme (F rede rick, 2001). . . . . . . . . . 34 Fig ure 221 Unit damping ve rsus SPT N values (Winters, 2002). . . . . . . . . 35 F i g u r e 3 1 S t a t n a m i c M i n i T e s t e r ......................................... 45 F i g u r e 3 2 M i n i m e p i s t o n a n d s p a c e r s ...................................... 45 F i g u r e 3 3 V e n t e d l i d a n d v e n t p i n ........................................ 46 Fig ure 34 Acc eler ometer a nd pressure transduce r. . . . . . . . . . . . . . . 46 F i g u r e 3 5 S i l e n c e r a n d r e a c t i o n m a s s e s .................................... 47 F i g u r e 3 6 C a t c h t o o t h r e l e a s e c a b l e s ...................................... 47 Fig ure 37 Drilling hole s for the integ rate d static fra me. . . . . . . . . . . . . 47 F i g u r e 3 8 I n t e g r a t e d s t a t i c f r a m e ......................................... 48 Fig ure 39 Bolt patter n of orig inal catc hing f rame base. . . . . . . . . . . . . 48 F ig ur e 310 En la rg ing ho le s f or bo lt h e a ds . . . . . . . . . . . . . . . . . 49 Fig ure 311 Modified ca tching fra me base mounted to the FCV. . . . . . . . . 49

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vi F ig ur e 312 L if t pi ns re tr a c te d ( le ft ) a nd e xten de d th ro ug h th e re a c tio n ma ss g u i d e s ( r i g h t ) ............................................... 49 F ig ur e 313 Wel din g pic k e y e s a nd do we l pi ns to e a c h r e a c tio n ma ss. . . . . . . 50 F ig ur e 314 Ca rr ia g e pla te wi th r a tc he t to oth wi nd ow s. . . . . . . . . . . . . 50 F ig ur e 315 Ca rr ia g e pla te wi th c a rr ia g e br a c ke t. . . . . . . . . . . . . . . . 51 Fig ure 316 Carria g e bra cket a fter c onstruction (left) and mounted to the top a n d b o t t o m t w o m a s s e s ( r i g h t ) .................................. 51 F ig ur e 317 F ro nt ( le ft ) a nd ba c ks ide (r ig ht) of ra tc he t to oth wi th r e c oil s p r i n g s .................................................... 52 F ig ur e 318 Pa rt ia lly fi nis he d c a rr ia g e a sse mbl ie s. . . . . . . . . . . . . . . 52 F ig ur e 319 Pla c e me nt o f c a rr ia g e g uid e s. . . . . . . . . . . . . . . . . . 53 Fig ure 320 Spring integ rate d shock absor bers dur ing ( left) a nd afte r (r ight) m o d i f i c a t i o n ................................................ 53 Fig ure 321 Additional plate welde d to the base. . . . . . . . . . . . . . . . 53 F i g u r e 3 2 2 R e a t t a c h i n g t h e f r a m e l e g s ..................................... 54 Fig ure 323 Modified mecha nical ca tch with a seve n-mass conf igur ation. . . . . . 54 Fig ure 324 Modified mecha nical ca tch with a full-mass c onfig uration. . . . . . . 55 F i g u r e 4 1 M i n i m e l o a d c e l l a n d p i s t o n ..................................... 68 F i g u r e 4 2 M i n i m e m o u n t e d t o r i g i d b a s e ................................... 68 F ig ur e 43 E xamp le of te st m a tr ix fl ow c ha rt . . . . . . . . . . . . . . . . . 69 F i g u r e 4 4 E x a m p l e o f t e s t m a t r i x t a b l e .................................... 69 Fig ure 45 Effe ct of spac ers on the initial volume and powe r stroke. . . . . . . . 70 F i g u r e 4 6 D a m a g e d 1 5 2 5 c m v e n t p i n ..................................... 70 F i g u r e 4 7 M i n i m e v e n t p i n s ............................................. 71

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vii F i g u r e 4 8 E x t r a p o l a t e d s t a t i c r e s p o n s e ..................................... 71 F i g u r e 4 9 I n t e r p o l a t e d s t a t i c r e s p o n s e ..................................... 72 F i g u r e 4 1 0 F r u s t u m t e s t s h a f t s ........................................... 72 Fig ure 51 Reproducibility of a te st (5 masses, 2 spac ers, 15.25 c m vent pin, and 1 f u e l p e l l e t ) .................................................. 89 Fig ure 52 Effe ct of mass c onfig uration on the load pulse ( 8.80 cm vent leng th and f u e l d e n s i t y o f 7 0 2 % ) ......................................... 89 Fig ure 53 Effe ct of mass c onfig uration on the load pulse ( 4.50 cm vent leng th and f u e l d e n s i t y o f 1 0 5 % ) ......................................... 90 F ig ur e 54 Co mpa ri so n o f t y pic a l st a tna mic loa d p uls e s. . . . . . . . . . . . . 90 F ig ur e 55 M a ss r a tio vs d ur a tio n ( 15 .2 5 c m ve nt p in) : Pa th o f i nc re a sin g sp a c e rs . . 91 F ig ur e 56 M a ss r a tio vs d ur a tio n ( 10 .9 5 c m ve nt p in) : Pa th o f i nc re a sin g sp a c e rs . . 91 Fig ure 57 Effe ct of ve nt distance on the loa d pulse (5 masses a nd fuel de nsity of 7 0 2 % ) ..................................................... 92 Fig ure 58 Effe ct of ve nt distance on the loa d pulse (7 masses a nd fuel de nsity of 7 0 2 % ) ..................................................... 92 F ig ur e 59 E ff e c t of fu e l de ns ity on the loa d p uls e (5 ma sse s a nd 8. 8 c m ve nt l e n g t h ) ..................................................... 93 F ig ur e 510 Ef fe c t of fu e l de ns ity on the loa d p uls e (5 ma sse s a nd 10 .9 5 c m ve nt l e n g t h ) .................................................... 93 F i g u r e 5 1 1 M a s s r a t i o v s d u r a t i o n : E f f e c t o f f u e l d e n s i t y ( r ) ................... 94 F ig ur e 512 Ma ss r a tio vs d ur a tio n ( 15 .2 5 c m ve nt p in) : Pa th o f i nc re a sin g fu e l p e l l e t s ..................................................... 94 F ig ur e 513 Ma ss r a tio vs d ur a tio n ( 10 .9 5 c m ve nt p in) : Pa th o f i nc re a sin g fu e l p e l l e t s ..................................................... 95 F i g u r e 5 1 4 L o a d p u l s e w i t h S F = 0 4 3 ..................................... 95

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vii i F i g u r e 5 1 5 L o a d p u l s e w i t h S F = 0 5 0 ..................................... 96 F i g u r e 5 1 6 L o a d p u l s e w i t h S F = 0 8 6 ..................................... 96 F ig ur e 517 Ma ss r a tio vs d ur a tio n: D ist ri bu tio n o f s ha pe fa c tor s. . . . . . . . . 97 F ig ur e 518 Va ri a tio n in the a mou nt o f s mok e le ss r if le po wd e r. Al l th re e te sts utiliz ed 6 masses, 3 spa cer s, 1fuel pellet, a nd the 15.25 cm vent pin. . . 97 F i g u r e 5 1 9 F u e l f o r c e c u r v e : 0 s p a c e r s ..................................... 98 F i g u r e 5 2 0 F u e l f o r c e c u r v e : 1 s p a c e r ..................................... 98 F i g u r e 5 2 1 F u e l f o r c e c u r v e : 2 s p a c e r s ..................................... 99 F i g u r e 5 2 2 F u e l f o r c e c u r v e : 3 s p a c e r s ..................................... 99 F i g u r e 5 2 3 F u e l f o r c e c u r v e : 4 s p a c e r s .................................... 100 Fig ure 524 Oper ator g raph #1: Mass r atio vs. forc e. . . . . . . . . . . . . . 100 F i g u r e 5 2 5 M a s s r a t i o v s d u r a t i o n ....................................... 101 Fig ure 526 Combined variable e ffe cts on the mass ra tio and duration. . . . . . 101 Fig ure 527 Oper ator g raph #2 w ith data points: Mass ratio vs. duration. . . . . . 102 Fig ure 528 Oper ator g raph #2 w ithout data points: Mass ratio vs. duration. . . . 102 Fig ure 529 Shape fa ctors as a function of the f orce and impulse. . . . . . . . . 103 Fig ure 530 Vent pin leng th as a func tion of forc e and impulse. . . . . . . . . 103 Fig ure 531 Oper ator g raph #3: F orce vs. impulse. . . . . . . . . . . . . . 104 Fig ure 532 Oper ator g raph #4: Jump height vs. impulse. . . . . . . . . . . . 104 F ig ur e 533 De sig n p ro c e du re ste p 1 : O pti on 1 ( 5 ma sse s, no sp a c e rs a nd 2 f ue l p e l l e t s ) ................................................... 105 F ig ur e 534 De sig n p ro c e du re ste p 1 : O pti on 2 ( 5 ma sse s, 1 s pa c e r, a nd 3 f ue l p e l l e t s ) ................................................... 105

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ix Fig ure 535 Desig n proce dure step 2: De termine the ma ss ratio. . . . . . . . . 106 F ig ur e 536 De sig n p ro c e du re ste p 3 : F ind the ra ng e of du ra tio n a nd se le c t a ve nt p i n ...................................................... 106 Fig ure 537 Desig n proce dure step 4: F ind the impulse. . . . . . . . . . . . 107 F ig ur e 538 De sig n p ro c e du re ste p 5 : F ind a sso c ia te d ju mp h e ig ht. . . . . . . . 107 Fig ure 539 Static and statnamic load te st cy cles pe rfor med on shaft S53. . . . . 108 Fig ure 540 Static and statnamic c y cles used in the a naly sis of the statnamic d a m p i n g c o e f f i c i e n t ......................................... 108 Fig ure 541 Predicted static r esponse in compa rison to the measure d statnamic s ta tn amic2 r e s p o n s e f o r F ........................................ 109 F ig ur e 542 Ca lc ula te d s ta tna mic da mpi ng c oe ff ic ie nt. . . . . . . . . . . . . 109 Fig ure 543 Damping coef ficient a s a func tion of time. . . . . . . . . . . . . 110 F i g u r e 6 1 F u e l f o r c e c u r v e s ............................................ 119 F i g u r e 6 2 O p e r a t o r g r a p h s ............................................. 120 Fig ure A -1 3 masses, 1 spa cer 2 fuel pe llets, and the 6.65 cm ve nt pin. . . . . . 120 Fig ure A -2 3 masses, 1 spa cer 3 fuel pe llets, and the 6.65 cm ve nt pin. . . . . . 120 Fig ure A -3 3 masses, 1 spa cer 1 fuel pe llets, and the 8.80 cm ve nt pin. . . . . . 121 Fig ure A -4 3 masses, 1 spa cer 2 fuel pe llets, and the 8.80 cm ve nt pin. . . . . . 121 Fig ure A -5 3 masses, 1 spa cer 1 fuel pe llets, and the 10.95 cm ve nt pin. . . . . . 122 Fig ure A -6 3 masses, 1 spa cer 2 fuel pe llets, and the 8.80 cm ve nt pin. . . . . . 122 Fig ure A -7 3 masses, 1 spa cer 2 fuel pe llets, and the 10.95 cm ve nt pin. . . . . . 123 Fig ure A -8 4 masses, 4 spa cer s, 1 fuel pellet, a nd the 15.25 cm vent pin. . . . . . 124 Fig ure A -9 4 masses, 3 spa cer s, 1 fuel pellet, a nd the 15.25 cm vent pin. . . . . . 124

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x Fig ure A -10 4 masses, 2 spa cer s, 1 fuel pellet, a nd the 15.25 cm vent pin. . . . . 125 Fig ure A -11 4 masses, 1 spa cer s, 1 fuel pellet, a nd the 15.25 cm vent pin. . . . . 125 Fig ure A -12 4 masses, 0 spa cer s, 1 fuel pellet, a nd the 15.25 cm vent pin. . . . . 126 Fig ure A -13 4 masses, 4 spa cer s, 2 fuel pellet, a nd the 15.25 cm vent pin. . . . . 126 Fig ure A -14 4 masses, 3 spa cer s, 2 fuel pellet, a nd the 15.25 cm vent pin. . . . . 127 Fig ure A -15 4 masses, 2 spa cer s, 2 fuel pellet, a nd the 15.25 cm vent pin. . . . . 127 Fig ure A -16 4 masses, 1 spa cer s, 2 fuel pellet, a nd the 15.25 cm vent pin. . . . . 128 Fig ure A -17 4 masses, 0 spa cer s, 1 fuel pellet, a nd the 15.25 cm vent pin. . . . . 128 Fig ure A -18 4 masses, 4 spa cer s, 3 fuel pellet, a nd the 15.25 cm vent pin. . . . . 129 Fig ure A -19 4 masses, 3 spa cer s, 3 fuel pellet, a nd the 15.25 cm vent pin. . . . . 129 Fig ure A -20 4 masses, 4 spa cer s, 4 fuel pellet, a nd the 15.25 cm vent pin. . . . . 130 Fig ure A -21 4 masses, 4 spa cer s, 5 fuel pellet, a nd the 15.25 cm vent pin. . . . . 130 Fig ure A -22 5 masses, 1 spa cer 2 fuel pe llet, and the 8.80 cm ve nt pin. . . . . . 131 Fig ure A -23 5 masses, 1 spa cer 1 fuel pe llet, and the 6.65 cm ve nt pin. . . . . . 131 Fig ure A -24 5 masses, 1 spa cer 2 fuel pe llet, and the 6.65 cm ve nt pin. . . . . . 132 Fig ure A -25 5 masses, 1 spa cer 3 fuel pe llet, and the 6.65 cm ve nt pin. . . . . . 132 Fig ure A -26 5 masses, 1 spa cer 1 fuel pe llet, and the 10.95 cm ve nt pin. . . . . . 133 Fig ure A -27 5 masses, 1 spa cer 1 fuel pe llet, and the 8.80 cm ve nt pin. . . . . . 133 Fig ure A -28 5 masses, 0 spa cer s, 1 fuel pellet, a nd the 10.95 cm vent pin. . . . . 134 Fig ure A -29 5 masses, 0 spa cer s, 1 fuel pellet, a nd the 10.95 cm vent pin. . . . . 134 Fig ure A -30 5 masses, 0 spa cer s, 1 fuel pellet, a nd the 10.95 cm vent pin. . . . . 135 Fig ure A -31 5 masses, 0 spa cer s, 1 fuel pellet, a nd the 10.95 cm vent pin. . . . . 135

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xi Fig ure A -32 5 masses, 0 spa cer s, 2 fuel pellets, a nd the 10.95 cm vent pin. . . . . 136 Fig ure A -33 5 masses, 1 spa cer 1 fuel pe llet, and the 10.95 cm ve nt pin. . . . . . 136 Fig ure A -34 5 masses, 1 spa cer 2 fuel pe llets, and the 10.95 cm ve nt pin. . . . . 137 Fig ure A -35 5 masses, 1 spa cer 3 fuel pe llets, and the 10.95 cm ve nt pin. . . . . 137 Fig ure A -36 5 masses, 2 spa cer s, 1 fuel pellet, a nd the 10.95 cm vent pin. . . . . 138 Fig ure A -37 5 masses, 2 spa cer s, 2 fuel pellets, a nd the 10.95 cm vent pin. . . . . 138 Fig ure A -38 5 masses, 1 spa cer 2 fuel pe llets, and the 10.95 cm ve nt pin. . . . . 139 Fig ure A -39 5 masses, 1 spa cer 2 fuel pe llets, and the 10.95 cm ve nt pin. . . . . 139 Fig ure A -40 5 masses, 4 spa cer s, 2 fuel pellets, a nd the 15.25 cm vent pin. . . . . 140 Fig ure A -41 5 masses, 3 spa cer s, 2 fuel pellets, a nd the 15.25 cm vent pin. . . . . 140 Fig ure A -42 5 masses, 2 spa cer s, 2 fuel pellets, a nd the 15.25 cm vent pin. . . . . 141 Fig ure A -43 5 masses, 1 spa cer 2 fuel pe llets, and the 15.25 cm ve nt pin. . . . . 141 Fig ure A -44 5 masses, 0 spa cer s, 2 fuel pellets, a nd the 15.25 cm vent pin. . . . . 142 Fig ure A -45 5 masses, 4 spa cer s, 3 fuel pellets, a nd the 15.25 cm vent pin. . . . . 142 Fig ure A -46 5 masses, 3 spa cer s, 3 fuel pellets, a nd the 15.25 cm vent pin. . . . . 143 Fig ure A -47 5 masses, 2 spa cer s, 3 fuel pellets, a nd the 15.25 cm vent pin. . . . . 143 Fig ure A -48 5 masses, 4 spa cer s, 4 fuel pellets, a nd the 15.25 cm vent pin. . . . . 144 Fig ure A -49 5 masses, 3 spa cer s, 4 fuel pellets, a nd the 15.25 cm vent pin. . . . . 144 Fig ure A -50 5 masses, 4 spa cer s, 5 fuel pellets, a nd the 15.25 cm vent pin. . . . . 145 Fig ure A -51 5 masses, 4 spa cer s, 1 fuel pellet, a nd the 15.25 cm vent pin. . . . . 145 Fig ure A -52 5 masses, 3 spa cer s, 1 fuel pellet, a nd the 15.25 cm vent pin. . . . . 146 Fig ure A -53 5 masses, 2 spa cer s, 1 fuel pellet, a nd the 15.25 cm vent pin. . . . . 146

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xii Fig ure A -54 5 masses, 2 spa cer s, 1 fuel pellet, a nd the 15.25 cm vent pin. . . . . 147 Fig ure A -55 5 masses, 1 spa cer s, 1 fuel pellet, a nd the 15.25 cm vent pin. . . . . 147 Fig ure A -56 5 masses, 0 spa cer s, 1 fuel pellet, a nd the 15.25 cm vent pin. . . . . 148 Fig ure A -57 6 masses, 4 spa cer s, 1 fuel pellet, a nd the 15.25 cm vent pin. . . . . 149 Fig ure A -58 6 masses, 3 spa cer s, 1 fuel pellet, a nd the 15.25 cm vent pin. . . . . 149 Fig ure A -59 6 masses, 2 spa cer s, 1 fuel pellet, a nd the 15.25 cm vent pin. . . . . 150 Fig ure A -60 6 masses, 4 spa cer s, 1 fuel pellet, a nd the 15.25 cm vent pin. . . . . 150 Fig ure A -61 6 masses, 3 spa cer s, 1 fuel pellet, a nd the 15.25 cm vent pin. . . . . 151 Fig ure A -62 7 masses, 1 spa cer 2 fuel pe llet, and the 10.95 cm ve nt pin. . . . . . 152 Fig ure A -63 7 masses, 1 spa cer 2 fuel pe llet, and the 8.80 cm ve nt pin. . . . . . 152 Fig ure A -64 7 masses, 1 spa cer 2 fuel pe llet, and the 6.65 cm ve nt pin. . . . . . 153 Fig ure A -65 7 masses, 1 spa cer 1 fuel pe llet, and the 10.95 cm ve nt pin. . . . . . 153 Fig ure A -66 7 masses, 1 spa cer 1 fuel pe llet, and the 8.80 cm ve nt pin. . . . . . 154 Fig ure A -67 7 masses, 1 spa cer 3 fuel pe llet, and the 8.80 cm ve nt pin. . . . . . 154 Fig ure A -68 7 masses, 1 spa cer 3 fuel pe llet, and the 6.65 cm ve nt pin. . . . . . 155 Fig ure A -69 7 masses, 1 spa cer 2 fuel pe llet, and the 6.65 cm ve nt pin. . . . . . 155 Fig ure A -70 7 masses, 1 spa cer 1 fuel pe llet, and the 8.80 cm ve nt pin. . . . . . 156 Fig ure A -71 7 masses, 1 spa cer 2 fuel pe llet, and the 6.65 cm ve nt pin. . . . . . 156 Fig ure A -72 9 masses, 1 spa cer 1 fuel pe llet, and the 10.95 cm ve nt pin. . . . . . 157 Fig ure A -73 9 masses, 1 spa cer 2 fuel pe llet, and the 10.95 cm ve nt pin. . . . . . 157 Fig ure A -74 9 masses, 1 spa cer 3 fuel pe llet, and the 10.95 cm ve nt pin. . . . . . 158 Fig ure A -75 9 masses, 1 spa cer 1 fuel pe llet, and the 8.80 cm ve nt pin. . . . . . 158

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xiii Fig ure A -76 9 masses, 1 spa cer 2 fuel pe llet, and the 8.80 cm ve nt pin. . . . . . 159 Fig ure A -77 9 masses, 1 spa cer 3 fuel pe llet, and the 8.80 cm ve nt pin. . . . . . 159 Fig ure A -78 9 masses, 1 spa cer 1 fuel pe llet, and the 6.65 cm ve nt pin. . . . . . 160 Fig ure A -79 9 masses, 1 spa cer 2 fuel pe llet, and the 6.65 cm ve nt pin. . . . . . 160 Fig ure A -80 9 masses, 1 spa cer 3 fuel pe llet, and the 6.65 cm ve nt pin. . . . . . 161 Fig ure A -81 9 masses, 1 spa cer 4 fuel pe llet, and the 6.65 cm ve nt pin. . . . . . 161 Fig ure A -82 11 masses, 1 spa cer 2 fuel pe llet, and the 8.80 cm ve nt pin. . . . . . 162 Fig ure A -83 11 masses, 1 spa cer 3 fuel pe llet, and the 8.80 cm ve nt pin. . . . . . 162 Fig ure A -84 11 masses, 1 spa cer 2 fuel pe llet, and the 6.65 cm ve nt pin. . . . . . 163 Fig ure A -85 11 masses, 1 spa cer 3 fuel pe llet, and the 6.65 cm ve nt pin. . . . . . 163 Fig ure A -86 11 masses, 1 spa cer 4 fuel pe llet, and the 6.65 cm ve nt pin. . . . . . 164 Fig ure A -87 11 masses, 1 spa cer 1 fuel pe llet, and the 10.95 cm ve nt pin. . . . . 164 Fig ure A -88 11 masses, 1 spa cer 2 fuel pe llet, and the 10.95 cm ve nt pin. . . . . 165 Fig ure A -89 11 masses, 1 spa cer 3 fuel pe llet, and the 10.95 cm ve nt pin. . . . . 165 Fig ure A -90 11 masses, 1 spa cer 2 fuel pe llet, and the 10.95 cm ve nt pin. . . . . 166 Fig ure A -91 11 masses, 1 spa cer 3 fuel pe llet, and the 10.95cm ve nt pin. . . . . 166 Fig ure A -92 11 masses, 1 spa cer 3 fuel pe llets, and the 10.95 cm ve nt pin. . . . . 167 Fig ure A -93 11 masses, 2 spa cer s, 3 fuel pellets, a nd the 10.95 cm vent pin. . . . 167 Fig ure A -94 11 masses, 2 spa cer s, 2 fuel pellets, a nd the 10.95 cm vent pin. . . . 168 Fig ure A -95 11 masses, 2 spa cer s, 1 fuel pellet, a nd the 10.95 cm vent pin. . . . . 168 Fig ure A -96 11 masses, 2 spa cer s, 4 fuel pellets, a nd the 10.95 cm vent pin. . . . 169 Fig ure A -97 11 masses, 3 spa cer s, 1 fuel pellet, a nd the 10.95 cm vent pin. . . . . 169

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xiv Fig ure A -98 11 masses, 3 spa cer s, 2 fuel pellets, a nd the 10.95 cm vent pin. . . . 170 Fig ure A -99 11 masses, 3 spa cer s, 3 fuel pellets, a nd the 10.95 cm vent pin. . . . 170 Fig ure A -100 11 masses, 3 spa cer s, 4 fuel pellets, a nd the 10.95 cm vent pin. . . . 171 Fig ure A -101 11 masses, 3 spa cer s, 5 fuel pellets, a nd the 10.95 cm vent pin. . . . 171 Fig ure A -102 11 masses, 4 spa cer s, 2 fuel pellets, a nd the 10.95 cm vent pin. . . . 172 Fig ure A -103 11 masses, 4 spa cer s, 1 fuel pellet, a nd the 10.95 cm vent pin. . . . 172 Fig ure A -104 11 masses, 4 spa cer s, 3 fuel pellets, a nd the 10.95 cm vent pin. . . . 173 Fig ure A -105 11 masses, 4 spa cer s, 4 fuel pellets, a nd the 10.95 cm vent pin. . . . 173 Fig ure A -106 11 masses, 4 spa cer s, 5 fuel pellets, a nd the 10.95 cm vent pin. . . . 174 Fig ure A -107 11 masses, 0 spa cer s, 1 fuel pellet, a nd the 10.95 cm vent pin. . . . 174 Fig ure A -108 11 masses, 1 spa cer 2 fuel pe llets, and the 10.95 cm ve nt pin. . . . 175 Fig ure A -109 11 masses, 0 spa cer s, 2 fuel pellets, a nd the 10.95 cm vent pin. . . . 175 Fig ure B -1 Taking bolts out of Frustum (left) and plac ing sta tic fra me (rig ht). . . . 186 Fig ure B -2 Placing load ce ll and jack ( left) a nd L VDT’s ( rig ht). . . . . . . . . 186 F i g u r e B 3 P e r f o r m i n g t h e s t a t i c t e s t ...................................... 187 F i g u r e B 4 R e m o v i n g t h e m a s s s t a c k ..................................... 187 Fig ure B -5 Removing the shocks (le ft) and the slide car riag es (r ight) . . . . . . 188 F i g u r e B 6 U n b o l t i n g t h e c a r r i a g e r a i l s .................................... 188 Fig ure B -7 Remove the top mass ( left) a nd the desire d mass stack (r ight) . . . . . 189 F i g u r e B 8 A t t a c h i n g t h e t o p m a s s ....................................... 189 Fig ure B -9 Re-a ttaching the ca rriag e slides (lef t) and locking the teeth ba ck ( r i g h t ) .................................................... 190

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xv F ig ur e B -1 0 B olt ing the c a tc h f ra me to t he F ru stu m. . . . . . . . . . . . . . 190 Fig ure B -11 Weig hing out the r equire d rifle powde r (0.5 g ). . . . . . . . . . . 191 Fig ure B -12 Placing the rifle pow der ( left) a nd the statnamic fue l (rig ht) into the p i s t o n .................................................... 191 Fig ure B -13 Tap the piston on side to pack rifle pow der. . . . . . . . . . . . 192 Fig ure B -14 Gre ase the vent pin and the piston. . . . . . . . . . . . . . . . 192 F ig ur e B -1 5 Se a t th e pis ton a nd low e r t he ma sse s. . . . . . . . . . . . . . . 193 F i g u r e C 1 S t a t n a m i c M i n i T e s t e r ........................................ 194

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x vi Labo r at or y St at nam ic Te st ing Michae l J Stokes AB STR AC T De sp ite a dv a nc e me nts in t he a na ly sis of sta tna mic loa d te sti ng da ta th e re e xists uncer tainty with underly ing pr ocedur al assumptions. Two such assumption are that the sy stem mass and soil-rela ted damping coef ficient re main constant throug hout the loading event. The se assumptions are the culprit of a berr ant pre dictions of the static ca pacity at small displacements whe n the over all displaceme nt is larg e. An e x ploration of the a ssu mpt ion s ma y va lid a te pr ior e xistin g te st r e su lts a s w e ll a s so lid if y the c ur re nt a na ly sis proce ss. Howeve r, an e x ploration could also re veal a n overe stimation or underestimation of po rt ion s o f t he pr e dic te d s ta tic loa d r e sp on se s. The testing prog ram outlined her ein consists of a twophase se quential ag enda devoted towa rd the pre para tion and familiarization of a ne w labora tory statnamic devic e. T h e f i rs t p h as e i n v o l v es t h e d ev el o p m en t o f u s er gu i d el i n es fo r a cc u ra t el y t ar get i n g a desired sta tnamic test, and the se cond incor porate s the g uidelines into a preliminary te sti ng re g ime sp e c if ic a lly ta rg e te d a t de te rm ini ng a su sp e c te d s tr a inde pe nd a nt s ta tna mic damping coef ficient. The steps taken in this thesis are intende d to launch future rese arc h e nd e a vo rs tow a rd ob ta ini ng a be tte r u nd e rs ta nd ing of the sta tna mic da mpi ng c oe ff ic ie nt.

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1 1.0 Introduction Statnamic load testing is rapidly becoming an ac cepta ble alter native to static load testing. Curr ent ana ly sis procedur es utiliz e some for m of the Unloading Point M ethod (Middendorp, 1992) to determine c the coe fficie nt of viscous damping from the fundame ntal equation of motion. Two assumptions made during the ana ly sis procedur e a re tha t m the sy stem mass, and c rema in constant throug hout the loading event. Ho we ve r, it i s p os sib le tha t th e c on tr ibu tin g so il m a ss s ur ro un din g the pil e va ri e s w ith tim e a s th e pil e dis pla c e s. Th e fo llo wi ng thr e e pr og re ssi ve sta g e s a re pr e su me d to e xist (F igur es 1-1 throug h 1-3): (1) throug hout the elastic ra ng e, the zone of influe nce inc rea ses radia lly outward f rom the pile prog ressively adding soil mass to t he ac cele rate d sy stem ma ss, (2 ) a t y ie ldi ng th e zon e of inf lue nc e re a c he s a ma ximum ma ss, a nd the so il adjac ent the pile re ache s a maxim um downwar d displaceme nt and shea r strain, a nd (3) a s y ielding c ontinues, the zone of influenc e shar ply diminis hes and the pile displaces re la tiv e to t he su rr ou nd ing so il m a ss. I f t his hy po the sis is t ru e th e n th e vo lum e of so il (mass) a lso varies a s the pile displaces, le aving doubt to loom over the assumption of a c on sta nt s y ste m ma ss ( F ig ur e 14) I f t he vo lum e of so il ( e ne rg y a bs or bin g ma te ri a l) is rela ted to the damping coef ficient, then doubt a lso looms over the assumption of a c on sta nt d a mpi ng c oe ff ic ie nt.

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2 On e me tho d o f i nv e sti g a tin g thi s h y po the sis is t o im ple me nt s ma ll s c a le labora tory testing to e x peditiously and ec onomically repr oduce the statnamic eve nt for further analy sis. This thesis ex plores the ope ration of a new labor atory statnamic devic e and the de velopment of ope rator ta bles for the desig n of any particula r load pulse. Chapter 2 r eviews the conce pt of statnamic and g ives a brie f history of its evolution; Cha pte r 3 dis c us se s th e la bo ra tor y e qu ipm e nt; Cha pte r 4 de sc ri be s th e te sti ng pr og ra m; Chapter 5 r eports the r esults of the prog ram; and Chapte r 6 pre sents a summary and c on c lus ion s. Fig ure 11 (1) Radia lly incre asing zone of influence Fig ure 12 (2) Ma x imum downward displace ment and shear strain.

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3 Fig ure 13 (3) The zone of influence sharply diminis hed as the pil e dis pla c e s r e la tiv e to t he so il. Fig ure 14 Presumed var iation of mass (M) with downwa rd displaceme nt (D).

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4 2.0 Literat ure Re view Sta tna mic loa d te sti ng is a re la tiv e ly ne w c on c e pt. Th e ide a wa s c on c e ive d in 19 87 by Pa tr ic k B e rm ing ha m, t he ow ne r o f B e rm ing ha mme r F ou nd a tio n E qu ipm e nt, during a conve rsation with Be ng t Fellenius. Mr. F ellenius had be en see king a n e qu ipm e nt m a nu fa c tur e r f or ne a rl y tw o y e a rs tha t w ou ld b e wi lli ng to b uil d a pil e impacting device His purpose be ing to make pile dy namic testing independe nt of the contra ctor. Actually other issues prompted the development of statnamic. At that time, the siz e of dr illed shafts wer e beg inning to excee d the re alistic capa biliti es of static loa d testing. D espite 25 y ear s of deve lopment, dy namic load testing was e x cluded f rom being a n o p ti o n b e c a u s e o f s k e p ti c is m a n d it s tw o ma in li mi ta ti o n s th e in a b il it y to mo b il iz e d ri l l ed s h af t s o r p i l es d ri v en t o re fu s al an d t h e d es t ru ct i v e c o n s eq u en ce s o f d ro p p i n g a larg e mass on a dr illed shaft. Spawned f rom these limitations and the demand f or a q u i ck er l es s ex p en s i v e t es t ca m e t h e q u es t fo r a n ew m et h o d o f l o ad t es t i n g. During the conve rsation, Mr. B erming ham aske d Mr. Fe llenius, “Why do y ou want to drop the w eig ht? Can’t y ou send it up in the air instead? After all, Newton state d that for e very action...” ( First I nterna tional Statnamic Seminar, 1995). Shortly there afte r, statnamic wa s born. I n less than a y ear the first prototy pe wa s fabr icated.

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5 2. 1 C onc e pt of St at nam ic Statnamic was c onceive d with Newton’s third law in mind, but i t monopoliz es on the se c on d la w, wh ic h s ta te s th a t “ the a c c e le ra tio n o f a n o bje c t is dir e c tly pr op or tio na l to the net for ce a cting on it and inversely proportional to its mass” (Serw ay 1992). I n a ty pical kentledg e test (F igur e 2-1) the larg e number of masses stac ked on top of the fo un da tio n r e ly up on the a c c e le ra tio n o f g ra vit y to p ro vid e the re a c tio n f or c e T his is a direc t way of apply ing the forc e, for the ac cele ration of g ravity rema ins constant while the amount of re action mass ca n be var ied. I n a statnamic loa d test, that same for ce, or rea ction mass weig ht, is achieve d by inversely proportioning the mass and a cce lera tion. To ob ta in a c c e le ra tio ns la rg e r t ha n w ha t g ra vit y pr ov ide s, a n e xtru de d s oli d p ro pe lla nt i s place d inside of a piston betwe en the top of the foundation and the bottom of the rea ction masses. When the fue l is ignited inside the conf ined volume of the piston, the g ases pr od uc e a n e no rm ou s p re ssu re a nd the ma sse s a re la un c he d u pw a rd s ( in a n a xial te st) with an ac cele ration on the orde r of twe nty times that of g ravity The for ce a pplied to the masses by the burning fuel is also applied in a n equal a nd opposite direction to the top of the re sis tin g fo un da tio n. Sin c e the a c c e le ra tio n is a mpl if ie d b y a ma g nit ud e of tw e nty it is only nece ssary to utili ze a re action mass of a bout five per cent the de sire ultimate load. 2.2 Device Com ponents The succ ess of the f irst statnamic prototy pe (44 kN maxi mum capac ity ) hastene d the produc tion of larg er de vices. The re a re c urre ntly at least 20 diff ere nt devices, a few of which a re listed in Table 2-1. Reg ardle ss of the size, all statnamic device s consist of thr e e c omp on e nts : a pis ton a sil e nc e r a nd re a c tio n ma sse s, a nd a c a tc hin g me c ha nis m.

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6 2.2.1 P iston The piston is usually the first piec e of e quipment placed w hen asse mbling the te sti ng a pp a ra tus (F ig ur e 22) A top the pis ton is a ve nte d li d w hic h c a n b e re mov e d to expose an internal c hamber containing a fue l basket. The f uel baske t serves a s the sto ra g e po int fo r t he sta tna mic fu e l ( F ig ur e 23) I nc or po ra te d in to t he ba se is a loa d c e ll siz ed in ac corda nce w ith the device ma x imum capabilities and a photovoltaic c ell used for displac ement mea surements. Perma nently mounted within the piston i s wiring for the loa d c e ll, ph oto vo lta ic c e ll, a nd the fu e l ig nit ion sy ste m. O nc e the pis ton is c ha rg e d w ith the desire d amount of fue l, the vented lid ca n be re place d, and a ve nt pin screwe d to the top of the lid (Fig ure 24). 2.2.2 Silencer and React ion Masses The primar y purpose of the silence r is to provide an e x pansive c ontainer f or the combustive rea ction that takes plac e within the piston. There are three components which Table 21 L ist of statnamic device s (Tra nsportation Resear ch B oard, 2003)

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7 comprise the silenc er: a cy linder, muffle r, and f lang e. The bottom ins ide portion of the silencer is the cy linder. The w alls of the cy linder ar e mac hined such that a near ly perf ect se a l is fo rm e d w he n th e sil e nc e r i s sl id o ve r t he pis ton A t th e top of the c y lin de r i s a vent hole that lea ds into the upper portion of the silenc er w here a muffle r is located. T he vent pin seals this hole when the silencer is lowered onto the piston. As g ases a re f ormed in the piston and flow throug h the vented lid into the cy linder, pre ssure builds until the silencer is lifted. Once the silencer trave ls a ce rtain distance the vent pin exits the vent ho le a nd e xha us t g a se s b e g in t o tr a ve l to the muf fl e r. Th e we ig ht o f t he sil e nc e r a lon e is insufficient to provide a rea ction mass, so a flang e is provided a t the bottom of the silencer to acc ommodate the stac king of additional masses (F igur es 2-5 a nd 2-6). Depe nding on the statnamic devic e, the a dditional masses are usually either do ug hn utsh a pe d o r r e c ta ng ula r w ith a ho le in t he c e nte r w hic h a llo ws the m to be sli d over the silencer They are structura lly -re inforce d steel ca nisters filled with concr ete or a ny fi e ld e xpe die nt m a te ri a l de ns e e no ug h to c on tr ibu te sig nif ic a nt w e ig ht ( i.e g ra ve l, soil, water) (F igur e 2-7) Empty canister s offe r the e ase of mobiliz ation, but time must be al l o t t ed at t h e j o b s i t e f o r f i l l i n g. 2 2 3 Ca tc h i n g Me ch a n i s ms After the test is initi ated, pr eventing the re turn of the a irborne ma sses is nece ssary for the pr otection of the piston and the se nsitive equipment within. There a re thre e catc hing sy stems used in curr ent device s: a g rave l catch, hy draulic c atch, a nd mecha nical catc h.

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8 The g rave l catch involves pla cing a stee l silo around the testing appar atus and filling the a nnular void betwe en the masse s and the silo with an uniformly -g rade d g rave l. Once the masses be g in their upwar d asce nt, the g rave l flows inward a round the piston and cushions the desc ent. The g rave l catch is a simple and reliable method used for larg er device s where it may be too difficult to hy draulica lly or mec hanica lly catc h an enor mous amount of mass. Howe ver, pe rfor ming a follow-up test is very time consuming, since the silo and g rave l must be removed be fore reloa ding the device The hy draulic c atch e ntails four ac tuators and a ccumulator s mounted in the corne rs of a catc hing f rame place d around the testing a ppara tus. Nitroge n g as within eac h a c c umu la tor pr e ssu ri zes hy dr a uli c fl uid a t th e be g inn ing of e a c h te st. Whe n th e te st i s initiated and the masses a scend, the pressurized fluid is forc ed into the ra ms which extend and cha se the masse s upward. O nce the masses re ach the apex of their asc ent, oneway valves pre vent the fluid inside the ra ms from esca ping, a nd the masses a re c apture d. After the test, the fluid ca n be ea sily draine d back into the a ccumulator s and the de vice reloa ded. Th e me c ha nic a l c a tc h a lso us e s a fr a me b ut m ult itoo the d r a ils a re a tta c he d to tw o o pp os ing sid e s. A s e ri e s o f r a tc he t te e th a re mou nte d to the sid e s o f t he ma sse s, so that when the ma sses asce nd, the teeth r ide in the ra ils and catc h the masses a t the peak of their asc ent (F igur e 2-8) Shock absorbe rs ar e integ rate d to cushion the ca tch and r educe the downwa rd impact on the te eth. Afte r the test, the tee th can be locked ba ck and the masses lower ed if a reloa d is desired.

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9 2. 3 I nt e r nal Bal lis ti c s o f Sta tn am ic The e ntire statnamic pr ocess is commonly likened to the powe r stroke of a four cy cle inter nal combustion eng ine, but can be more a ppropriate ly likened to the interior ballistics of a fire arm (the motion of a projec tile before it ex its the barre l). I n a moder n firea rm, ca rtridg es ar e used a s storing de vices for the essential c omponents of the firing proce ss: a primer, pr opellant, and pr ojectile (F igur e 2-9) A primer ma de of e x plosive barium and a ntimony compounds locate d in the rea r of the c artridg e is used to ig nite a propellant. When struck by a blunt metallic firing pin, the compounds inside the primer e xplod e a nd se nd a fl a sh thr ou g h a sma ll f la sh ho le in t he ba se of the c a rt ri dg e T he fl a sh ignites the propellant within the main cha mber of the car tridg e. As the pr opellant burns a nd pr od uc e s g a se s, pr e ssu re inc re a se s in the c ha mbe r u nti l it ov e rc ome s th e sta tic friction betwe en the pr ojectile and the bore of the bar rel. The projec tile acc eler ates down the leng th of the bar rel, incr easing the cha mber volume a s it displ ace s. The pea k g as pr e ssu re in t he c ha mbe r i s a tta ine d w he n th e pr oje c til e dis pla c e s a bo ut 2 .5 c m ( Jame s, 1997). The pr essure slightly decr ease s as the proje ctile trave ls the remaining leng th of the ba rr e l. O nc e the pr oje c til e e xits th e ba rr e l, t he g a se s a re re le a se d a nd pr e ssu re wi thi n the bar rel re turns to atmospheric. I n the spec ialized case of an automatic r ifle, a g as port exists near the e nd of the barr el that allows some of the g ases to be dive rted a nd utiliz ed in the re -cha mbering of a no the r c a rt ri dg e T ho ug h th e ve nti ng pr oc e ss i s me nti on e d, the op e ra tio n a ft e rw a rd s is of no re lative sig nificanc e in the compa rison to statnamic testing a nd will not be further discussed.

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10 The following example will use the pressure curve of a pa rticular 3006 rifle load (F igur e 2-10) to illus trate the enormous ra tio between the maxi mum propelling f orce and the projec tile weig ht. Wi th reg ards to statnamic te sting, this number ( F/ m ) i s r e fe rr e d to as the ma ss r ati o Note fr om the fig ure tha t the entire e vent transpire s in one milli second, and the maximum attained pressure is 350 MPa. The c omponents of a statna mic device are analog ous to the above me ntioned fi re a rm c omp on e nts (F ig ur e 29) I n a sta tna mic te st, the pis ton se rv e s th e sa me pu rp os e as the c artridg e; it contains the primer propellant, a nd the initial combustion chamber. The re action mass ac ts as the projec tile, while the cy linder alone acts a s the barr el. Be fore the test, the static we ight of the re action mass is felt as a preload on the foundation (F igur e 2-11, Z one 1). The statnamic eve nt is ini tiated elec trically by passing a dire ct cur rent throug h a primer located in the bottom of the f uel baske t stationed inside the piston. A flash is sent throug h a small opening in the fuel ba sket wher e the pr opellant

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11 lies. As the prope llant burns, g ases pr oduced inside the piston chamber e x pand and cre ate a larg e cha mber pre ssure. When the pre ssure e x cee ds the static weig ht of the rea ction mass, the masses a cce lera te upwar ds, increa sing the chambe r volume (Z one 2). Th ou g h g a se s a re sti ll b e ing pr od uc e d, the inc re a se in c ha mbe r v olu me pr od uc e s a fa ir ly linear de g rada tion of pressure past the point of maxim um pressure (Z one 3). A s discussed in the pre vious parag raph r eg arding the venting of g ases, the g ases in a statnamic test ar e vente d prior to piston-cy linder sepa ration. This is acc omplished when the vent pin sea l brea ks, allowing for dissipation of the pre ssure a nd resulting in a smooth unload curve ( Z one 4). The distance tra veled by the masses up to the point when the vent hole is exposed and exhaust g ases tra vel out of the c y linder is ref err ed to as the power stroke This distance a lso corre sponds to the vent distance or the leng th of the vent pin that is seated within the vent hole. Thoug h much similarity exis ts betwee n a fire arm a nd a statnamic de vice, two distinguishing c hara cter istics seg reg ate statna mic: (1) its relatively long loa d duration and (2) small mass ra tio. I n the illustration of the fire arm a bove, it was noted tha t the load duration lasted only one millisecond, and the ma ss ratio was 168000. The duration of the statnamic load pulse a nd mass ratio in Fig ure 211 are approximately 100 milli seconds (100 times that of a f irea rm) and 20 ( compar atively less than 0.02 per cent) Both the loa d duration and ma ss ratio help to deve lop the unique shape of the statnamic load pulse. This quasi-tr iang ular shape can be quantified by taking the ra tio of the statnamic impulse and the pr oduct of the loa d duration and ma x imum load (Fig ure 212). The r atio is refe rre d to as the shape factor (S F ) a nd fl uc tua te s w ith e a c h s ta tna mic

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12 device The c hara cter istics of statnamic, espe cially the load dura tion and shape f actor wi ll b e re vis ite d th ro ug ho ut t his c ha pte r a nd the sis 2. 4 Ev olu ti on o f Sta tn am ic Te st ing and A nal ys is Since the adve nt of the first prototy pe in 1988, more tha n 100 publications dealing wi th s ta tna mic te sti ng ha ve g a ine d g lob a l r e c og nit ion E le ve n p ub lic a tio ns pe rt ine nt t o thi s th e sis a re c on sid e re d in the e ns uin g se c tio ns 2.4.1 The Early Years F ro m th e fi rs t a pp lic a tio n in 19 89 to t he F ir st I nte rn a tio na l Sta tna mic Se min a r i n 1995, 25 paper s were published. The majority of these publica tions about the “innovative” load test dea lt with particular c ase studies. I nitially the common fe eling was that statnamic r esults were compar able to other conventional methods, na mely the static load test. B y the time the seminar w as held, howe ver, a few case studies reporte d re su lts tha t c ha lle ng e d th e c omp a ra ble sta tus of sta tna mic re su lts I t be c a me ob vio us to mos t us e rs tha t a dju stm e nts ne e de d to be ma de to t he re su lts Th e imp uls ive na tur e of the sta tna mic te st i ntr od uc e s r a te -d e pe nd e nt c omp on e nts to t he sta tic re sp on se of the sy ste m. T he e qu a tio n o f m oti on de sc ri bin g the sta tna mic e ve nt i s: Equation 2-1 statnamic wher e F is the applied for ce, kx is the desired e quivalent static re sponse (spring forc e), m is the mass of founda tion and soil contributing to inertial e ffe cts, a and v are the acc eler ation and veloc ity of the founda tion, and c is the coef ficient of visc ous damping All values re quired for solving the e quivalent static re sponse ar e either rec orded or can be

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13 e a sil y fo un d s a ve tw o, the sp ri ng c oe ff ic ie nt ( k ) a nd the da mpi ng c oe ff ic ie nt ( c ). One of the most significa nt publications that emerg ed nea r the e nd of this time period hera lded a n a na ly sis pr oc e du re us e fu l in de te rm ini ng the tw o u nk no wn s. The Unloading Point Method. The Unloa ding Point Method (UPM) (Middendor p, 1992) is an ana ly sis procedur e commonly used to deter mine the equivale nt static response of a p i l e f ro m s t at n am i c d at a. I t m ak es t wo cr i t i ca l as s u m p t i o n s re gar d i n g kx and c : th e sta tic capa city of the pile is constant throug hout the plunging zone and the coe fficie nt of da mpi ng is c on sta nt t hr ou g ho ut t he te st. With the se tw o a ssu mpt ion s in min d, it i s possible to determine the da mping c oeff icient, and thus the e quivalent static re sponse. Tw o p oin ts o n th e sta tna mic loa ddis pla c e me nt c ur ve a re of pa rt ic ula r i nte re st when de veloping the proc edure (F igur e 2-13) The fir st (1) is the point at which the maxi mum statnamic forc e is ac hieved. This point corr esponds to the point of y ield on a theore tical static cur ve (1' ). The se cond (2) is the point of max imum dis place ment, wher e the velocity of the founda tion and resulting damping forc e ( cv ) equa l zero. This point also corr esponds to the point of maxi mum displ ace ment on the theore tical static cur ve (2' ). Afte r the da mping f orce is eliminated from the e quation, the only rema ining un kn ow n is k Equation 2-2 The va lue of kx is determined a nd assumed consta nt from point (1) to (2). T his enables the damping coef ficient to be f ound within this rang e. Ty pically the ave rag e value of c is taken, but re viewing the over all trend may lead to a mor e appr opriate va lue (Tra nsportation Resear ch B oard, 2003) (F igur e 2-14)

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14 2.4.2 The Fir st International Statnam ic Sem inar Th e F ir st I nte rn a tio na l Sta tna mic Se min a r w a s h e ld i n V a nc ou ve r, B ri tis h Columbi a in 1995. Of the near 30 paper s published that y ear only 25 wer e pre sented a t the seminar. F ourtee n of the pa pers de alt with theoretica l and pra ctical a spects, while the rema ining 11 we re of particula r ca se studies. Only two of the publica tions are r eleva nt for this discussion. Factors Influencing the Statnamic Load Pulse. Th e py ro te c hn ic a l a sp e c t of sta tna mic testing a nd load pulse sculpting wer e addr essed f or the fir st tim e by Patrick B erming ham a nd J. Whit e (B e rm ing ha m, 1 99 5) T he a rt of sc ulp tin g a loa d p uls e is i mpo rt a nt, sin c e it is the are a under the load pulse c urve tha t determines the impulse de livered to the foundation. Also, controlling the loading event pr events stre ss wave pr opag ation and the formation of te nsion in a pile. Fue l quantity rea ction mass, and vent distanc e ar e the fac tors which dete rmine the mag nitude, duration, and sha pe of the statnamic load pulse. As sta te d e a rl ie r, the fu e l us e d in a sta tna mic te st i s a nit ro c e llu los e -b a se d, so lid pr op e lla nt; it i s n ot a n e xplos ive b ut r a the r a hig hly fl a mma ble so lid T he fu e l is extruded into a cy lindrical for m, simi lar to smokeless rifle powder containing 19 perf orations that offe r it a honey comb appe ara nce ( Fig ure 215). The a vera g e mass of eac h pellet is 4.17 g The shape of the fue l give s it the advantag e of a n incre asing surfa ce a re a thr ou g ho ut t he c omb us tio n p ro c e ss. B y pe rf or a tin g the fu e l pe lle ts t he bu rn ra te incre ases a nd the point of maxi mum pressure is shifted to a point where the silence r has moved awa y from the piston. I n this reg ards, statna mic fuel pe rfor ms simi lar to neutra l burning rifle powde rs (Scha efe r, 2002).

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15 I t is no t th e a mou nt o f f ue l, b ut r a the r t he ra tio of fu e l to ini tia l c ha mbe r v olu me that deter mines the g as pre ssure. I n reg ards to statnamic, this ra tio is refer red to a s the fue l de ns ity (r ). Howe ver, since the initial volume of most st atnamic de vices is fixed, the amount of fue l becomes the defining fac tor. Be rming ham re asoned tha t increa sing the amount of fue l increa ses the maximum forc e and de cre ases the loa d duration (F igur e 216). I t is acce pted that only 5% of the de sired maximum load is neede d when deter mining the we ight of rea ction mass to use in a test. This ensure s that excessive re a c tio n ma ss j ump he ig hts a re a vo ide d. I nc re a sin g the we ig ht o f t he re a c tio n ma ss w ill incre ase the maxi mum force and the load dur ation (F igur e 2-17) The ve nt distance e ssentially has little bearing on the maxim um force but incre ases the loa d duration (F igur e 2-18) Z one 3 (F igur e 2-11) is leng thened a s it takes longe r for the vent pin sea l to break a nd the g ases to vent. I t is not t he long er dur ation that is undesirable, but the a ssociated lar g er jump heig ht. As mentioned, the ar ea unde r the loa d p uls e de te rm ine s th e imp uls e de liv e re d to the fo un da tio n, a nd c on se qu e ntl y deter mines the ene rg y delivere d to the upwar d acc eler ating rea ction mass. The re sults of an excessive jump may prove c atastrophic if it surpasses the c apabilities of the c atching me c ha nis m. Influence of Stress W ave P henome na. Thoug h the usual distinction among the three c a te g or ie s o f l oa d te sti ng (s ta tic d y na mic a nd ra pid ) i s th e me tho d in wh ic h th e loa d is applied, it is more appr opriate f or the purpose s of this thesis to di stinguish them by the duration of their loading cy cles. How ever it is not simply the dura tion of the loading

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16 event that c lassifies these te st, but the duration rela tive to the natura l freque ncy of the foundation. I f the fr equenc y of the loading imparted to the founda tion is l arg er tha n the natura l freque ncy then it is possi ble to induce a series of tension and compre ssion waves. In c o n t r a s t i f t h e f r e q u e n c y o f t h e l o a d i n g i s m u c h s m a l l e r t h a n t h e n a t u r a l f r e q u e n c y, then a c ontinuous compression wave will be sent throug hout the foundation. w This idea ca n be quantifie d by what is known as the w ave numbe r (N ) (M idd e nd or p e t a l., 19 95 ). Th e e qu a tio n s te ms f ro m tr a dit ion a l w a ve me c ha nic s, bu t is ma nip ula te d f or the a pp lic a tio n to fo un da tio ns Equation 2-3 I n this application, c is t he str e ss w a ve ve loc ity c ha ra c te ri sti c to t he fo un da tio n ma te ri a l, T is the period or dur ation of the loading event, a nd L is the leng th of the founda tion. Wav e nu mbe rs fo r a sta tic loa d te st a re on the or de r o f 1 00 0, ra pid loa d te sts us ua lly fa ll betwee n 12 and 50, and dy namic load tests ca n produce wave numbers less than 6. The UPM is valid when wave numbers excee d 12, but a cor rec tion for stress wa ve phenome na mus t be a pp lie d w he n w a ve nu mbe rs a re le ss. 2.4.3 The Second In ter national Statnam ic Sem inar The Sec ond I nterna tional Statnamic Seminar was he ld in Toky o, J apan in Oc tober 1998. Key note lectur es g iven by Professor Poulos and Kusa kabe f ocused the mood of the seminar towa rd standar dization of statnamic testing a nd application throug hout the int e rn a tio na l a re na T he se min a r c on ta ine d a 43 pa pe r c on g lom e ra tio n o f v a ri ou s c a se

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17 studies, applications, interpre tations and model testings, a nd g lobal standardizations. The pa pe rs dis c us se d h e re in t y pif y the pr og re ss o f s ta tna mic up to 1 99 9 a nd e mph a size so me of the a sp e c ts o f s ta tna mic te sti ng pe rt ine nt t o th is t he sis Cas e Stu die s. I n a pape r pre sented by Mullins et al. (2000, an extensive rese arc h prog ram develope d throug h the support of state a nd fede ral a g encie s expl ored a nd ref ined exist ing statnamic ana ly sis procedur es. The most per tinent subject are a discussed in the pa per inv olv e s st a tna mic te sti ng on sh a llo w f ou nd a tio ns A n a na ly sis pr oc e du re s imi la r t o wh a t w ill be pr e se nte d la te r i n Ch a pte r 4 c omp a re s th e me a su re d s ta tna mic re sp on se to the tr ue sta tic re sp on se of a se ri e s o f p la te loa d te sts F ro m th e tw o c ur ve s, the sta tna mic damping coef ficient wa s calc ulated and f ound to significa ntly vary with displacement. Values c alculate d in the elastic re g ion of the static cur ve y ielded much hig her ma g nitudes than those ca lculated in the inela stic reg ion. Also, it was noted that the static der ived reloa d stiffness of a cy clic statnamic te st was hig her tha n the true static stiff ness. The discrepa ncy was a ttributed to soil densification. Un iv e rsi ty In v olv e me nt. Universities throug hout the world have contributed to the development of statnamic, and a re la rg ely responsible for its success. L isted below ar e universities that have either c ompleted or a re c urre ntly perf orming statnamic re lated rese arc h (Tra nsportation Resear ch B oard, 2002) United States Au bu rn Un iv e rsi ty Da n B ro wn a xial a nd la te ra l a na ly sis of dr ill e d s ha ft s Br igh am Y ou ng Un iv e rsi ty Ky le Rol lin s, la te ra l a na ly sis a nd pil e g ro up s

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18 J oh ns Ho pk ins Un iv e rsi ty Ra ja h A na nd a na ra ja h, c y c lic la te ra l a na ly sis St a tna mic ear thquake simulator T e x a s A &M J ea n L o u i s Br i au d co m p ar i s o n t es t i n g Un iv e rsi ty of M as sa c hu se tts ( Lowe ll) S a m u e l P a i k o w s k y, r a t e o f l o a d i n g i n c l a y University of South Florida Gra y Mullins, s eg mental unloading point method, model pile testing in fr ustum confining ve ssel Canada University of W estern Ontario M. Hesham El Na g g ar, a x ial analy sis using sig nal ma tc hin g la te ra l a na ly sis Mc Ma ste r U niv e rsi ty Robert Horva th and Dieter Stoll e, ra te of loading model pile in frustum confining vessel I ndonesia Pe tra Chr ist ian Un iv e rsi ty S. Prawono, axial and latera l testing J apan Tokyo Institute of Technology O. Ku sa ka be s ta nd a rd iza tio n a nd bu ild ing c od e s Ky us y u Ky or its u U niv e rsi ty Y. Mae da, axial analy sis methods, including wa ve a na ly sis Kan az awa Un iv e rsi ty T at s u n o ri M at s u m o t o an al y s i s m et h o d s an d fi el d t es t i n g Y am ag uc hi U niv e rsi ty T. As o a nd T. Ai da s ig na l ma tc hin g te c hn iqu e s Nippon Instit ute of Technology H. Ku bo ta a nd F K uw a ba ra lo a din g ra te Ky oto Un iv e rsi ty M. Kimura, model pile testing using a ir-pre ssure de vice Kore a Seoul Unive rsity M.M. Kim, ax ial testing, a naly sis methods

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19 Eng land Sheffield University Ad ri a n H y de r a te of loa din g in c la y mo de l pi le te sti ng in clay consolidation chambe r Au str a lia University of W estern Australia Ma rk Ra nd olp h, mod e l pi le te sti ng us ing so il anchor s as re action Proposed ASTM Standard. A proposed A STM St andar d for piles unde r ra pid axi al compre ssive load was introduc ed at the se minar for the re view and c ritique of the participa nts (J anes e t al., 1997). I t defines the te rms specific to rapid load testing and outlines the require ments of measur ing de vices a nd the sug g ested testing proce dure. Model Pile Testing. Until the advent of the Fr ustum Confini ng Vessel ( FCV) by Be rming hammer F oundation Equipment and McMa ster Univer sity in 1995, model pile testing w as almost exclusively confine d to a ce ntrifug e. Te sting wa s expensive and ver y difficult, for soil stresse s were repr oduced by machines in a rapidly rotating container Human intera ction during the proc ess was quite a quag mire, but the F CV posed a solution to t he pr ob le m. The F CV is a conica l, steel device (F igur e 2-19) that due to its ge ometric shape enable s users to re plicate in-situ soil stresses. I t is filled with sand and pressur ized using a hy draulica lly -inflated r ubber bla dder loc ated a t the bottom of the device (F igur e 2-20) The F CV can “ repr oduce stre ss levels within a portion of the sand spe cimen, known a s the control volume” (Sedra n et al., 2000). The stresses a long the cente rline of the c ontrol vo lum e mim ic fu llsc a le str e sse s a nd a re e sp e c ia lly us e fu l in te sti ng fr ic tio n p ile s.

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20 Sc a lin g fa c tor s to us e wi th t he F CV de pe nd e nti re ly on the de g re e to w hic h it is m pressurized. A model pile of leng th L can e ither be dr iven or c ast into the control volume under a ny rang e of a pplied hy draulic pr essure The simulated in-situ depth at the p toe of the pile de termines the leng th of the pile prototy pe, L F ro m th e se tw o q ua nti tie s, the sca ling f actor s are obtained. Ta ble 2-2 display s the particula r set of sc aling fac tors rele vant to the FCV. When dealing with the Fr ustum, there must be an unde rstanding of the applicability of sca le fa ctors and the ir role in validating the unique re sponse of the la bo ra tor y sta tna mic de vic e T ho ug h th e F ru stu m sc a le s in -s itu str e ss v ia lin e a r d e pth dimensions, material prope rties ca nnot be sca led, henc e soil damping and stress wa ve velocities ar e take n as a one -to-one r atio. There fore the ac tual model shaft leng th, not scale d leng th, should be used in the applica tion of Equation 2-1. Consequently the require d load dura tion should be very short when tar g eting a wa ve number within the statnamic ra ng e (10 to 50). Since the re quired load dur ation is very short, it is of no gr eat c o n c e r n w h e n l a b o r a t o r y s t a t n a m i c d u r a t i o n s f a l l s l i g h t l y b e l o w 1 0 0 m i l l i s e c o n d s In Ta ble 22 F CV sc a lin g fa c tor s.

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21 fa c t, t he du ra tio ns a re lon g e r t ha n w ha t is re qu ir e d. With thi s in min d, it u nd e rs ta nd a ble why the labora tory device mass ratios ar e re latively small when load dura tions reac h 100 milli seconds, a s shown in Ch. 5. A serie s of tests utiliz ing the FCV a nd a 50 kN modelscale statnamic devic e wa s pe rf or me d to de te rm ine the e ff e c ts o f p re loa din g on a pil e (K oji ma e t a l., 20 00 ). Sta tic loa d te sts we re pe rf or me d f ir st o n te n p ile s, the n o n n ine pil e s su bje c te d to a sta tna mic preloa d cy cle. The results of the study indicated that the initial static re sponse of the preloa ded piles wa s much stiffer than the piles not subjected to a preloa d. 2.4.4 Addition al Analysi s P roce dures The limitations set forth in the UPM as a re sult of assumed rig id body motion make a naly zation of long piles with wave numbers less than 12 a nd short piles that behave elastica lly difficult. I n both case s, the top and toe of the pile do not move downwar d in unity causing a phase lag I n long piles, stre ss wave phe nomena a re responsible for the lag ; in short piles, it is the elastic beha vior. The Modified Unloading Point Method. The Modified U nloading Point M ethod was develope d to addre ss the problem of e lastic beha vior commonly found among st short piles tipped in rock. I n most statnamic load tests, only the top of the pile is instrumented for de termining acc eler ation and displace ment. Wit h the MUP, acc eler ation is measure d at both the top and the toe. T he ave rag e ac cele ration is then used to per form re g ular UPM calcula tions. MUP calculations prove suc cessf ul in some cases, but lac ks the ability to addre ss the phase la g issue in longe r piles.

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22 The Segme ntal Unloading Point Method. An a ly sis pr oc e du re s u p to thi s p oin t f a ile d to re c og nize the fa c t th a t lo ng pil e s w ill no t de ve lop the ir ult ima te c a pa c ity sim ult a ne ou sly a t a ll p oin ts a lon g the ir le ng th. I ns te a d, on e se g me nt o f a pil e ma y re a c h u lti ma te c a pa c ity while another seg ment is only partially mobiliz ed. The Seg mental Unloading Point Method (SUP) was de veloped to comba t this st rain incompa tibili ty issue as we ll as the int ro du c tio n o f s tr e ss w a ve ph e no me na T he SUP e sse nti a lly dis c re tize s a pil e int o smaller seg ments, eac h acting as individual rig id bodies and thus meeting the cr iteria for the UPM (L ewis, 1999). This is ac complished by integ rating strain g ag es at va rious levels along the leng th of the pile and r ecor ding the individual seg ment response to the loading event. B y knowing the cr oss-sectional a rea of the pile a nd Young ’s Modulus of the mater ial, it is poss ible to develop loaddisplaceme nt curve s for e ach se g ment. The ultimate capa city of the pile is then dete rmined fr om the summation of the seg mental c a pa c iti e s a t e a c h p a rt ic ula r t ime ste p, a nd no t si mpl y the su mma tio n o f p e a k c a pa c iti e s. 2. 4. 5 So ftwar e De ve lop m e nt Statnamic load testing is rapidly g aining acc eptanc e throug hout the United States. Gover nment ag encie s and many private c ompanies such a s the Fe dera l Highw ay Administration, Florida De partment of T ranspor tation, Be rming hammer F oundation Eq uip me nt, a nd Ap pli e d F ou nd a tio n T e sti ng ha ve a lr e a dy inc or po ra te d s ta tna mic int o their load testing scheme s. Wi th the incre ased usa g e of the test method comes the de sire fo r s of tw a re c a pa ble of qu ic kly ma nip ula tin g la rg e da ta se ts a nd pe rf or min g te dio us UPM calc ulations. I n 1999, the Univer sity of South Florida a cce pted the cha lleng e.

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23 De vis e d a s p a rt of a Ma ste r’ s T he sis th e Sta tna mic An a ly sis Wor kb oo k ( SAW) is a “ma crodriven Excel sprea dsheet whic h utiliz es Visual B asic for Application (VB A) pr og ra mmi ng ” (Wi nte rs 2 00 2) I t c a n p e rf or m bo th U PM a nd MU P c a lc ula tio ns a nd is ve ry us e fu l f or a na ly zing sta tna mic da ta on sh a llo w a nd de e p, ri g id f ou nd a tio ns b ut i s unable to re g ress the stra in ga g e data nece ssary for the SUP. Th e Se g me nta l U nlo a din g Poi nt E nh a nc e d Re vis ion 4. 0 St a tna mic An a ly sis Workbook (SUPERS AW) is the latest statnamic re g ression softwa re. SUPERSAW pe rf or ms a se g me nta l a na ly sis thr ou g h th e us e of thr e e Exc e l w or kb oo ks o ne of wh ic h is SAW. I t acc omplishes this by org anizing strain da ta into its respective se g mental loc a tio n, e va lua tin g the fo rc e a nd dis pla c e me nt a t e a c h le ve l, p e rf or min g UPM c a l c u l a t i o n s f o r e a c h l e v e l t h e n e v a l u a t i n g t h e t o t a l s t a t i c p i l e c a p a c i t y. I n the thesis entitled “SUPERSAW Statnamic Analy sis Software,” Wint ers ( 2002) proposed that with the a dvent of SUPERSAW it may be “possible to eva luate the varia bles associa ted with the statnamic da mping c oeff icient.” His a pplication of SUPERS AW to several c ase studies re sulted in a corr elation betwe en SPT N values and unit damping va lues (F igur e 2-21) His corr elations wer e lar g ely based on a proposed va ri a tio n o f u nit da mpi ng va lue s a s a fu nc tio n o f s oil ty pe H ow e ve r, thi s th e sis is direc ted towar d providing a labor atory device /methodology for investig ating dis pla c e me ntde pe nd a nt d a mpi ng va lue s.

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24 Fig ure 21 Kentledg e static load te st (PMC, 2004). F ig ur e 22 1 6 M N p ist on wi th p ic kin g lid and stee l plate attac hed.

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25 Fig ure 24 16 MN vent pin. F ig ur e 23 1 6 M N f ue l ba sk e t.

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26 Fig ure 25 4 MN silencer (left) and 16 MN silence r with picking collar ( rig ht). Fig ure 26 Muffler of the 16 MN silenc er.

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27 F ig ur e 27 4 MN (l e ft ) a nd 16 MN (r ig ht) re a c tio n ma sse s. Fig ure 28 16 MN multi-toothed catching rails (lef t) and ra tchet tee th (rig ht).

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28 F ig ur e 29 Co mpa ri so n o f s ta tna mic to a c omm on fi re a rm

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29 Fig ure 210 Pressure c urve f or a 3006 rifle loade d with 52 gr ains of I MR 4064 and a 150 g rain bullet (F abrique Scientific, I nc., 2001). Fig ure 211 Ty pical statnamic loa d pulse.

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30 Fig ure 213 UPM tim e window f or c deter mination (Tra nsportation Resear ch B oard, 2003) Fig ure 212 Def inition of the shape fa ctor (SF ).

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31 Fig ure 214 Var iation in c betwee n times (1) and ( 2) (Tra nsportation Resear ch B oard, 2003) Fig ure 215 Statnamic fuel pe llets, partially consumed (left) and whole ( rig ht).

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32 Fig ure 216 Var y ing the amount of fue l with the rea ction mass and vent distance c onstant (B erming ham, 1995). Fig ure 217 Reac tion mass equal to 2.5%, 5%, 10% and 20% of expected te st l oa d w ith a c on sta nt a mou nt o f f ue l a nd ve nt d ist a nc e (B e rm ing ha m, 1995).

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33 Fig ure 219 Fr ustum Confini ng Vessel with static load te st frame Fig ure 218 Venting for diff ere nt vent distances with a c onstant amount of fuel a nd rea ction mass (B erming ham, 1995).

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34 Fig ure 220 Fr ustum pressurization scheme (F rede rick, 2001).

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35 Fig ure 221 Unit damping ve rsus SPT N values (Winters, 2002).

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36 3. 0 La bor at or y Equ ipm e nt To better e valuate the data r eg ression methods it is often nece ssary to conduct labora tory tests or computer mode ling to fur ther c onfidenc e. I n this particular the sis, a new labor atory statnamic devic e is eva luated to furthe r future rese arc h eff orts in a better understanding of the statnamic c oeff icient of viscous da mping. This cha pter introduce s the la bo ra tor y sta tna mic de vic e d isc us se s c e rt a in d e vic e mod if ic a tio ns ne c e ssa ry to withstand a robust testing reg ime, and addr esses the c urre nt state of the Unive rsity of South Florida owne d Fr ustum Confini ng Vessel ( FCV or F rustum). 3.1 Laboratory Statnam ic Devic e The Statnamic Mini Tester nicknamed Minime, incor porate s a mec hanica l catc hing me chanism and is ca pable of delivering a 178 kN load. I t was deve loped by Be rming hammer F oundation Equipment in March 2002 f or spec ific usag e with the Fr ustum and donated to the Unive rsity of South Florida ( Fig ure 31). Simil ar to the components of the la rg er de vices, Minime is comprised of a piston, sil ence r and r eac tion ma sse s, a nd c a tc hin g me c ha nis m. T ho ug h s imi la r i n c omp os iti on to t he la rg e r d e vic e s, Min ime is t he fi rs t a nd on ly de vic e of su c h s c a le th e re by ma kin g it q uit e un iqu e in i ts response to load altering para meters. Minime ar rived a t the university rela tively untested and with much unce rtainty conseque ntly no manufa cture r g uidelines exist The following sections re fer to the orig inal state of the de vice a s rec eived by Be rming hammer

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37 in April 2002. Refer to the Statnamic Tester Assembly draw ings throug hout the following sections (Appe ndix C). 3.1.1 P iston The Minime piston is 20 cm long and 5 c m in diameter a nd has an inter nal chambe r (32 c m ) which house s the initial combustion reaction (F igur e 3-2) The 3 statnamic fue l is not contained within a fuel ba sket but is placed dire ctly into the chambe r. As par t of the standar d opera ting pr ocedur e, a mode l airplane longrea ch g low plu g is u se d to ig nit e 0. 5 g of smo ke le ss r if le po we r ( H4 35 0) w hic h in tur n ig nit e s a maxi mum of five statnamic f uel pellets. The e x haust g ases pa ss throug h a vente d lid and int o th e c y lin de r w he re pr e ssu re bu ild s u nti l th e re a c tio n ma sse s li ft At op the ve nte d li d is a thr e a de d h ole wh ic h a c c omm od a te s a 15 .2 5 c m ve nt p in (F ig ur e 33) T wo po rt s a re ma c hin e d a nd thr e a de d in to t he ba se of the pis ton T he fi rs t port is intended for the g low plug, a nd the sec ond port exist s for a n optional pressure transduce r. Attac hed to the exterior of the base f lang e in Fig ure 34 is an ac cele rometer uti lize d in the da ta c oll e c tio n p ro c e ss. Four doug hnut-shaped spa cer s (Fig ure 32) that slide over the piston can be used to decr ease the usable stroke of the piston while simultaneously incre asing the initial chambe r volume. Eac h space r is 2.15 cm in thickness, re sulting in a stroke decr ease of 2.15 cm and a n initial volum e incr ease of 43.5 cm Utiliz ing a ll spacer s and the 15.25 3 c m ve nt p in d e c re a se s th e po we r s tr ok e to 6 .6 5 c m.

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38 3.1.2 Silencer and React ion Masses The bottom portion of the silence r asse mbly contains the c y linder; the top portion is the silencer or muffle r. De taching the muffler from the c y linder exposes the cy linder head a nd the vent hole. An ove r-pr essure plug is situated in the c y linder hea d to protect the device ag ainst excessive g as pre ssures. The bottom flang e of the silencer and the silencer end plate ( muffler cap) serve as re action mass re tainers ( Fig ure 35). There are eleve n steel-plate rea ction masses, ea ch we ighting approximately 720 N. With t he additional we ight of the silence r (a pproxi mately 820 N), the ma x imum re a c tio n ma ss w e ig ht c a n to ta l 8. 74 kN A se ri e s o f h ole s a re loc a te d in e a c h ma ss t o fa c ili ta te the ins e rt ion of a n a lig nme nt r od a nd the ro uti ng of the c a tc h to oth re le a se cable s (Fig ure 36). The bottom two masses a re ma chined to interna lly house the mecha nical ca tching teeth; the top mass is machined to support the r eac tion mass guides. Be cause of this, it is important to note the particula r orde r in which the ma sses are stacke d. 3. 1. 3 C at c hing M e c hani sm As previously mentioned, the devic e is equipped w ith a mecha nical ca tching mecha nism. Teeth locate d within the bottom t wo masses ra chet a long the leng th of two ra ils mou nte d o n e ith e r s ide of the c a tc hin g fr a me F ou r s tif f s pr ing s w e re int e g ra te d in to the low e r m a sse s to c us hio n th e imp a c t on the c a tc h te e th. Af te r t e sti ng th e c a tc h to oth re le a se c a ble s c a n b e pu lle d f ro m a bo ve to u nlo c k th e te e th a nd low e r t he ma sse s. The ba se of the c atching fra me is desig ned with a pa rticular bolt patter n that fac ilitates the mating of the device to the top of the F rustum. Attaching the device

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39 require s removing the top flang e of the Fr ustum, thereby assumably relieving stresses near the top and cha ng ing the soil matrix within. This, along with other fac tors, prompted a n in e vit a ble mov e me nt t ow a rd de vic e mod if ic a tio ns 3. 2 M inim e M odi fic at ion s Throug hout the course of many tests, a larg e number of modifications we re ma de to the statnamic devic e out of both conve nience and nec essity Thoug h only a fe w ar e curr ently implemented, all of the de vice modifica tions are pr esente d here in. 3 2 1 I n te g ra te d S ta ti c L o a d T es t Fr a me I n order to expediti ously perf orm a ser ies of static/statnamic tests, a r eac tion beam was c onstructed to mount betwee n the leg s of the statnamic c atching fra me (F igur es 3-7 and 3-8) This addition allowed for a rapidly intercha ng eable testing c onfig uration, since the sta tna mic de vic e did no t ha ve to b e re mov e d f or pla c e me nt o f a n in de pe nd e nt s ta tic fra me. Since the r eac tion beam only spanned a short distance, a rela tively small steel Hpile section prove d adequa te to match the 178 kN c apac ity of the statnamic de vice. 3.2.2 Catc hin g F ram e Bolt Holes As previously mentioned, it is necessa ry to remove the top flang e of the Fr ustum wh e n a tta c hin g the sta tna mic de vic e b e c a us e the mou nti ng bo lts a re no t lo ng e no ug h to re a c h th ro ug h b oth the c a tc hin g fr a me ba se a nd the fl a ng e H ow e ve r, do ing so a ssu ma bly relieve s all of the stresse s in the upper c ontrol volume of the F rustum. To preve nt the re mov a l of the fl a ng e tw o o pti on s w e re c on sid e re d: o bta in e ig ht l on g e r b olt s o r o bta in four long er bolts and use ever y other e x isting bolt as alig nment dowels (F igur e 3-9)

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40 The sec ond option, though it require d more wor k, seeme d more c onducive to an eff icient mounting pr ocedur e. I mplementing the option meant that ever y other e x isting bolt would not be removed, but the he ad utiliz ed as a dowel pin for the alig nment of the ca t ch i n g fr am e b as e. T h e h o l es co rr es p o n d i n g t o t h e b o l t h ea d s we re re s i z ed u s i n g a ma g ne tic dr ill a nd a la rg e dr ill bit (F ig ur e 310 ). On c e po sit ion e d, the c a tc hin g fr a me base c ould be sec ured w ith four long er bolts (F igur e 3-11) 3. 2. 3 Li ft P ins For the purpose of mounting atop the F rustum, the orig inal device made no provisions for simultaneously lifting the r eac tion masses and the c atching fra me. The mounting proc edure involved secur ing the fra me to the Fr ustum first, then lowering the masses throug h the fra me. To eliminate the twostep proce ss, lift pins were built into the leg s of the fr ame ( Fig ure 312). This allowed both the f rame and masses to be lifted and secur ed in one step. 3. 2. 4 R e ac ti on M as s P ic k Eye s a nd A lig nm e nt Do wel s Th e a bil ity to c ha ng e ma ss c on fi g ur a tio ns is a n im po rt a nt a sp e c t of loa d te st desig n. Removing ma sses requir ed that the a lignment r ods be driven out of the masses. T h i s p ro v ed d i ff i cu l t wi t h i n cr ea s i n g u s age d u e t o n ar ro w t o l er an ce s an d t h e l ar ge amount of fr iction developed be tween the rods and the ma sses. Even whe n the rods we re remove d, the weig ht of the masses made them cumber some to manually lift and place aside. The a lignment r ods were cut into smaller dowel r ods, two of which we re w elded into the pre-e x isting holes of e ach ma ss. Placement of the dowel rods a llows the masses

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41 to stack and r emain alig ned throug hout their flig ht. Pick ey es we lded to opposing sides ease the proc ess of sepa rating the masses a nd invite the use of a n overhe ad lifting sy stem (F igur e 3-13) A number of masses ca n be handle d at one time by attaching a cha in to the pick ey es of the bottommost mass to be removed. 3.2.5 Catc h Sys tem During a routine disasse mbly and inspec tion of the device it was noted that minor str e ss f ra c tur e s h a d b e g un fo rm ing a lon g the imp a c t su rf a c e of the c a tc hin g te e th. Sho rt ly there afte r, at lea st one tooth would almost reliably become wedg ed in the down, or locked, position during a test. These behavior s posed a sig nificant thre at, not only to the opera tion of the ca tching sy stem, but to the data ac quisiti on device s and piston located benea th the masses. An e x tensive re desig n of the c atching sy stem was initiated, making this the larg est modification to the statnamic de vice. At first, an a pproac h entailing the pursuit of re place ment teeth fr om B e r m i n g h a m m e r s e e m e d s u f f i c i e n t b u t e f f o r t s w e r e r e d i r e c t e d a f t e r t h e t e e t h a r r i v e d It was de cided that r eplac ing the teeth would only solve the stress fr actur e proble m, not the “sticking ” proble m. Another, more drastic, a pproac h was c onsidered; the te eth must be reloc ated into a f org iving a tmosphere whe re the collection of g rea se and dirt would not be c ome a hin dr a nc e A n e xter na l me c ha nic a l c a tc h s y ste m, s imi la r t o w ha t is uti lize d in the 16 MN statnamic de vice, e nvisioned the use of shoc k absorbe rs and both sets of catc hing te eth. Two indepe ndently sliding ca rriag es, ea ch conta ining a n upper a nd lower catc h tooth, became the ce ntral theme a round which the sy stem would be deve loped.

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42 The sliding c arr iag es ar e construc ted from 1/4" plate cut to a r ecta ng ular shape with the leng th being equal to the he ight of the full rea ction mass stack. Two r ecta ng ular ho le s c ut a t th e top a nd bo tto m of e a c h p la te a re wi nd ow s w he re the c a tc h te e th r e st (F igur e 3-14) Ang le sec tions welded to the outside edg es of the pla tes form g rooves wher e the c arr iag e bra ckets slide (F igur e 3-15) The c arr iag e bra ckets a re f itted such that they can be bolted to the top and bottom two masses, thus requiring a minimum of three masses to be include d for a ny test (Fig ure 316). Calculated spa cing of the uppe r and lowe r ca tching teeth dec rea ses the drop he ight nece ssary to catch the device This improvement theore tically lessens the impac t on the teeth by half, but mea ns that only the top or bottom set of teeth c an ar rest the f alling ma sse s. Ea c h to oth piv ots a bo ut a pin a nd re tur ns to i ts o ri g ina l ho ri zon ta l lo c a tio n v ia two spring s attache d to the back ( Fig ures 317 and 3-18) Guides we lded to the fa ce of the ca rriag es ensur es that the re action masses r emain ce ntere d throug hout the test (Fig ure 3-19). Four spring integ rate d shock absor bers a lso help to reduce the impact on the tee th. On e a c h s ho c k a bs or be r, tw o s tif f s pr ing s ( k = 28 6 k N/ m) a re sta c ke d in se ri e s a s to double the displace ment at any g iven compre ssive forc e (F igur e 3-20) I ncre asing the rebound displac ement in turn incre ases the tr avel of the shock a bsorber allowing for more e nerg y to be dissipated. The shoc k absorbe rs ar e the c onnecting link between the re a c tio n ma sse s a nd the c a rr ia g e pla te s. I ns uf fi c ie nt s pa c ing be tw e e n th e ma sse s a nd the c a tc hin g fr a me le g s le d to altera tions in t he fr ame. To a ccommodate the sliding c arr iag es, the leg spacing was

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43 incre ased. This de mand for spa cing also resulted in a require ment to ext end both sides of the base (F igur es 3-21 a nd 3-22). Onc e alter ed, the c atching fra me re ndere d both the integ rate d static fra me and the lift pins useless. Thoug h the nec essar y modifications re ma in o n th e de vic e f utu re a lte ra tio ns c ou ld i nc lud e the re -i mpl e me nta tio n o f t he se convenie nce items. F igur es 3-23 a nd 3-24 show the c ompleted ca tching mecha nism as mounted. 3.3 F rustum Conf inin g Vessel I n 1999, Be rming hammer F oundation donated a Fr ustum to t he Univer sity of South Florida. As pre viously mentioned, the F rustum is a conica l device ma de of thick steel plate tha t due to its ge ometric shape enable s users to re plicate in-situ soil stresses. Th e so il w ith in i s p re ssu ri zed via a hy dr a uli c a lly inf la te d r ub be r b la dd e r i n o rd e r t o mimic overburde n stresses a t a par ticular de pth (Fig ure325). Since a rrival, two r esea rch projec ts have incor porate d the Fr ustum for the purpose of drilled shaf t capa city and con st ruct io n i mp rov eme nt s. Frus tu m p repa rat io n t act ics are ad dres sed in App end ix B. 3.3.1 P ost G rout of Drilled Sh afts A s tud y c on du c te d b y F re de ri c k ( 20 01 ) e va lua te d ti p g ro uti ng dr ill e d s ha ft s a s a me a ns of imp ro vin g the tip c on tr ibu tio n to ov e ra ll s ha ft c a pa c ity A se ri e s o f 2 6 s ta tic load tests wer e per formed on dr illed shafts ca st within t he F rustum to quantify the capa city improvements. Results from this study show a strong rela tionship between shaf t c a pa c ity imp ro ve me nt a nd ma ximum su sta ine d g ro ut p re ssu re de liv e re d to the tip w ith overa ll capac ities increa sing a s much as 559%. F rede rick a nnounced tha t the Fr ustum “ pr ov e d to be a su ita ble e nv ir on me nt f or te sti ng mod e l sc a le dr ill e d s ha ft s. ” Al so

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44 me nti on e d w a s th e fa br ic a tio n o f s pe c ia lize d c on str uc tio n e qu ipm e nt t ha t w a s u se d in la te r r e se a rc h e ff or ts, to i nc lud e thi s th e sis 3.3.2 Inf luence of Water Table on Drilled Sh aft Construction As pa rt of a F lor ida De pa rt me nt o f T ra ns po rt a tio n f un de d r e se a rc h p ro je c t, G a rb in (2003) c onstructed more than 50 model sca le drilled shaf ts within t he F rustum in an eff ort to reproduc e and ide ntify construction tec hniques responsible f or var ious anomalies found within drilled shafts. I nitial effor ts cong reg ated a round the e ffe cts of the wa ter table but soon expanded into fac tors such as c oncre te slump loss and casing extraction ra te St a tic loa d te sts we re pe rf or me d o n e a c h s ha ft to d e te rm ine the e ff e c ts o f t he se fac tors on total capa city A pre liminary investiga tion of the potential of an inside/outside concr ete he ad diffe rential to produc e anoma lies was initiated. Curre nt resea rch a t the University of South Florida is expounding upon that idea as we ll as investiga ting the a no ma ly c a us ing po te nti a l of dr ill ing slu rr ie s w ith hig h s a nd c on te nts

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45 F ig ur e 32 M ini me pis ton a nd sp a c e rs Fig ure 31 Statnamic Mini Tester.

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46 Fig ure 33 Vented lid and ve nt pin. Fig ure 34 Acc eler ometer a nd pressure transduce r.

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47 Fig ure 37 Drilling hole s for the integ rate d static fra me. F ig ur e 35 Si le nc e r a nd re a c tio n ma sse s. F ig ur e 36 Ca tc h to oth re le a se c a ble s.

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48 Fig ure 38 I nteg rate d static fra me. Fig ure 39 Bolt patter n of orig inal catc hing fra me base

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49 Fig ure 312 L ift pins retrac ted (lef t) and e x tended throug h the re action mass g uides (rig ht). F ig ur e 311 Mo dif ie d c a tc hin g fr a me ba se mounted to the FCV. F ig ur e 310 En la rg ing ho le s f or bo lt h e a ds

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50 F ig ur e 313 Wel din g pic k e y e s a nd do we l pi ns to e a c h r e a c tio n ma ss. Fig ure 314 Carria g e plate w ith ratche t too th w ind ow s.

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51 Fig ure 316 Carria g e bra cket a fter c onstruction (left) and mounted to the top and bottom two masses (rig ht). F ig ur e 315 Ca rr ia g e pla te wi th c a rr ia g e br a c ke t.

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52 F ig ur e 317 F ro nt ( le ft ) a nd ba c ks ide (r ig ht) of ra tc he t to oth wi th r e c oil sp ri ng s. Fi gu re 3 -1 8 P ar t i al l y fi n i s h ed ca rr i age a sse mbl ie s.

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53 F ig ur e 320 Spr ing int e g ra te d s ho c k a bs or be rs du ri ng (l e ft ) a nd a ft e r ( ri g ht) modification. Fig ure 321 Additional plate welde d to the base. F ig ur e 319 Pla c e me nt o f c a rr ia g e g uid e s.

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54 F ig ur e 322 Re a tta c hin g the fr a me le g s. Fig ure 323 Modified mecha nical ca tch with a seve n-mass conf igur ation.

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55 F ig ur e 324 Mo dif ie d me c ha nic a l c a tc h w ith a fu llmass config uration.

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56 4.0 Test P rogram To beg in the quest for a better unde rstanding of the statnamic da mping c oeff icient throug h the use of la boratory equipment, a testing prog ram wa s instit uted with a twophase, se quential ag enda. T he initial focus of the prog ram c oncentr ated on study ing the response of Minime to load test altering varia bles and de veloping calibra tion guidelines for f uture ope rator usa g e. Onc e cr eate d, these g uidelines would be utiliz ed in the development of the sec ond phase of the prog ram, a preliminary labora tory pursuit of the da mpi ng c oe ff ic ie nt u sin g a n a lte rn a tin g se ri e s o f l oa d te sts wi thi n th e F ru stu m. T his chapte r desc ribes both phase s of the testing prog ram a nd discusses the instrumentation us e d th ro ug ho ut t he pr og ra m. 4.1 Instrum entation I n order to capture the ra pid statnamic loading event, it was ne cessa ry to positi on va ri ou s tr a ns du c e rs a mon g st t he dif fe re nt s ta tna mic c omp on e nts a nd re c or d th e ou tpu ts using a high spe ed data acquisition computer. B eca use of its hig hly flexibl e natur e and a bil ity to a c c e pt m ult ipl e inp ut c ha nn e ls, the ME GA DA C w a s c ho se n a s th e da ta acquisition computer f or the testing prog ram (O ptim Electronics; Gar bin, 1999). I t was pr og ra mme d to sc a n a t a fr e qu e nc y of 50 00 Hz; a pp ro xima te ly 50 0 d a ta po int s w ou ld define the ty pical 100 millisecond loading event. This fr equenc y is commonly used for re c or din g sta tna mic te sts a nd pr ov e s su ff ic ie nt i n o bta ini ng e no ug h d a ta po int s to

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57 minimi ze error s associate d with various data r eg ression methods. A maximum of four ty pes of e lectric al transduc ers pr ovided input to the MEGADAC by direc tly measuring loa d, pr e ssu re a c c e le ra tio n, a nd dis pla c e me nt. I n order to measure the load produc ed by the statnamic de vice, a 10 ton (89 kN) column-ty pe load c ell (Toky o/Sokki KC -10A) w as ce ntere d betwee n the piston and fo un da tio n ( F ig ur e 41) T he loa d c e ll i s n ot i nte g ra te d in to t he ba se of the pis ton a s in the larg er de vices, so prope r alig nment befor e ea ch test bec ame c rucia l in the avoidance of ec centr ic loading To provide r edundanc y and validation of the load ce ll reading s, a 10 ksi (69 MPa) pre ssure tra nsducer (Da ta I nstruments AB H P) was introduce d into the side of the pis ton du ri ng the la te r p a rt of the te sti ng pr og ra m ( F ig ur e 34) K no wi ng the c ro sssectional a rea of the piston/cy linder and pe rfor ming simple ca lculations aff orded a n indirect c omparison of the a pplied load mag nitude. The ne ed to deter mine rapid displace ments ushere d the use of a capa citance -ty pe acc eler ometer ( PCB 3701D1FA 50G). Whether it wa s the downwa rd motion of the foundation or the upw ard motion of the r eac tion masses, the ac cele rometer proved convenie nt in its mounting and a ccur ate in its measure ments. The ac cele rometer was not lim ite d to a sp e c if ie d r a ng e of tr a ve l li ke dis pla c e me nt t ra ns du c e rs b ut i t r e qu ir e d th e us e of numeric integ ration methods to transfor m the raw acc eler ation data into displace ments. During the ca libration phase of the prog ram, the a cce leromete r wa s used to rec ord the flig ht of the re action masses; during the load testing phase, it wa s used to measure fo un da tio n d isp la c e me nt.

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58 4. 2 C ali br at ion Te st ing F a mil ia ri zat ion of Min ime a nd its re sp on se to l oa d a lte ri ng pa ra me te rs re su lte d in the per formanc e of more than 100 ca libration tests. The mass conf igur ation, initial volume, vent pin leng th, and fue l quantity wer e individually adjusted so as to dete rmine the outcome on the ma g nitude, duration, and ove rall shape of the load pulse. T houg h the rea ction mass jump height ha s no eff ect on the loa d pulse, it defines a maxi mum and min imu m sa fe bo un da ry to w hic h th e te st c a n b e pe rf or me d, the re by wa rr a nti ng its attention. To deve lop the larg est load and w orst case jump height, the sta tnamic device was attache d to a larg e conc rete base tha t simul ated a rig id foundation (F igur e 4-2) Once mounted to the base, a series of statnamic tests wer e conduc ted by altering only one para meter a t a time to determine the eff ect on the loa d pulse (re fer to Appendix B for calibra tion test procedur es). The jump height wa s phy sically measure d afte r ea ch test by taking the diffe renc e in the fina l and initial reac tion mass posit ions. The MEGADA C initially rec orded the compre ssive load experienc ed by the load ce ll but later included the chambe r pre ssure a nd rea ction mass acc eler ation. 4. 2. 1 Te st M at r ix B e c a us e of the nu me ro us va ri a ble s c a pa ble of be ing a lte re d in a pa rt ic ula r t e st, it was ne cessa ry to establish a test matrix, or methodology for testing that would ensure a sy stematic eva luation. Phy sical limitations of the device c atching fra me dictated to wha t extent a series c ould be per formed by providing a maximum and minimum jum p heig ht. The maximum jump height wa s depende nt on the heig ht of the last teeth on the c atch

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59 rails, while the minimum was depe ndent on the leng th to pist on/cy linder sepa ration. The eff ect e ach va riable ha s on the jump heig ht and the cor responding limit ations are discussed later The test matrix can be se en in Fig ures 43 and 4-4. 4.2.2 Mass Confi guration Al te ri ng the ma ss c on fi g ur a tio n h a s n o e ff e c t on the oth e r d e vic e c omp on e nts only the founda tion preload (T able 41), so diffe ring config urations wer e chose n as the first delinea tion in the test matrix A par ticular mass c onfig uration re mained consta nt while all other va riables we re a ltered. B ey ond this, the init ial volume, vent pin, then fue l wer e alter ed (F igur e 4-3) This decision was lar g ely based on the eff ort and time re quired to chang e mass conf igur ations. Orig inally it required a t least two people to saf ely lift eac h 68 kg mass when c hang ing c onfig urations. On ave rag e, it would take ne arly an hour to e ith e r r e mov e or pla c e ma sse s b e tw e e n e a c h te st s e ri e s. Th e tim e a s w e ll a s e ff or t, decr ease d three fold once picking ey es and a lignment dowe ls were welded to e ach ma ss. Ta ble 41 F ou nd a tio n p re loa ds

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60 Mu lti ple ma sse s c ou ld b e lif te d w ith the a id o f a n o ve rh e a d li ft ing sy ste m a nd e a sil y po si ti on ed. Th e pro cedu re fo r cha ngin g mas s co nfi gurat io ns is lo cat ed i n Ap pen di x B. 4 2 3 I n i ti a l Vo l u me After the mass conf igur ation was e stablished, tests were conducte d within the rang e of piston spac ers. The piston can be f itted with any combination of four to zero space rs, depe nding on the desired initial volume and powe r stroke ( d ). The spa cer s essentially preve nt the rea ction masses fr om fully seating on the piston. Not only does the initial volume of the combustion chamber incre ase w ith each a dditional spacer but the stroke c hang es (Ta ble 4-2 a nd Fig ure 45). Also, adding space rs to the piston inc re a se s th e ini tia l st a rt ing po sit ion of the ma sse s, the re by de c re a sin g the a va ila ble maxi mum jump height and the minimum require d jump height. I nitial tests varied spac er c ombinations, but compil ing r esults led to a pre sumption tha t de vic e pe rf or ma nc e wa s o pti ma l w ith the a dd iti on of on ly on e sp a c e r. An e la bo ra te Table 42 Effe ct of spac ers on the initial volume and powe r stroke ( d ).

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61 d i s c u s s i o n o f t h e s e r e s u l t s a r e i n c l u d e d i n C h a p t e r 5 b u t t h e l o a d p u l s e g e n e r a t e d b y a one spac er te st y ielded a c urve more repr esenta tive of a ty pical statnamic e vent. Afte r discounting the other spac er c ombinations, the test matrix quickly narr owed to a mor e manag eable siz e. 4.2.4 Vent Distance Orig inally the device came equipped with one 15.25 c m vent pin, so only the ini tia l vo lum e a nd fu e l w e re a lte re d f or e a c h ma ss c on fi g ur a tio n. Ho we ve r, a mid st testing of the third mass config uration, the orig inal vent pin was da mag ed (F igur e 4-6) This unfortunate mishap a ctually aff orded the opportunity to develop a host of thr ee re pla c e me nt v e nt p ins e a c h o f d if fe ri ng le ng ths Re su lts of the da ta c oll e c te d u p to thi s point led to the presumption that the orig inal vent pin was too long As a re sult, shorter vent pins of 10.95 cm, 8.80 cm, a nd 6.65 cm wer e construc ted (F igur e 4-7) Note that the vent pins are cut in incre ments such that they corr espond to the thickness of the space rs (2.15 cm). D oing so a llows for the interc hang ing of vent pins with the addition of space rs to maintain a constant powe r stroke. O nce the 15.25 cm was de stroy ed and r eplac ed, the te sti ng ma tr ix ha d to be re sta rt e d in or de r t o a c qu ir e da ta fo r t he dif fe ri ng ve nt p in le ng ths T he ne w s e ri e s o f t e sts be g a n w ith the min imu m c on fi g ur a tio n o f t hr e e ma sse s, the n te ste d e ve ry od d c on fi g ur a tio n u p to the ma ximum of e le ve n ma sse s. 4.2.5 F uel Ranges Th e la st a nd e a sie st v a ri a ble to a lte r i s th e fu e l qu a nti ty A s p re vio us ly mentioned, the piston can hold up to a ma x imum of five statnamic fue l pellets. I ncre asing the number of pellets incre ases the f uel density wher e the f uel density is taken

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62 as the ra tio of statnamic fue l volume to the total chamber volume. During the test, the volume occupie d by the pellet is reg ained a s the pellet is consumed, ther efor e it is not excluded from the f uel density calc ulations due to the complexit y of the numer ous varia bles eff ecting the combustion proce ss. Table 4-3 show s the rela tionship between the a mou nt o f s ta tna mic fu e l, i nit ia l vo lum e a nd the fu e l de ns ity (f ue l vo lum e /in iti a l vo lum e x 100%). The number of pe llets was incre ased in e ach se ries of te sts until either the maxi mum jump height obtained, or the oper ator fe lt it unwis e to continue that pa rticular s er i es fo r f ea r o f e x ce ed i n g t h e c at ch i n g fr am e c ap ab i l i t i es On l y i n t es t s u s i n g a l ar ge rea ction mass stack did the minimum boundary exis t to where lower pe llet combinations wer e avoide d. Th e fu e l c on su me d w ith in t he c omb us tio n c ha mbe r i nc lud e s b oth the sta tna mic pellets and the smokele ss rifle powde r used to ig nite the pellets. The sta ndard ope rating proce dure a dopted by the oper ators and sug g ested by the manufa cture r is to use only 0.5 g of smokeless powde r. Not only wer e the number of statnamic pe llets altered, but se ven additional tests were conducte d to determine the eff ect of altering the amount of Table 43 Effe ct of spac ers a nd fuel on the f uel density (%)

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63 smokeless powder I n these pa rticular te st, all variables w ere held constant a nd the am o u n t o f s m o k el es s p o wd er i n cr ea s ed fr o m 0 5 g t o 1 5 g, t h en t o 2 5 g. 4. 2. 6 Te st M at r ix L im it at ion s: Jum p He igh t L imitations to the test matrix due to excessive or insuff icient jump heig hts were briefly mentioned above but a re alization of the compounding eff ects of the test variable s must be understood whe n assessing the risk of pe rfor ming a particula r test. I ncre asing the mass config uration and initial volume dec rea ses the mag nitude of the jump heig ht, but i n c r e a s i n g t h e v e n t p i n l e n g t h a n d a m o u n t o f f u e l i n c r e a s e s t h e j u m p h e i g h t C o l l e c t i v e l y, th ese v ari abl es p rod uce t est s t hat fal l o ut si de o f t he cap abl e ran ge of t he d evi ce. By explodi ng Fig ure 43 to a minimum of five mass config urations, up to 375 test variations are possible. After c onsidering the constra ints placed on the jump heig ht and the e xclu sio ns of the 15 .2 5 c m ve nt p in a nd sp a c e r c omb ina tio ns a la rg e nu mbe r o f t he se te sts c a n b e e xclu de d. Ho we ve r, it i s im po ssi ble to f or e c a st t he jum p h e ig ht o f a te st wi tho ut h a vin g pr ior da ta to u se a s a re fe re nc e T he sy ste ma tic te st m a tr ix ma de it possible to only alter one varia ble and c autiously approa ch the maximum and mini mum bo un da ri e s. Th is m e tho d o f r e fe re nc ing sim ila r t e st c on fi g ur a tio ns to f or e c a st t he jum p heig ht was used e x tensively throug hout the calibra tion tests in an effor t to reduce phy sical da ma g e to t he de vic e O n o c c a sio n, the se lim ita tio ns we re vio la te d a nd the c omp on e nts inadver tently damag ed, ultimately leading into the previously mentioned device mod if ic a tio ns

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64 4. 3 P r e lim ina r y P ur suit of t he St at nam ic Da m ping Co e ffici e nt Af te r a n e xten siv e c a lib ra tio n p ro c e ss, Min ime wa s e mpl oy e d in a se ri e s o f s ta tic and statnamic loa d test cy cles to expeditiously and inexpensively produce data se ts for use in a pre liminary analy sis of the statnamic damping coef ficient. The conce pt of the opera tion was to predict a n acc urate static response ( kx ) fr om two static tests taken bef ore and af ter the statna mic test, then implement the predic ted re sponse into the equation of motion. This wil l eliminate one unknown, making it possibl e to direc tly solve for the damping coef ficient a nd reve al its true time-depe ndent or stra in-depe ndent nature as wa s perf ormed by Mullins et al. (2000). The f ollowing se ctions discuss the evolution of the te sti ng c on c e pt a nd the te st c on du c te d w ith in t he F ru stu m. 4. 3. 1 St at ic -S ta tn am ic Co m par iso ns Many case studies have be en per formed w orldwide with the intent of c omparing static load test re sults to s tatnamic-de rived static r esponses (K usakabe et al. 2000). O ne method of compa rison is to first perfor m a static test on a pile, then f ollow with a statnamic test. Afte r the initial static test, a pre dicted static re load ca n then be e stimated fr om t he loa ddis pla c e me nt p lot (F ig ur e 48) T his pr e dic te d s ta tic re loa d is us e d a s a basis of compa rison for the de rived static r esponse f rom a statnamic te st. Howeve r, problems associa ted with the unce rtainty of extrapolation y ield a lar g e enve lope of po ssi ble pr e dic te d s ta tic re sp on se s. Another me thod of compar ing sta tic and statnamic da ta is to load test two identical piles within close proximi ty of ea ch other This method does not require the e xtra po la tio n o f a pr e dic te d s ta tic re loa d. Th e sta tic re sp on se of on e pil e is d ir e c tly

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65 c omp a re d to the sta tna mic -d e ri ve d s ta tic re sp on se of the oth e r. Th e on ly un c e rt a int y wi th thi s me tho d d e a ls w ith va ri a bil ity of the so il m a tr ix sur ro un din g e a c h p ile w hic h in so me c a se s c a n p ro ve to b e qu ite su bs ta nti a l. Another me thod is to perform an a lternating series of static-statnamicstatic load te sts on a sin g le pil e Pe rf or min g the se c on d s ta tic c y c le e lim ina te s th e ne e d to extrapolate and a llows for the interpola tion of a pre dicted static re sponse. Once plotted, a po rt ion of the se c on d s ta tic c y c le c a n b e sh if te d b e tw e e n th e fi rs t lo a d c y c le a nd its orig inal location to produce a more rea sonable pre dicted cur ve (F igur e 4-9) I n order to re pr e se nt t he pr e dic te d r e sp on se fr om t he se c on d s ta tic c y c le th e se c on d s ta tic c y c le mus t be e xec ute d to the sa me dis pla c e me nt a s th e sta tna mic te st. Th is n e w p re dic te d s ta tic re sp on se c a n th e n b e c omp a re d to the sta tna mic -d e ri ve d s ta tic re sp on se T his me tho d is pr ob a bly the mos t a c c ur a te me a ns of ob ta ini ng a va lid c omp a ri so n, bu t e no rm ou s c os ts incurre d from the multiple load tests discourag e its use. For this reason, the option of re la tiv e ly ine xpe ns ive mod e l sc a le te sts a ttr a c te d a tte nti on to s c a le d te sti ng de vic e s, na me ly the F ru stu m. 4. 3. 2 F r ust um Te st ing I n collabora tion with an ongoing rese arc h projec t (Gar bin, 2003), fifty drilled shafts we re c ast within the confines of the Fr ustum (Fig ure 410). Throug hout casting and testing of the model-sc ale sha fts, numerous proble ms associated w ith the Frustum wer e enc ountere d and addr essed on a n individual basis. During the construc tion phase, the Fr ustum ex hibited a ver y high liquef action potential as the casing was drive n. The ina bil ity of e xce ss p or e pr e ssu re to e sc a pe the c on fi ne s o f t he ve sse l r e su lte d in so il

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66 expuls ion throug h the top of the F rustum and plung ing of the ca sing f or seve ral centimeter s. The occ urre nce undoubte dly disturbed the soil matrix within and g ave a pr e lud e to p ro ble ms e nc ou nte re d d ur ing the sta tna mic loa d te sts Re su lts of the sta tna mic data c ollected f or these te sts were deeme d ambig uous with the liquefac tion problem labeled a s the culprit. Also, the susce ptibili ty of the soil within the Frustum to rela tive de ns ity c ha ng e wa s n ote d. Vi br a tio ns ind uc e d d ur ing c a sin g ins til la tio n a nd the sta tna mic tests severe ly altere d the soil matrix contained in the c ontrol volume, and there by produce d inconsistent load test results. These pa rticularities we re c onsidered w hen d e v e lo p in g th e te s ti n g ma tr ix. For the purposes of this thesis, t he F rustum testing matrix incorporate d a ser ies of a lte rn a tin g sta tic a nd sta tna mic loa d te st c y c le s o n a 4. 5 in (1 1. 43 c m) dia me te r, 36 in (91.44 cm) long model-sca le drilled shaf t cast in the control volume of the Fr ustum (F ig ur e 410 ). As pa rt of the sta nd a rd op e ra tin g pr oc e du re th e F ru stu m w a s f ill e d w ith clea n sand, alluviated, a nd pressurized 24 hrs be fore drilling be g an. The entire pr ocedur e is outli ned in Appendix B. Afte r this period, the shaf t was ca st within t he F rustum using mortar with a w ater -ce ment ratio of 0.485 ( Appendix B). I t was allowe d a 48 hr c uring p er i o d t o en s u re s u ff i ci en t s t ru ct u ra l s t re n gt h b y t h e t i m e o f t es t i n g. During the initial static load cy cle, the intent wa s to displace the sha ft to a point past full side fric tion mobil ization and allow an initial set of the shaft. As note d by Mullins et al. (2000), vibration induce d from cy clic statnamic loa d tests show a tende ncy toward la rg er c apac ities due to soil densification. Be cause of this phenomenon, the second te st, a statnamic load c y cle, wa s perf ormed with the sole pur pose of pr oviding

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67 vibrations nece ssary to increa se the de nsity of the soil within the Frustum. B oth the initial st atic and sta tnamic tests prepa red the shaft and the soil for the upcoming static and sta tna mic c y c le s u se d in the a na ly sis of the sta tna mic da mpi ng c oe ff ic ie nt. The sec ond static load test per formed on the shaft initiated the testing cy cle. The ultimate streng th obtained during the static test dictated the desig n of the statnamic loa d tests. Two consec utive statnamic load tests we re c onducted a nd the maxim um shaft displaceme nt from the last test noted as a g oal for a final static cy cle displac ement. The first statnamic test utiliz ed a f ive mass conf igur ation, one spac er, the 10.95 cm vent pin, a nd tw o f ue l pe lle ts. I n o rd e r t o s ur pa ss t he ult ima te str e ng th d e fi ne d b y the se c on d s ta tic test, it was nece ssary to use an e x tra fue l pellet for the two c onsecutive statna mic tests. Also, the 6.65 cm vent pin wa s incorpora ted to compensa te for the incre ased jump heig ht from the a dditional pellet. The shape and mag nitude of the late r two statnamic loaddisplaceme nt plots proved more intellig ible than any previous test. I t appea red tha t the first statnamic test induce d enoug h vibration to fully compac t the soil in t he contr ol volume. To ensure a we ll-defined f ailure slope a nd ease the alig nment of the pre dicted static response during data a naly sis, the final static test corr alled the statna mic data a nd conclude d the testing cy cles. Onc e the last static c y cle wa s completed, the da ta was analy zed using the me thod mentioned above a nd outlined in Mull ins et al. (2000). Ref er to A pp e nd ix B fo r s ta tic a nd sta tna mic loa d te st p ro c e du re s. A f ull dis c us sio n o f t he te st results is presente d in Chapter 5.

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68 Fig ure 42 Minime mounted to rigid base Fig ure 41 Minime load cell and piston.

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69 F ig ur e 43 E xamp le of te st m a tr ix fl ow c ha rt Fig ure 44 Ex ample of te st matrix table.

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70 Fig ure 45 Effe ct of spac ers on the initial volume and powe r stroke. Fig ure 46 Damag ed 15.25 cm ve nt pin.

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71 F ig ur e 47 M ini me ve nt p ins Fig ure 48 Ex trapolate d static response

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72 Fig ure 49 I nterpolate d static response F ig ur e 410 F ru stu m te st s ha ft s.

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73 5.0 Results Th e fi rs t ph a se of the te sti ng pr og ra m e nta ile d n ume ro us c a lib ra tio n te sts perf ormed solely with the purpose of developing g uidelines to aid future opera tors in the desig n of a loa d test. After analy zing the re sults of the calibra tion tests, four distinct g raphs we re de veloped that whe n marrie d offe r a pa thway for de termining the c omb ina tio n o f t e st v a ri a ble s r e qu ir e d to a c hie ve a pa rt ic ula r l oa d, du ra tio n, a nd jum p heig ht. After de velopment of the g raphs, f ocus shifted towa rds employ ing the device in a series of alterna ting static a nd statnamic load test cy cles. The opera tor g raphs we re use d to targ et ce rtain loads during the load test cy cles. This cha pter pre sents and discusses the data c ollected dur ing both pha ses of the te sting prog ram a nd the deve lopment of the op e ra tor g ra ph s. 5.1 Calibration Test Results Results obtained from the c alibration tests wer e g rouped into var ious families of curve s, where in only one test var iable wa s altere d to determine the eff ect on the loa d pu lse D oin g so a llo we d f or a c omp a ri so n a g a ins t th e pr e dic te d s ta tna mic loa d p uls e response experience d by many previous load tests and outlined by Be rming ham (1995). To rig htfully compar e the a ctual and the oretica l load pulse response as we ll as to ensure the validity of the da ta, it was nec essar y to verify the re producibility of the c alibration te sts by pe ri od ic a lly re pe a tin g a pa rt ic ula r t e st. Th ou g h th e loa d p uls e s p re se nte d in

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74 Fig ure 51 do not offer the ty pical g eometric appea ranc e of a statnamic load pulse, they emphasize the consistent re producibility of the de vice. The following sections pre sent only a sele cted sa mple of cur ves asse mbled to punctuate the e ffe ct of e ach va riable. The individual load pulses for ea ch ca libration test can be found in Appendix A. 5.1.1 Mass Confi guration Thoug h ty pical statnamic te sts targ et a r eac tion mass weig ht approxim ately equal to f ive pe rc e nt o f t he de sir e d ma ximum fo rc e e xce ssi ve jum p h e ig hts re qu ir e Min ime to us e a re a c tio n ma ss w e ig ht m uc h la rg e r. I t is re a so ne d th a t in c re a sin g the re a c tio n ma ss siz e will require more e nerg y or fue l, to overcome the additional inertial e ffe cts when acc eler ating the masses upwa rd. I f the fue l is held constant, then the upwa rd ac cele ration of the ma sse s w ill de c re a se r e su lta ntl y de c re a sin g the ve loc ity a nd inc re a sin g the tim e to rea ch venting (the dura tion). Theore tically as the pre -load a pproac hes 100% of the ma ximum fo rc e (F /m = 1) a nd the du ra tio n c on tin ue s to inc re a se th e te st b e c ome s st a tic in nature due an incr easing wave number. The loss of acc eler ation is compensated by the incre asing rea ction mass siz e, ther eby holding the ma x imum force f airly constant. As seen in F igur es 5-2 a nd 5-3, the maximum forc e incr ease s uniformly and re spectively by 8.6 kN and 13.7 kN w ith the increme ntal addition of two masses (4.3 kN and 6.9 kN f or ea ch ad d i t i o n al m as s ), b u t t h e l o ad d u ra t i o n i s o n l y s l i gh t l y ef fe ct ed T h es e f i n d i n gs contra dict Be rming ham’s portra y al of a n insignifica nt increa se in the maxim um load and a lar g e incr ease in the load dura tion, and only help to reinfor ce the unique beha vior of Minime.

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75 An e xpla na tio n f or the va ri a tio n in be ha vio r i s th e po ssi bil ity of a n in c omp le te fu e l bu rn me a nin g tha t th e de vic e ve nts be fo re the ma jor ity of fu e l is e xpe nd e d. Th is idea is fe asible whe n considering the tests with a re latively low mass config uration. Afte r conducting eac h test of the thre e mass conf igur ation series, it wa s noted that the fue l was only partially spent (F igur e 2-15) When increa sing to a four mass c onfig uration, partially consumed pe llets ex isted in the piston but were not extinguished upon pistoncy linder sepa ration. A sec ondary flash appe are d throug h the vent lid afte r the masse s had a lr e a dy be e n a rr e ste d, a nd fl a me s c on su me d th e re ma ini ng fr a g me nts of fu e l. 5 1 2 I n i ti a l Vo l u me To rema in consistent with Ber mingha m’s discussion on the eff ect of an incr easing vo lum e th e va ri a tio n o f s pa c e rs a nd fu e l is c omb ine d in to o ne fa mil y via the pr e vio us ly define d fuel de nsity J oining the two va riables a lso proves conve nient considering the complexit y of incre asing the volume and holding all other va riables c onstant. For example, since the a ddition of spacer s has a dire ct bea ring on the vent distance or powe r stroke, it is nece ssary to chang e the ve nt pin in order to ac hieve a constant vent distance This is not so m uch of a task, but jump height limitations and the loss of the 15.25 cm vent pin reduc ed the number of ca ndidate cur ves to compile a f amily Using a consta nt vent pin does not alter the maxi mum force since the ve nt pin only eff ects the dur ation and the jump heig ht (discussed in the following section). I f the dura tion is t hen disreg arde d, the ef fec t of additional space rs on the maximum load ca n be addr essed. Table 51 shows that within a particula r ser ies of tests, the maximum forc e is reduc ed by near ly 50% with the addition of the f irst space r; there afte r, the for ce is re duced by much

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76 less. The dra stic reduc tion of forc e with the addition of the f irst space r is not surprising considering the dra stic increa se in initial volum e. Shortly afte r the loss of the 15.25 c m vent pin, it was decide d to utili ze only one space r for the re maining te st series. The decision wa s based on the c lose rese mblance betwee n the shape of one spa cer tests and the distinct shape of a ty pical statnamic loa d pulse (F igur e 5-4) A fe w tests wer e conduc ted with various spac er c ombinations after the re place ment vent pins were constructe d, but particular attention had to be g iven to the resulting vent distance (powe r stroke) Some vent pin/spacer combinations were automatically deeme d impractica l, for the ve nt pin was not of suffic ient leng th to seat within the vent hole (Ta ble 4-2). T he ef fec t of incre asing space r combinations ca n be seen in F igur es 5-5 a nd 5-6, bea ring in mind the additional effe cts of the unc ompensated vent distance I t should be noted that althoug h four spa cer s provide an a ppare nt lower boundary those data r epre sent a wide rang e of f uel and mass c onfig urations (1 to 3 pe lle ts a nd 3 to 11 ma sse s) T he tr e nd ind ic a te d b y the a rr ow re pr e se nts tha t w he re on ly the number of space rs was va ried. Upon a naly zing the re sults of all 10.95 cm vent Table 51 Effe ct of incr easing space rs on the maxi mum force (kN).

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77 pin/four spac er c ombinations, the associated ve nt distance (pow er stroke ) prove d ina de qu a te to r e a c h th e ma ximum po te nti a l lo a d. Th is c lus te r o f d a ta po int s e xhibi t a pa ltr y ma ss r a tio a nd we re the re fo re re mov e d f ro m th e fi na l da ta se t ( F ig ur e 56, a lso ref lected in Ta ble 4-2). 5.1.3 Vent Distance Thoug h the leng th of the vent pin incre ases the ove rall vent distance (powe r str ok e ), it i s p a rt ic ula rl y the la te r p a rt of the str ok e zo ne 3 ( F ig ur e 210 ), tha t is elong ated. F igur es 5-7 a nd 5-8 ar e examples of the e x pecte d incre asing linear r eg ion associate d with differ ing ve nt distances. Note tha t the mag nitude of the maximum forc e is relatively unaff ecte d, but the duration incre ases with an inc rea sing ve nt distance a nd ult ima te ly y ie lds a la rg e r i mpu lse (a re a un de r t he c ur ve ). B e c a us e of the re la tiv e ly un a lte re d ma ximum loa d a nd inc re a se d im pu lse s ho rt e r v e nt d ist a nc e s a re c hie fl y targ eted whe n desiring to reduc e jump heig hts. Howeve r, by adjusting the duration, the wave number for a g iven test ca n be sculpted. A direc t link between the impar ted impulse and the vent distance will be explored in a later disc ussion about the de ve lop me nt o f t he op e ra tor g ra ph s. Whe n c on str uc tio n o f t he re pla c e me nt v e nt p ins be g a n, it w a s d e c ide d n ot t o re c on str uc t a lon g e r 1 5. 25 c m ve nt p in. Th e de c isi on ste mme d f ro m a no ma lou s e ff e c ts prese nt in the data prior to ve nting. I nstead of a quasi-linear decr ease following the maxi mum force the re g ion y ielded a sha pe that appe are d conca ve (F igur e 5-1) I nitial su sp ic ion s w e re tha t a n e xce ssi ve ve nt d ist a nc e a llo we d e xpa ns ion of the c ha mbe r t o continue past a point where the ra te of pre ssure incr ease was re duced by a tre mendous

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78 inc re a sin g vo lum e H ow e ve r a c los e r i ns pe c tio n in dic a te s th a t th e fo rc e wa s a c tua lly being reta ined, not lost to a net suction force Ag ain, an incomplete burn may prove to be the culprit. Additional pressur e deve loped prior to venting indicates that the c hamber volume may not be incre asing faster than the produc tion rate of e x haust g ases. I f the exhaust ga ses ar e still being r apidly produce d in zone 3, then it is likely that the fue l is not tot a lly c on su me d b e fo re ve nti ng oc c ur s. 5.1.4 F uel Ranges and the Shap e F actor I ncre asing the quantity of fue l, or rathe r the fue l density larg ely eff ects both the maxi mum force and the load dur ation. Fue l densities rang ing f rom 6.5% to 10.5% produce load pulses with a hig her a ffinity toward the ty pical shape of a statna mic load pulse (Ta ble 5-2). Table 52 Effe ct of spac ers a nd fuel on the f uel density (%)

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79 As the fue l density incre ases pa st 10.5%, the pea k forc e (a nd mass ratio) incr ease s, and the load dura tion decre ases ( Fig ures 59 and 5-10) When the fuel de nsity falls below 6.5%, the pe ak for ce ( and mass ra tio) dimini shes, and the dur ation incre ases immensely Ba sed on the load pulse plots and F igur es 5-11, tests appr oach a dy namic beha vior when the fu e l de ns ity is c on tin ua lly inc re a se d a nd a sta tic be ha vio r w he n th e fu e l de ns ity is decr ease d (F /m = 1). F igur es 5-12 a nd 5-13 also portra y the ef fec t of incre asing the nu mbe r o f f ue l pe lle ts. Fr om the definition of the shape fac tor, it can be deter mined that the produc t of the forc e, dura tion, and shape f actor is the impulse. W hen the sha pe fa ctor is less than 0.5, the shape of the load pulse is ra ther triang ular a nd char acte ristic of statnamic ( Fig ure 5-14); a sha pe fa ctor of 0.5 g ives the smooth appea ranc e with a g radua l buildup to t he maxi mum force (F igur e 5-15) ; and when the shape f actor is much larg er tha n 0.5, the load is applied rapidly then linge rs ar ound the maxim um force befor e venting occur s (Fig ure 5 -1 6 ). T h o u gh d i ff i cu l t t o s t er eo t y p e, t h e s h ap e f ac t o rs o f l ar ger s t at n am i c d ev i ce s ra n ge from 0.35 to 0.50. Minime load pulses with simil ar g eometric proper ties tend to produce sh a pe fa c tor s r a ng ing fr om 0 .5 0 to 0. 60 (F ig ur e 517 ). Th e c on tr a st c a n b e pa rt ly a ttr ibu te d to the fa c t th a t th e ra te of loa d a pp lic a tio n b e g ins a lmo st i ns ta nta ne ou sly wi th Min ime w he re a s la rg e r s ta tna mic de vic e s e xhibi t a g ra du a l in c re a se in l oa din g ra te (F ig ur e 54) T his c ha ra c te ri sti c of Min ime is a re su lt o f t he pr ime r/ ig nit ion sy ste m. The piston is first char g ed with 0.5 g of smokeless rifle powder prior to placing the fue l pellets. The rifle powder serve s as an ig nitor for the statna mic pellets. Since the powder is designe d to rapidly develop pr essure within the chamber of a f irea rm, pressur e

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80 is developed r apidly within the piston. Once the pe llets are ig nited, the pre ssure develope d by the statnamic fue l blankets the ef fec ts of the powder and loading pr og re sse s a s n or ma l. T he e ff e c ts o f v a ry ing the a mou nt o f r if le po wd e r i n a re la tiv e ly low fuel de nsity test is shown in Fig ure 518. 5. 1. 5 Op e r at or G r aphs The ultimate g oal of the c alibration testing was to deve lop user-f riendly g uidelines be ne fi c ia l in sc ulp tin g a de sir e d lo a d p uls e T he pr od uc t of the nu me ro us c a lib ra tio n te sts is a set of five fuel-f orce curve s and four interlocking opera tor g raphs. The five c urves and the f irst two opera tor g raphs se rve a s the primary desig n aids, and the la st two opera tor g raphs a re simply used as sa fety chec ks ag ainst the jump heig ht. When assembled, the g raphs f ormulate a path along which test var iable combinations ca n be c ho se n to pr od uc e a de sir e d f or c e a nd du ra tio n, a s w e ll a s v e ri fy the a sso c ia te d ju mp he ig ht. Fu e lFo rc e Cur v e s. Fue l-forc e cur ves unique to ea ch devic e ar e the usua l desig n aids utiliz ed by most of the larg er statna mic device s. From these curve s, information reg arding the amount of fue l require d to achieve a par ticular for ce c an be obta ined. As mentioned, the initial volume of the larg er de vices is fa irly constant, eliminating the nee d fo r n ume ro us c ur ve s. Ho we ve r, Min ime is c a pa ble of a wi de ra ng e of po ssi ble config urations and ther efor e dema nds the use of nume rous cur ves. Eac h curve prese nted in Fig ures 519 throug h 5-23 is particula r to a spec ified spac er c ombination. W ith the exception of hig her ma ss config urations, the tre nds are mostly linear. Points highlig hted along eac h trac e sig nify the ave rag e for ce obta ined from a ctual ca libration tests. Most of

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81 the desig n para meters c an be obta ined from one of these f ive cur ves. Eac h space r cur ve can be quickly scanne d to determine w hich mass conf igur ation and fue l combination produce s a for ce c losest to the desired f orce Note that the f uel pellets coinc iding to ea ch da ta po int a re in w ho le nu mbe r v a lue s. Th ou g h n o c a lib ra tio n te sts we re pe rf or me d w ith partial pe llets ( pellets), it may be possible to interpolate a fuel qua ntity betwee n the da ta po int s. Operator Graph #1: Mass Ratio vs. Force. Th e fi rs t op e ra tor g ra ph wa s o ri g ina lly develope d (F igur e 5-24) as an a fterthoug ht with the intent of conver ting the nondimensional mass ratio of ope rator g raph #2 into a more useful value Essentially the g raph plots the linear rela tionship between the ma x imum force a nd the mass ra tio for eac h mass config uration, with the slope of e ach line be ing the static weig ht of that particula r mass conf igur ation. Thoug h the g raph is ra ther simplisti c, it provides a link betwee n the mass ra tio and the more c ommon design pa rame ter, for ce. Operator Graph #2: Mass Ratio vs. Duration. Plott ing the entire da ta set ag ainst F/m and duration, minus a fe w anomalous da ta points mentioned above, pr oduces a n asy mptotical trend that visually define s the ca pabilities of Minime (Fig ure 525). At a ty pical statnamic load dura tion of 100 mill iseconds, mass ra tios fall betwee n three and seve n. Hig her ma ss ratios are attainable but only at the sac rifice of the load dur ation. Se g re g a tin g e a c h d a ta po int by its fu e l qu a nti ty s pa c e r c omb ina tio n, a nd ve nt p in uncover s embedde d trends within the g raph ( Fig ure 526). As discussed in the pr evious sections, incre asing the fue l quantity incre ases the ma ss ratio and de cre ases the loa d duration; the opposite occ urs when the space r combination is incre ased. H aving

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82 previously shown that vent distance alters only the load dura tion, it i s of no surprise tha t inc re a sin g the ve nt p in l e ng th t ra ns la te s th e da ta po int la te ra lly to t he ri g ht. Bounding the data w ith trend lines allows for a more c omprehe nsible g rasp of the individual variable e ffe cts (F igur e 5-27 a nd 5-28). The boundarie s are color-c oordinated to signify pellet ra ng es with blue, re d, g ree n, black, a nd pink repre senting one, two, thre e, fo ur a nd fi ve pe lle ts r e sp e c tiv e ly T he se ra ng e s a re pe tit ion e d in to zo ne s th a t c or ra l te sts of the same space r combination. The zone is numeric ally labeled to identify the spac er combination that it repre sents. Wit hin eac h zone, increa sing ve nt pin lengths tra nslate the data points from lef t to right, such tha t the left and r ight bounda ries mar k the limits of the 6.65 cm and 15.25 c m vent pins. I n some space r zones, an insuffic ient power stroke incre ases the le ftmost boundary to the 10.95 cm vent pin. The throng of informa tion pr e se nt w ith in t he ma ss r a tio vs d ur a tio n p lot a c tua lly e na ble s th e g ra ph to b e us e d a s a stand-alone desig n tool, but the addition of the remaining g raphs make for a n easie r de sig n p ro c e ss a nd pr ov ide int e rn a l sa fe ty c he c ks Operator Graph #3: Impulse vs. Forc e. Gi v en t h at t h e i m p u l s e i m p ar t ed d u ri n g a sta tna mic te st g ra ph ic a lly re pr e se nts the a re a un de r t he loa d p uls e c ur ve it is r e a so na ble to assume a r elationship exi sts with the max imum force. T his relationship is established throug h the load dura tion and the shape fac tor. Plott ing the shape f actor ag ainst the maxi mum force and the impulse shows that idea l shape fa ctors, 0.50 < SF < 0.60, ar e available in a wide r ang e (F igur e 5-29) ; it is possible to design f or a la rg e for ce a nd impulse without sacrificing the shape of the load pulse.

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83 After considering the re lationship between loa d duration and impulse, then rec alling the link between ve nt distance a nd duration, it is not surprising to find that inc re a sin g the ve nt p in l e ng th i nc re a se s th e imp uls e (F ig ur e 530 ). I t is up on thi s a sso c ia tio n th a t op e ra tor g ra ph #3 wa s d e ve lop e d ( F ig ur e 531 ). Simi la r t o th e fi rs t g raph, c olor-coor dinated boundar ies mark the e x tent of their r espec tive test series. Wit hin eac h colore d boundary are lines that demarc ate zones of e qual vent pin leng ths. Af te r d e te rm ini ng the c on fi g ur a tio n f or a te st, a sa fe ty c he c k o n th e ma ximum jum p heig ht can be obtained via this g raph. Operator Graph #4: Impulse vs. J ump Height. Both the ma g nitude of the impulse and the re action mass size are fac tors in controlling the jump height. The masses displace up wa rd s to a po int wh e re a ll k ine tic e ne rg y de ve lop e d b y the imp uls e is c on ve rt e d to potential ener g y so reduc ing the kinetic ene rg y by focusing on the impulse become s an option. Usually the maxim um force is the chief de sign pa rame ter, so suppre ssing the imp uls e by de c re a sin g the fo rc e ma y no t be fe a sib le T he mor e c omm on a pp ro a c h is to decr ease the vent distance or use a shorter ve nt pin. However combining the eff ects of both a larg e mass conf igur ation and a shor t vent pin prove e ffe ctive in obtaining safe jum p h e ig hts O pe ra tor g ra ph #3 pr ov ide s a lin k f ro m th e ma ximum fo rc e to t he jum p he ig ht v ia the imp uls e A s a fi na l sa fe ty c he c k, op e ra tor g ra ph #4 wa s d e ve lop e d to combat the e x cessive jump heig hts associated w ith larg e impulses (F igur e 5-32) After deter mining the test c onfig uration and the associate d impulse, the jump height c an be e s t i m a t e d a n d a r e d e s i g n p e r f o r m e d i f n e c e s s a r y.

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84 Procedure for Use. T h e f o l l o wi n g s t ep s ar e i n t en d ed t o o u t l i n e t h e s t at n am i c d es i gn proce ss as well as c larify the use of the fuel-f orce curve s and oper ator g raphs. The example desig n para meter use d throug hout the proce dure is a de sired maximum forc e of 50 kN. 1. En te r t he a bs c iss a of e a c h f ue lfo rc e c ur ve wi th t he de sir e d f or c e a nd pr oje c t a vertica l line. Deter mine which mass and f uel combination from the dif fer ent curve s provides a da ta point closest to the projec ted line (F igur e 5-33 a nd 5-34). The c losest data point repr esents the test c onfig uration that is closest to producing the desire d forc e. Note the space r combination annota ted at the top of the curve the mass conf igur ation line wher e the da ta point falls, and the a ssociated f uel quantity Two options are available to achieve a 60 kN f orce : (1) 5 masses, no sp a c e rs a nd 2 f ue l pe lle ts, a nd (2 ) 5 ma sse s, 1 s pa c e r, a nd 3 f ue l pe lle ts. 2. Enter the a bscissa of ope rator g raph #1 w ith the desired f orce Project a ve rtical line from the load. F ind the associate d mass ratio by projec ting a horizontal li ne from the inter section of the ve rtical line a nd mass config uration (F igur e 5-35) The mass ra tio for options 1 and 2 is 13.6. 3. Project a hor izont al line from the or dinate of ope rator g raph #2 to de termine the a va ila ble ra ng e of du ra tio ns (F ig ur e 536 ). I f p e rf or me d p ro pe rl y th e lin e sh ou ld enter the fue l reg ion and spac er zone de termined in step 1. Choose an a pp ro xima te du ra tio n a nd ve nt p in l e ng th. Th e du ra tio n r a ng e fo r o pti on 1 is 0.044 to 0.072 seconds; the ra ng e for option 2 is 0.053 t o 0.069 seconds. The 8. 80 c m ve nt p in i s a rb itr a ri ly c ho se n f or bo th o pti on s.

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85 4. Project the a line from the de sired for ce into the f uel zones of oper ator g raph #3. After locating wher e the test fa lls withi n the vent pin and f uel zones, determine the associa ted impulse (2.1 kN-s f or option 1 and 1.8 kN-s f or option 2) (F igur e 537). 5. Project the impulse to opera tor g raph #4, a nd knowing the mass conf igur ation, f i n d t h e r e s u l t i n g j u m p h e i g h t ( 1 4 0 c m f o r o p t i o n # 1 a n d 1 0 6 c m f o r o p t i o n # 2 ) If the jump heig ht is not acce ptable, re desig n as nec essar y (F igur e 5-38) 6. Be fore finalizing a te st, it i s worthwhile to explore other test options and per haps develop a conting ency config uration. 5.2 Statnam ic Dam pin g Coeffi cient Re sults The sec ond g oal of the te sting prog ram wa s to employ the newly define d labora tory statnamic devic e in a se ries of static a nd statnamic load test cy cles on a scale d dr ill e d s ha ft c a st w ith in t he c on tr ol v olu me of the F ru stu m. F ra min g a sta tna mic te st betwee n two static tests allowed for the compar ison of the statnamic c urve to a predic ted static response The diff ere nce be tween the statnamic and static loa d-displace ment c ur ve s y ie lde d th e c omb ine d in e rt ia l a nd da mpi ng e ff e c ts. Sin c e the sy ste m ma ss, a c c e le ra tio n, a nd ve loc ity a re e ith e r k no wn or me a su re d, the da mpi ng c oe ff ic ie nt ( a s w e ll as the static c apac ity ) could e asily be found. The following sections pre sent the re sults of the loa d te sts a nd e la bo ra te s o n p ro ble ms e nc ou nte re d w ith the F ru stu m. 5.2.1 F rustum Testing Results Analy sis of previous data sets collecte d from we t shafts during a collabor ative rese arc h projec t led to the prema ture c onclusion that the hig h liquefac tion potential of the

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86 F ru stu m w a s p la g uin g the int e lli g ibi lit y of the da ta T he re sp on se to t his qu a g mir e wa s to e lim ina te the liq ue fa c tio n p ote nti a l by c a sti ng a nd te sti ng the sh a ft us e d in thi s th e sis un de r d ry c on dit ion s. s ta tn amic1 The initial statnamic test (F ) wa s ran with the intent of pr e-shoc king the F ru stu m w ith sta tna mic ind uc e d v ibr a tio ns pr ior to c oll e c tin g da ta fo r t he se ri e s o f s ta tic and statnamic loa d cy cles (F igur e 5-39) The loaddisplaceme nt curve s of the sec ond and thi rd sta tna mic te sts be g a n to ta ke the mor e c ha ra c te ri sti c wh a le -h e a d s ha pe c omm on to mos t st a tna mic te sts b ut s us pic ion su rr ou nd e d th e un us ua lly low re loa d s tif fn e ss o f b oth s ta ti c2 s ta ti c3 statnamic tests in comparison to the bounda ry static tests (F and F ) (F igur e 5-40) Usually inertial and da mping c ontributions result in a statnamic forc e that is larg er tha n the static for ce thr oug hout the elastic ra ng e, but both statnamic load-displac ement cur ves exhibi t a smaller f orce throug hout this rang e. s ta ti c2 s ta ti c3 A weig hted ave rag e of the second a nd third static cy cles (F and F ) wa s s ta tn amic2 taken a nd scale d to the maxi mum displ ace ment of the sec ond statnamic cy cle ( F ) (F ig ur e 541 ). Ag a in, it c a n b e se e n th a t th e re loa d s tif fn e ss o f t he sta tna mic c y c le is much less than the stiffne ss of the pre dicted static re sponse up to a point past y ielding. Perfor ming c alculations to deter mine the mag nitude of the da mping c oeff icient at var ious locations results in a tra ce tha t closely mimics UPM damping values obta ined from SAW calc ulations (Fig ure 542). Thoug h the ca lculated da mping c oeff icient re sults in nega tive values, it is worthwhile to note that the shape of the c urve c lear ly display s differ ent values betwee n the elastic a nd inelastic zones linked by a smooth, quasi-linear transition. The

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87 da ta su g g e sts tha t th e da mpi ng c oe ff ic ie nt i s n ot c on sta nt t hr ou g ho ut t he e nti re sta tna mic e ve nt b ut i s d isp la c e me nt o r s tr a in d e pe nd e nt. I t is more probable that the abe rra nt neg ative value s obtained during the calc ulations are a result of a n inacc urate predic ted static re sponse instead of a m i s c a l c u l a t i o n o n b e h a l f o f t h e s ys t e m m a s s In m o s t c a s e s a c o n c r e t e d e n s i t y ( g = 150 pcf) and shape (per fec t cy linder) is assumed. D iffer ing c oncre te mix desig ns and anomalous re g ions within t he shaf t result in invalid assumptions Howeve r, the shaf t c on str uc te d f or thi s te sti ng re g ime wa s e xhume d a nd we ig he d to de te rm ine a n a c c ur a te sh a ft ma ss ( 20 .9 kg or g = 13 8. 8 p c f) le a vin g on ly the pr e dic tio n o f t he sta tic re sp on se in question. 5. 2. 2 F r ust um F r ust r at ion s Th ou g h mo stl y a dd re sse d p ri or to t he c on str uc tio n o f t he te st s ha ft us e d in thi s Th e sis u nd e rl y ing pr ob le ms w ith the F ru stu m pl a g ue d th e int e lli g ibi lit y of pr e vio us ly collecte d data se ts. I nitially conce rns surrounde d the expulsi on of soil from the top of the Fr ustum when excess pore pr essure s were introduced via pressurization (F rede rick, 2001), ca sing installation, and statna mic tests. The problem wa s not resolved but ra ther c ir c umv e nte d b y c on fi nin g the te sts to d ry c on dit ion s. Another pr oblem surfa ced a s an inability to reproduc e in-situ soil conditions within the Frustum for the replica tion of identically perf orming shafts. This mere inconvenienc e did not threa ten the integ rity of the da ta collec ted for this thesis since the te st r e su lts we re no t c omp a re d to the pe rf or ma nc e of oth e r t e st s ha ft s, bu t it did ra ise conce rns about the se nsitivi ty of the F rustum to soil prepa ration methods. The a lluviation

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88 pr oc e ss u se d d ur ing so il p re pa ra tio n s e e me d to be the c ulp ri t of the ir re pr od uc ibi lit y pr ob le m. D ur ing a llu via tio n, the sa nd is v iol e ntl y dis tur be d th e n a llo we d to se ttl e thr ou g h w a te r u nd e r i ts o wn we ig ht. Th is p ro c e ss e ns ur e s th a t a un if or m de ns ity e xists thr ou g ho ut t he F ru stu m, b ut t he re su lt i s a ve ry loo se ma tr ix tha t is hig hly su sc e pti ble to vibration-induce d rela tive density chang e. Random vibrations induce d from any source inc lud ing the sta tna mic te sts c ou ld s ig nif ic a ntl y a lte r t he sta te of the so il w ith in. Th is re a liza tio n b e c a me pr e va le nt w hil e a na ly zing pr e vio us da ta se ts, fo r i de nti c a l sh a ft s wo uld e xhibi t r a dic a lly dif fe re nt s tr e ng ths The most perple x ing c oncer n, howeve r, wa s the fac t that statnamic tests reve aled a much lowe r re load stiffness than the enveloping static tests. The mag nitude of the inconsistency had not bee n observe d in ear lier studies, and full dismantling of the Fr ustum was schedule d. Conclusions, as well as re commendations re g arding future testing w ith the Frustum and Minime, ar e addr essed in Chapter 6.

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89 Fig ure 52 Effe ct of mass c onfig uration on the load pulse ( 8.80 cm vent leng th and fue l density of 7.02 %) Fig ure 51 Reproducibility of a te st (5 masses, 2 spac ers, 15.25 c m vent pin, and 1 fue l pellet).

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90 Fig ure 53 Effe ct of mass c onfig uration on the load pulse ( 4.50 cm vent leng th and fue l density of 10.5 %) F ig ur e 54 Co mpa ri so n o f t y pic a l st a tna mic loa d p uls e s.

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91 Fig ure 55 Mass ratio vs. dura tion (15.25 cm vent pin): Path of incre asing sp a c e rs Fig ure 56 Mass ratio vs. dura tion (10.95 cm vent pin): Path of incre asing sp a c e rs

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92 Fig ure 58 Effe ct of ve nt distance on the loa d pulse (7 masses a nd fuel density of 7.02%) Fig ure 57 Effe ct of ve nt distance on the loa d pulse (5 masses a nd fuel density of 7.02%)

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93 Fig ure 59 Effe ct of fue l density on the load pulse (5 ma sses and 8.8 c m vent leng th). Fig ure 510 Effe ct of fue l density on the load pulse (5 ma sses and 10.95 cm vent leng th).

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94 Fig ure 512 Mass ratio vs. dura tion (15.25 cm vent pin): Path of inc re a sin g fu e l pe lle ts. F i g u r e 5 1 1 M a s s r a t i o v s d u r a t i o n : E f f e c t o f f u e l d e n s i t y ).

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95 Fig ure 514 L oad pulse with SF = 0.43. Fig ure 513 Mass ratio vs. dura tion (10.95 cm vent pin): Path of inc re a sin g fu e l pe lle ts.

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96 Fig ure 515 L oad pulse with SF = 0.50. Fig ure 516 L oad pulse with SF = 0.86.

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97 F ig ur e 517 Ma ss r a tio vs d ur a tio n: D ist ri bu tio n o f s ha pe fa c tor s. Fig ure 518 Var iation in the amount of smokeless rifle pow der. A ll three tests utili zed 6 masses, 3 space rs, 1fue l pellet, and the 15.25 c m vent pin.

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98 F ig ur e 519 F ue lfo rc e c ur ve : 0 s pa c e rs Fig ure 520 Fue l-forc e cur ve: 1 spac er.

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99 F ig ur e 521 F ue lfo rc e c ur ve : 2 s pa c e rs F ig ur e 522 F ue lfo rc e c ur ve : 3 s pa c e rs

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100 F ig ur e 523 F ue lfo rc e c ur ve : 4 s pa c e rs Fig ure 524 Oper ator g raph #1: Mass r atio vs. forc e.

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101 Fig ure 526 Combined variable e ffe cts on the mass ra tio and duration. Fig ure 525 Mass ratio vs. dura tion.

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102 Fig ure 527 Oper ator g raph #2 w ith data points: Mass ratio vs. duration. Fig ure 528 Oper ator g raph #2 w ithout data points: Mass ratio vs. duration.

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103 Fig ure 529 Shape fa ctors as a function of the f orce and impulse. Fig ure 530 Vent pin leng th as a func tion of forc e and impulse.

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104 Fig ure 531 Oper ator g raph #3: F orce vs. impulse. Fig ure 532 Oper ator g raph #4: Jump height vs. impulse.

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105 Fig ure 533 Desig n proce dure step 1: Option 1 (5 ma sses, no space rs, and 2 fuel pe llets). Fig ure 534 Desig n proce dure step 1: Option 2 (5 ma sses, 1 space r, and 3 fuel pe llets).

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106 Fig ure 536 Desig n proce dure step 3: F ind the rang e of dur ation and sele ct a vent pin. Fig ure 535 Desig n proce dure step 2: De termine the ma ss ratio.

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107 Fig ure 537 Desig n proce dure step 4: F ind the impulse. F ig ur e 538 De sig n p ro c e du re ste p 5 : F ind a sso c ia te d ju mp h e ig ht.

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108 Fig ure 539 Static and statnamic load te st cy cles pe rfor med on shaft S53. Fig ure 540 Static and statnamic c y cles used in the a naly sis of the sta tna mic da mpi ng c oe ff ic ie nt.

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109 F ig ur e 542 Ca lc ula te d s ta tna mic da mpi ng c oe ff ic ie nt. Fig ure 541 Predicted static r esponse in compa rison to the measure d s ta tn amic2 statnamic re sponse for F

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110 Fig ure 543 Damping coef ficient a s a func tion of time.

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111 6. 0 C onc lusi ons and R e c om m e ndat ion s I n 2002, the Univer sity of South Florida r ece ived a r elatively untested and unique l ab o ra t o ry s ca l e s t at n am i c d ev i ce fr o m Be rm i n gh am m er Fo u n d at i o n E q u i p m en t T h o u gh conce ptually simil ar to lar g er statna mic device s, uncer tainty associate d with the new la bo ra tor y de vic e de ma nd e d a n e xplor a tio n o f i ts c a pa bil iti e s a nd lim ita tio ns A s a re su lt, a two-pha se, seque ntial testing prog ram wa s develope d and implemented. The product of the exploration was a se ries of f ive fue l-forc e cur ves and f our oper ator g raphs ( Fig ures 61 and 6-2) When married, the curve s and g raphs a llow for the de sign of a statnamic loa d test and pre diction of the three test outcomes: the maxim um force load dura tion, and associate d jump height. A loa d test desig n example is contained within Chapter 5. Analy sis of more than 100 c alibration tests define d the nature of the de vice. The Sta tna mic Min i T e ste r, or Min ime p ro ve d d iss imi la r t o a n e xpe c te d s ta tna mic re sp on se in t hr e e a sp e c ts: the e ff e c t of inc re a sin g the re a c tio n ma ss s ize th e ra ng e of ma ss r a tio s, a nd the ra ng e of sh a pe fa c tor s. As dis c us se d in Cha pte r 2 th e re a c tio n ma ss s ize ty pic a lly has a sig nificant e ffe ct on the load dur ation and a minimal ef fec t on the maxi mum load. Howeve r, re sults presented in Chapter 5 show that Minime responds diffe rently ; the rea ction mass siz e has a minimal effec t on the load dura tion and a sig nificant e ffe ct on the maxi mum force Although dif ficult to determine, this inconsistency may be a r esult of an inc omp le te c omb us tio n o f s ta tna mic fu e l in low e r m a ss c on fi g ur a tio ns T he sli g htl y

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112 inc re a se d d ur a tio n o f t he la rg e r m a ss c on fi g ur a tio ns ma y a ff or d th e ne c e ssa ry tim e to completely consume the statna mic fuel prior to venting a nd piston/cy linder sepa ration. Minime mass ratios rang e fr om an appa rent minimum of two to ten for conventional load dur ations (0.08 to 0.12 seconds) while it is conventionally thought that mass ratios fluctua te ar ound twenty (5% r eac tion mass). Also, fea sible Minime shape fac tors rang e fr om 0.5 to 0.6, where as larg er de vices produc e shape fac tors in the rang e of 0.35 to 0.5. Differ ence s in the output, as well as the phy sical diffe renc e in device c omp on e nts a id i n e mph a sizi ng the ind ivi du a lit y of Min ime a mon g st i ts l a rg e r c oh or ts. Wit h the deve lopment of the fue l-forc e cur ves and the opera tor g raphs, it is now possible to effe ctively expeditious ly and ec onomically utiliz e Minime in future r esea rch eff orts. One suc h eff ort lies in the pursuit of a be tter g rasp on the sta tnamic damping c oe ff ic ie nt (c ). I nitial steps were made towa rd this goa l in the second pa rt of the testing pr og ra m. B ou nd ing sta tna mic da ta be tw e e n s e ts o f s ta tic da ta pr ov e d e ff e c tiv e in predic ting a static response worthy of compa ring to the measure d statnamic re sponse. Fr om this predicted static re sponse, statnamic da mping va lues wer e ca lculated f rom initiation of the test to the point of max imum dis place ment. The c alculate d damping coef ficient c lear ly shows a discre pancy betwee n values obtaine d in the elastic a nd inelastic ra ng es. The va lue appe ars to be c onstant, but differe nt, in each r ang e or zone. The zones ar e linked by an almost linear tr ansition. Neg ative damping values c alculate d in the inelastic zone ca n be attributed to the de velopment of the pr edicted sta tic response for e ven with the ela borate analy sis procedur e used to e valuate the predic ted re sponse, a min ima l a mou nt o f u nc e rt a int y re ma ins

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113 Conclusions drawn fr om the results of data collecte d during both phases of the testing pr og ram off er r ecommenda tions reg arding the future usag e of Minime and the F ru stu m f or the ult ima te g oa l of re de fi nin g the sta tna mic da mpi ng c oe ff ic ie nt. Th e se rec ommendations include: 1. Replace the larg er f uel pellets cur rently used in Minime with smaller pellets of a simil ar g eometric shape. B y decr easing the size of the fue l pellets, but keeping the fue l density constant, the a vailable surf ace are a and a ccompa ny ing bur n rate of the fue l will increase This chang e will presumably decr ease the load dura tion, de c re a se the sh a pe fa c tor a nd a lle via te c on c e rn s a sso c ia te d w ith a n in c omp le te fuel burn. 2. Adopt a better method for pr epar ing the Fr ustum that will reduc e the potential f or vibration-induce d rela tive density chang e. Vibra ting the c asing during the shaft construction phase may incre ase the rela tive density of the c ontrol volume to a p o in t w h e r e s ta tn a mi c in d u c e d v ib r a ti o n s h a v e li tt le e f f e c t o n th e s o il ma tr ix. 3. Apply the same c onstruction, testing, a nd analy sis procedur es to shafts ca st in a controlled a rea larg er tha n what the F rustum offer s, with the intent of incre asing the inertial a nd damping contributions from statnamic tests. Thoug h the Fr ustum is an ideal tool for la boratory scale d tests and may be suitable for other a naly tical approa ches f ocused towa rd better defining the statnamic da mping c oeff icient, the ina bil ity to s c a le ma te ri a l pr op e rt ie s r e nd e rs it i na pp ro pr ia te fo r t he a na ly sis proce dure utilized herein.

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114 The testing prog ram initiated in this thesis is not merely the end but cr eate s a new path for the c on tin ua nc e of sta tna mic te c hn olo g y Wit h th e a id o f M ini me mo re a c c ur a te methods of pre dicting the static ca pacity of a pile c an be soug ht and deve loped.

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115 F ig ur e 61 F ue lfo rc e c ur ve s.

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116 F ig ur e 62 O pe ra tor g ra ph s.

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117 Refere nces Be rming ham, P., and White, J ., (1995), “ Py rotec hnics and the A ccur ate of Prediction of Statnamic Peak L oading and F uel Charg e Size,” Fi rst In te rn ati on al S tat na mi c Seminar 1995, Vanc ouver, B ritish Col umbia Canada Be rming ham, P. D., (2000), “ STATNAMI C: The first ten y ear s,” Procee dings of the Second I nternational Stat namic Sem inar Toky o, J apan, O ctober 28-30, 1998, pp. 457-464. Fa brique Scientific, I nc., (N ovember 2001), Me as ur e d P re ssu re Cur v e An aly sis Fa brique Scientific, I nc., Mar ch 2004, . Fr eder ick, E. M., (2001), “ Pressure G routing Drilled Shaft Tips: L abora tory Scale Study in a Fr ustum Confini ng Vessel,” Master’ s Thesis, University of South Florida, Tampa, F lorida. Gar bin, E. J ., (1999), “ Data I nterpre tation for Axial St atnamic Te sting a nd the De ve lop me nt o f t he Sta tna mic An a ly sis Wor kb oo k, ” Ma ste r’ s T he sis U niv e rs ity o f S o u t h F l o r i d a T a m p a F L. Gar bin, E. J ., (2003), “ The I nfluenc e of Water Table in Dr illed Shaft Construction,” Doctora te Disserta tion, University of South Florida, Ta mpa, Flor ida. Jame s, C. R ., (1 99 7) “ TH E A B C’ S OF REL OA DI NG ,” 6 e d. K ra us e Pub lic a tio ns th I nc., I ola, Wisconsin. J anes, M.C., Jus tason, M.D., B rown, D.A ., (2000), “ L ong period dy namic load testing ASTM standard dr aft,” Pr oc e e din gs of t he Se c on d I nte rn ati on al S tat na mi c Seminar Toky o, October 1998, pp. 199-218. Ko jim a I ., Ni sh imu ra S. T a na ka M ., a nd Ku wa ba ra F ., (2 00 0) “ I mpr ov e me nt o f p ile toe ca pacity by the STATNAMI C pre-loa ding on the model pile test in a frustum confining vessel,” Procee dings of the Second Inte rnational St atnamic Seminar Toky o, J apan, O ctober 28-30, 1998, pp. 433-441.

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118 L ewis, C., (1999), “ Analy sis of Ax ial Statnamic Testing by the Seg mental Unloading Point M ethod,” Ma ster’s The sis, University of South Florida, Ta mpa, Flor ida. Middendorp, P., Be rming ham, P., and Kuiper B., ( 1992), “Statnamic loa d testing of foundation piles,” Proc eeding s, 4 I nterna tional Confere nce O n Application of th Stress-Wave The ory To Piles. The Hag ue, Holland, 1992, pp. 581588. Middendorp, P. and B ielefe ld, M. W ., (1995) “ Statnamic load testing and the influe nce of Stress phenomena ,” Procee dings of the First International Statnamic Seminar Vanc ouver, B ritish Col umbia, September 2730, 1995. Mu lli ns G ., Ga rb in, E. J., L e wi s, C., (2 00 0) “ STA TN AM I C te sti ng : U niv e rs ity of Sou th Florida rese arc h,” Procee dings of the Second Inte rnational St atnamic Seminar Toky o, J apan, O ctober 28-30, 1998, pp. 117-132. PMC, (2004), “Kentledg e load test,” Online I mag e, PMC Marc h 2004, . Schaef er, J. C., (2002), A ( Very) Short Course in Internal Balli stics The Stey r Scout Website, (Marc h 2004), . Se dr a n, G. St oll e D F E ., a nd Ho rv a th, R. G ., (2 00 0) “ Phy sic a l mo de lin g of loa d te sts on piles,” Procee dings of the Second Inte rnational St atnamic Seminar Toky o, J apan, O ctober 28-30, 1998, pp. 355-364. Serwa y R. A., (1996), Ph y sic s F or Sc ie nti sts An d E ng ine e rs 4 ed S au n d er s C o l l ege th Publis hing, Philadelphia. T ra n s p o rt at i o n R es ea rc h Bo ar d o f t h e N at i o n al Ac ad em i es (2 0 0 3 ), “P re fa b ri ca t ed Br i d ge El e me nts a nd Sy ste ms t o L imi t T ra ff ic Di sr up tio n D ur ing Con str uc tio n: A Sy nthesis of Hig hway Practice ,” NCHRP Synthesis 324 Washington, D. C. Wint e rs D ., (2 00 2) “ SUP ERS AW St a tna mic An a ly sis Sof tw a re ,” Ma ste r’ s T he sis University of South Florida, Ta mpa, Flor ida.

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119 Append ices

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120 Append ix A: F am ily of Curves A. 1 3 M as s C onfig ur at ion s Fig ure A -1 3 masses, 1 spa cer 2 fuel pe llets, and the 6.65 cm ve nt pin. Fig ure A -2 3 masses, 1 spa cer 3 fuel pe llets, and the 6.65 cm ve nt pin.

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121 App e ndix A: (C ont inue d) Fig ure A -4 3 masses, 1 spa cer 2 fuel pe llets, and the 8.80 cm ve nt pin. Fig ure A -3 3 masses, 1 spa cer 1 fuel pe llets, and the 8.80 cm ve nt pin.

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122 Fig ure A -5 3 masses, 1 spa cer 2 fuel pe llets, and the 8.80 cm ve nt pin. App e ndix A: (C ont inue d) Fig ure A -6 3 masses, 1 spa cer 1 fuel pe llets, and the 10.95 cm ve nt pin.

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123 App e ndix A: (C ont inue d) Fig ure A -7 3 masses, 1 spa cer 2 fuel pe llets, and the 10.95 cm ve nt pin.

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124 App e ndix A: (C ont inue d) A. 2 4 M as s C onfig ur at ion s Fig ure A -8 4 masses, 4 spa cer s, 1 fuel pellet, a nd the 15.25 cm vent pin. Fig ure A -9 4 masses, 3 spa cer s, 1 fuel pellet, a nd the 15.25 cm vent pin.

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125 App e ndix A: (C ont inue d) Fig ure A -10 4 masses, 2 spa cer s, 1 fuel pellet, a nd the 15.25 cm vent pin. Fig ure A -11 4 masses, 1 spa cer s, 1 fuel pellet, a nd the 15.25 cm vent pin.

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126 App e ndix A: (C ont inue d) Fig ure A -12 4 masses, 0 spa cer s, 1 fuel pellet, a nd the 15.25 cm vent pin. Fig ure A -13 4 masses, 4 spa cer s, 2 fuel pellet, a nd the 15.25 cm vent pin.

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127 App e ndix A: (C ont inue d) Fig ure A -14 4 masses, 3 spa cer s, 2 fuel pellet, a nd the 15.25 cm vent pin. Fig ure A -15 4 masses, 2 spa cer s, 2 fuel pellet, a nd the 15.25 cm vent pin.

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128 App e ndix A: (C ont inue d) Fig ure A -16 4 masses, 1 spa cer s, 2 fuel pellet, a nd the 15.25 cm vent pin. Fig ure A -17 4 masses, 0 spa cer s, 1 fuel pellet, a nd the 15.25 cm vent pin.

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129 App e ndix A: (C ont inue d) Fig ure A -18 4 masses, 4 spa cer s, 3 fuel pellet, a nd the 15.25 cm vent pin. Fig ure A -19 4 masses, 3 spa cer s, 3 fuel pellet, a nd the 15.25 cm vent pin.

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130 App e ndix A: (C ont inue d) Fig ure A -20 4 masses, 4 spa cer s, 4 fuel pellet, a nd the 15.25 cm vent pin. Fig ure A -21 4 masses, 4 spa cer s, 5 fuel pellet, a nd the 15.25 cm vent pin.

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131 App e ndix A: (C ont inue d) A. 3 5 M as s C onfig ur at ion s Fig ure A -22 5 masses, 1 spa cer 2 fuel pe llet, and the 8.80 cm ve nt pin. Fig ure A -23 5 masses, 1 spa cer 1 fuel pe llet, and the 6.65 cm ve nt pin.

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132 App e ndix A: (C ont inue d) Fig ure A -24 5 masses, 1 spa cer 2 fuel pe llet, and the 6.65 cm ve nt pin. Fig ure A -25 5 masses, 1 spa cer 3 fuel pe llet, and the 6.65 cm ve nt pin.

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133 App e ndix A: (C ont inue d) Fig ure A -27 5 masses, 1 spa cer 1 fuel pe llet, and the 8.80 cm ve nt pin. Fig ure A -26 5 masses, 1 spa cer 1 fuel pe llet, and the 10.95 cm ve nt pin.

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134 App e ndix A: (C ont inue d) Fig ure A -28 5 masses, 0 spa cer s, 1 fuel pellet, a nd the 10.95 cm vent pin. Fig ure A -29 5 masses, 0 spa cer s, 1 fuel pellet, a nd the 10.95 cm vent pin.

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135 App e ndix A: (C ont inue d) Fig ure A -30 5 masses, 0 spa cer s, 1 fuel pellet, a nd the 10.95 cm vent pin. Fig ure A -31 5 masses, 0 spa cer s, 1 fuel pellet, a nd the 10.95 cm vent pin.

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136 App e ndix A: (C ont inue d) Fig ure A -32 5 masses, 0 spa cer s, 2 fuel pellets, a nd the 10.95 cm vent pin. Fig ure A -33 5 masses, 1 spa cer 1 fuel pe llet, and the 10.95 cm ve nt pin.

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137 App e ndix A: (C ont inue d) Fig ure A -34 5 masses, 1 spa cer 2 fuel pe llets, and the 10.95 cm ve nt pin. Fig ure A -35 5 masses, 1 spa cer 3 fuel pe llets, and the 10.95 cm ve nt pin.

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138 App e ndix A: (C ont inue d) Fig ure A -36 5 masses, 2 spa cer s, 1 fuel pellet, a nd the 10.95 cm vent pin. Fig ure A -37 5 masses, 2 spa cer s, 2 fuel pellets, a nd the 10.95 cm vent pin.

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139 App e ndix A: (C ont inue d) Fig ure A -38 5 masses, 1 spa cer 2 fuel pe llets, and the 10.95 cm ve nt pin. Fig ure A -39 5 masses, 1 spa cer 2 fuel pe llets, and the 10.95 cm ve nt pin.

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140 App e ndix A: (C ont inue d) Fig ure A -40 5 masses, 4 spa cer s, 2 fuel pellets, a nd the 15.25 cm vent pin. Fig ure A -41 5 masses, 3 spa cer s, 2 fuel pellets, a nd the 15.25 cm vent pin.

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141 App e ndix A: (C ont inue d) Fig ure A -42 5 masses, 2 spa cer s, 2 fuel pellets, a nd the 15.25 cm vent pin. Fig ure A -43 5 masses, 1 spa cer 2 fuel pe llets, and the 15.25 cm ve nt pin.

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142 App e ndix A: (C ont inue d) Fig ure A -44 5 masses, 0 spa cer s, 2 fuel pellets, a nd the 15.25 cm vent pin. Fig ure A -45 5 masses, 4 spa cer s, 3 fuel pellets, a nd the 15.25 cm vent pin.

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143 App e ndix A: (C ont inue d) Fig ure A -46 5 masses, 3 spa cer s, 3 fuel pellets, a nd the 15.25 cm vent pin. Fig ure A -47 5 masses, 2 spa cer s, 3 fuel pellets, a nd the 15.25 cm vent pin.

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144 App e ndix A: (C ont inue d) Fig ure A -48 5 masses, 4 spa cer s, 4 fuel pellets, a nd the 15.25 cm vent pin. Fig ure A -49 5 masses, 3 spa cer s, 4 fuel pellets, a nd the 15.25 cm vent pin.

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145 Fig ure A -51 5 masses, 4 spa cer s, 1 fuel pellet, a nd the 15.25 cm vent pin. App e ndix A: (C ont inue d) Fig ure A -50 5 masses, 4 spa cer s, 5 fuel pellets, a nd the 15.25 cm vent pin.

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146 App e ndix A: (C ont inue d) Fig ure A -53 5 masses, 2 spa cer s, 1 fuel pellet, a nd the 15.25 cm vent pin. Fig ure A -52 5 masses, 3 spa cer s, 1 fuel pellet, a nd the 15.25 cm vent pin.

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147 App e ndix A: (C ont inue d) Fig ure A -54 5 masses, 2 spa cer s, 1 fuel pellet, a nd the 15.25 cm vent pin. Fig ure A -55 5 masses, 1 spa cer s, 1 fuel pellet, a nd the 15.25 cm vent pin.

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148 App e ndix A: (C ont inue d) Fig ure A -56 5 masses, 0 spa cer s, 1 fuel pellet, a nd the 15.25 cm vent pin.

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149 App e ndix A: (C ont inue d) A. 4 6 M as s C onfig ur at ion s Fig ure A -57 6 masses, 4 spa cer s, 1 fuel pellet, a nd the 15.25 cm vent pin. Fig ure A -58 6 masses, 3 spa cer s, 1 fuel pellet, a nd the 15.25 cm vent pin.

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150 App e ndix A: (C ont inue d) Fig ure A -59 6 masses, 2 spa cer s, 1 fuel pellet, a nd the 15.25 cm vent pin. Fig ure A -60 6 masses, 4 spa cer s, 1 fuel pellet, a nd the 15.25 cm vent pin.

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151 App e ndix A: (C ont inue d) Fig ure A -61 6 masses, 3 spa cer s, 1 fuel pellet, a nd the 15.25 cm vent pin.

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152 App e ndix A: (C ont inue d) A. 5 7 M as s C onfig ur at ion s Fig ure A -62 7 masses, 1 spa cer 2 fuel pe llet, and the 10.95 cm ve nt pin. Fig ure A -63 7 masses, 1 spa cer 2 fuel pe llet, and the 8.80 cm ve nt pin.

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153 App e ndix A: (C ont inue d) Fig ure A -64 7 masses, 1 spa cer 2 fuel pe llet, and the 6.65 cm ve nt pin. Fig ure A -65 7 masses, 1 spa cer 1 fuel pe llet, and the 10.95 cm ve nt pin.

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154 App e ndix A: (C ont inue d) Fig ure A -67 7 masses, 1 spa cer 3 fuel pe llet, and the 8.80 cm ve nt pin. Fig ure A -66 7 masses, 1 spa cer 1 fuel pe llet, and the 8.80 cm ve nt pin.

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155 App e ndix A: (C ont inue d) Fig ure A -69 7 masses, 1 spa cer 2 fuel pe llet, and the 6.65 cm ve nt pin. Fig ure A -68 7 masses, 1 spa cer 3 fuel pe llet, and the 6.65 cm ve nt pin.

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156 App e ndix A: (C ont inue d) Fig ure A -70 7 masses, 1 spa cer 1 fuel pe llet, and the 8.80 cm ve nt pin. Fig ure A -71 7 masses, 1 spa cer 2 fuel pe llet, and the 6.65 cm ve nt pin.

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157 App e ndix A: (C ont inue d) A. 6 9 M as s C onfig ur at ion s Fig ure A -72 9 masses, 1 spa cer 1 fuel pe llet, and the 10.95 cm ve nt pin. Fig ure A -73 9 masses, 1 spa cer 2 fuel pe llet, and the 10.95 cm ve nt pin.

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158 App e ndix A: (C ont inue d) Fig ure A -74 9 masses, 1 spa cer 3 fuel pe llet, and the 10.95 cm ve nt pin. Fig ure A -75 9 masses, 1 spa cer 1 fuel pe llet, and the 8.80 cm ve nt pin.

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159 App e ndix A: (C ont inue d) Fig ure A -76 9 masses, 1 spa cer 2 fuel pe llet, and the 8.80 cm ve nt pin. Fig ure A -77 9 masses, 1 spa cer 3 fuel pe llet, and the 8.80 cm ve nt pin.

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160 App e ndix A: (C ont inue d) Fig ure A -78 9 masses, 1 spa cer 1 fuel pe llet, and the 6.65 cm ve nt pin. Fig ure A -79 9 masses, 1 spa cer 2 fuel pe llet, and the 6.65 cm ve nt pin.

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161 App e ndix A: (C ont inue d) Fig ure A -80 9 masses, 1 spa cer 3 fuel pe llet, and the 6.65 cm ve nt pin. Fig ure A -81 9 masses, 1 spa cer 4 fuel pe llet, and the 6.65 cm ve nt pin.

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162 App e ndix A: (C ont inue d) A. 7 1 1 M as s C onfig ur at ion s Fig ure A -82 11 masses, 1 spa cer 2 fuel pe llet, and the 8.80 cm ve nt pin. Fig ure A -83 11 masses, 1 spa cer 3 fuel pe llet, and the 8.80 cm ve nt pin.

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163 App e ndix A: (C ont inue d) Fig ure A -84 11 masses, 1 spa cer 2 fuel pe llet, and the 6.65 cm ve nt pin. Fig ure A -85 11 masses, 1 spa cer 3 fuel pe llet, and the 6.65 cm ve nt pin.

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164 App e ndix A: (C ont inue d) Fig ure A -86 11 masses, 1 spa cer 4 fuel pe llet, and the 6.65 cm ve nt pin. Fig ure A -87 11 masses, 1 spa cer 1 fuel pe llet, and the 10.95 cm ve nt pin.

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165 App e ndix A: (C ont inue d) Fig ure A -88 11 masses, 1 spa cer 2 fuel pe llet, and the 10.95 cm ve nt pin. Fig ure A -89 11 masses, 1 spa cer 3 fuel pe llet, and the 10.95 cm ve nt pin.

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166 App e ndix A: (C ont inue d) Fig ure A -90 11 masses, 1 spa cer 2 fuel pe llet, and the 10.95 cm ve nt pin. Fig ure A -91 11 masses, 1 spa cer 3 fuel pe llet, and the 10.95cm ve nt pin.

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167 App e ndix A: (C ont inue d) Fig ure A -92 11 masses, 1 spa cer 3 fuel pe llets, and the 10.95 cm ve nt pin. Fig ure A -93 11 masses, 2 spa cer s, 3 fuel pellets, a nd the 10.95 cm vent pin.

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168 App e ndix A: (C ont inue d) Fig ure A -95 11 masses, 2 spa cer s, 1 fuel pellet, a nd the 10.95 cm vent pin. F ig ur e A94 11 ma sse s, 2 s pa c e rs 2 fu e l pe lle ts, a nd the 10 .9 5 c m ve nt pin.

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169 App e ndix A: (C ont inue d) Fig ure A -97 11 masses, 3 spa cer s, 1 fuel pellet, a nd the 10.95 cm vent pin. Fig ure A -96 11 masses, 2 spa cer s, 4 fuel pellets, a nd the 10.95 cm vent pin.

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170 App e ndix A: (C ont inue d) Fig ure A -99 11 masses, 3 spa cer s, 3 fuel pellets, a nd the 10.95 cm vent pin. Fig ure A -98 11 masses, 3 spa cer s, 2 fuel pellets, a nd the 10.95 cm vent pin.

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171 App e ndix A: (C ont inue d) Fig ure A -101 11 masses, 3 spa cer s, 5 fuel pellets, a nd the 10.95 cm vent pin. Fig ure A -100 11 masses, 3 spa cer s, 4 fuel pellets, a nd the 10.95 cm vent pin.

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172 App e ndix A: (C ont inue d) Fig ure A -103 11 masses, 4 spa cer s, 2 fuel pellets, a nd the 10.95 cm vent pin. Fig ure A -102 11 masses, 4 spa cer s, 1 fuel pellet, a nd the 10.95 cm vent pin.

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173 App e ndix A: (C ont inue d) Fig ure A -104 11 masses, 4 spa cer s, 3 fuel pellets, a nd the 10.95 cm vent pin. Fig ure A -105 11 masses, 4 spa cer s, 4 fuel pellets, a nd the 10.95 cm vent pin.

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174 App e ndix A: (C ont inue d) Fig ure A -107 11 masses, 0 spa cer s, 1 fuel pellet, a nd the 10.95 cm vent pin. Fig ure A -106 11 masses, 4 spa cer s, 5 fuel pellets, a nd the 10.95 cm vent pin.

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175 App e ndix A: (C ont inue d) Fig ure A -109 11 masses, 1 spa cer 2 fuel pe llets, and the 10.95 cm ve nt pin. Fig ure A -108 11 masses, 0 spa cer s, 2 fuel pellets, a nd the 10.95 cm vent pin.

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176 Append ix B: P roce dures Contained here in are the cur rent re commended pr ocedur es to be used w ith the Fr ustum Confini ng Vessel ( FCV or F rustum) and labor atory statnamic devic e (Minime). These pr ocedur es include: F rustum prepa ration and pr essurization, drilled shaft c on str uc tio n, sta tic loa d te st, sta tna mic loa d te st, a nd sta tna mic c a lib ra tio n te st. B.1 Fr ustum P reparat ion an d Pr essurization 1. Remove the top flang e and middle se ction of the F rustum, expos ing the rubber bla dd e r l oc a te d w ith in t he bo tto m se c tio n. Che c k f or the pr e se nc e of hy dr a uli c fl uid p un c tur e s in the bla dd e r, a nd c log g e d d ra in f ilt e rs 2. Open the bottom dra ins and fill the bottom section of the Fr ustum with clean sand, a tte mpt ing to r e mov e a ll f or e ig n d e br is a nd ro c ks Wh ile fi lli ng u se a wa te r h os e to help remove all air voids. Do not over fill or heap the sand above the flang e of the bottom section, since this may become a hindra nce w hen later repla cing the middle section. 3. Thoroug hly clea n the top flang e of the bottom section and the bottom flang e of the middle section. I f it is desired to have the wate r table hig her tha n the top flang e of the bottom section, then apply a g ener ous bead of silicone to the g roove loc a te d w ith in t his fl a ng e I f i t is de sir e d to op e ra te un de r d ry c on dit ion s, the n th is ste p is op tio na l. 4. Place, a lign, a nd bolt the middle section on top of the bottom section. 5. Continue filling the F rustum with sand in the same manne r as Step 2.

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177 App e ndix B: (C ont inue d) 6. Once the level of sand is approximately half wa y up the middle section, stop filling a nd beg in alluviation. 7. Connect the hose of the alluviation to a conve nient fauc et, point the alluviation awa y from any sensitive equipment, and ope n the fa ucet. Chec k to ensure tha t the ports located a t the bottom of the alluviation are not plug g ed with sand, a nd that they spray a substantial strea m. Turning the wate r on bef ore inser ting the a llu via tio n h e lps to a vo id f utu re c log g ing of the po rt s. 8. Using scaf folding or some sort of w orking platform, slowly push the alluviation into the soil. Do not force the alluviation, it shoul d prac tically insert itself under its ow n w e ig ht. 9. Allow the alluviation to penetra te throug h the sand to the bladde r, taking car e not to puncture the bladder 10. Once the alluviation rea ches the bottom of the Frustum, slowly pull the alluviation up and continue this proc ess in a cloc kwise patter n (F igur e B -1). 11. After alluviation is completed, remove the alluviation befor e turning off the fa uc e t. T his wi ll a lso he lp t o a vo id f utu re c log g ing of the po rt s. 12. Rinse off any sand that may have c ollected on the top f lang e of the middle section. I f i t is de sir e d to ha ve the wa te r t a ble hig he r t ha n th e top fl a ng e of the mid dle se c tio n, the n a pp ly a g e ne ro us be a d o f s ili c on e to t he g ro ov e loc a te d w ith in t his fl a ng e I f i t is de sir e d to op e ra te un de r d ry c on dit ion s, the n th is s te p is op tio na l. 13. Place, a lign, a nd bolt the top flang e (lid) to the middle sec tion.

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178 App e ndix B: (C ont inue d) 14 Con tin ue to f ill the F ru stu m by us ing a wa te r h os e to w a sh sa nd fr om a bu c ke t (F igur e B -2). This allows the top portion of the sand to settle throug h water under its ow n w e ig ht. 15 On c e c omp le te d, a llo w a t le a st a n h ou r f or the sa nd to s e ttl e a nd wa te r t o d ra in ( if desired) befor e beg inning pr essurization. Additional sand may need to be added a s th e sa nd wi thi n th e F ru stu m se ttl e s. 16 On c e the de sig na te d w a iti ng pe ri od ha s e la ps e d, ins pe c t th e oil le ve l w ith in t he oil p r e s s u r e p o t a n d f i l l i f n e c e s s a r y. 17. Connect an a ir hose fr om a pre ssurized air supply to the dry er, a nd drain a ny e xistin g wa te r f ro m th e sy ste m. 18. Slowly incre ase the pressure in 5 psi increments, continuously monitoring the hy draulic pr essure inside the bladder via a pr essure transduce r loca ted at the bo tto m of the F ru stu m. 19. After waiting for the sy stem to stabiliz e, re peat Step 18 until the maxi mum desired pr essure is reac hed. 20 Al low a 24 hr wa iti ng pe ri od be fo re be g inn ing a ny c on str uc tio n p ro c e du re s. B.2 Drilled Sh aft Construction 1. Pr e pa re a nd pr e ssu ri ze t he F ru stu m in a c c or da nc e wi th t he pr oc e du re ou tli ne d in “F rustum Prepara tion and Pressurization.” 2. Se c ur e the c a sin g te mpl a te to t he top of the F ru stu m us ing tw o la rg e c -c la mps ensuring not to over-tig hten the cla mps and distort the template.

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179 App e ndix B: (C ont inue d) 3 S l i d e t h e b o t t o m o f t h e t e m p o r a r y c a s i n g i n t o t h e t e m p l a t e a n d a t t e m p t t o s l o w l y push and rotate the ca sing in by hand. 4. On c e the c a sin g c a n n o lo ng e r b e a dv a nc e d, us e the sin g le fl ig ht a ug e r t o e xca va te the so il i ns ide the c a sin g do wn to w ith in t hr e e inc he s o f t he bo tto m. D oin g so remove s and soil plugs that may form in the ca sing. A ttempt to advance the casing ag ain by rotating and pushing with the hands. I f the c asing advanc es, then repe at this step until i t will no longer advanc e by hand. 5 P l ac e t h e d ri v i n g an v i l o n t o p o f t h e c as i n g, an d b egi n t o ad v an ce i t b y d ro p p i n g a sle dg e ha mme r f ro m a he ig ht o f f ou r i nc he s o nto the a nv il. Af te r f if ty re pe tit ion s, remove the anvil and use the sing le flig ht aug er to e x cava te sand to within three inches of the bottom. R epea t this st ep until the casing is driven to the prope r depth. 6. Use the c lean out bucke t to ex cava te the re maining soil down to the bottom of the casing Under wet conditions, it is advisable to leave the clea n out bucket in the e xca va tio n to he lp m a int a in a fl a t bo tto m. 7. Measur e the pr oportions of sand, ce ment, and wa ter to use in the mix design. To ensure sufficie nt mortar volume and w orkability use 37.14 kg of sand, 18.48 kg of ce ment, and 10.17 kg of wa ter ( w/c = 0.55). 8. Mix the mortar in a ccor dance with ASTM standards for mix ing c oncre te, disreg arding any ref ere nces to c oarse ag g reg ate.

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180 App e ndix B: (C ont inue d) 9. Plu g the bo tto m of the tr e mie pip e wi th a pie c e of a pla sti c ba g a nd se c ur e wi th tape. Avoid a pply ing too much ta pe, or the mortar may not be able to br eak the se a l up on pla c e me nt. I t is he lpf ul t o c ut s ma ll s lit s in the ta pe a ft e r s e c ur ing to e ns ur e tha t th e mor ta r w ill br e a k th e se a l. 10. Remove the driving template fr om around the c asing and slide a pe rmane nt casing sleeve over the temporar y casing Push the permane nt casing sleeve ha lf wa y int o th e so il. 11. Place a plastic g arba g e bag around the perma nent ca sing a nd on top of the Fr ustum to catch any excess mortar dur ing the pour. 12. Slide the casing reta iner ring over the temporar y casing and position above the perma nent ca sing. Sec ure the fee t of the re tainer r ing to the f lang e of the Fr ustum wi th t he c -c la mps 1 3 Fi l l t h e h o p p er wi t h m o rt ar an d p o s i t i o n i t o v er t h e c as i n g. 14. I nsert the tre mie into the casing and attac h to the hopper using the quick conne ct a s s e m b l y. 15. L ower the tremie until it rests on the bottom of the excavation. 16. Open the va lve on the hopper and fully char g e the tre mie. L ift the tremie to bre ak the plu g a nd a llo w t he mor ta r t o f low O c c a sio na lly lif t th e tr e mie if the fl ow ra te beg ins to decre ase. H oweve r, take car e to avoid bre aching the tremie, or lifting the tremie a bove the r ising mortar head.

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181 App e ndix B: (C ont inue d) 17. Allow the mortar to f low up and over the top of the c asing befor e closing the valve on the hoppe r. Disconne ct the hopper and re move the tre mie. 18. Caref ully alig n the over head lift a nd extract the ca sing in a continuous manner. 19. Remove the c asing reta iner ring and cclamps, then c ut the plastic bag awa y from t h e p er m an en t ca s i n g. 20 Ad d mo rt a r t o th e top of the sh a ft a nd fi nis h u sin g a tr ow e l. 21 Whe n th e mor ta r b e g ins to s e t, s pr a y the le ve lin g dis k w ith lub ri c a nt t o a vo id sticking to the morta r, and pla ce it on top of the sha ft to cast a le vel surfa ce f or fu t u re t es t i n g. 22 Cle a n th e e qu ipm e nt. B.3 St at ic Loa d Te st 1 At t ac h t h e s t at i c l o ad t es t fr am e t o t h e F ru s t u m u s i n g fo u r o f t h e m i d d l e f l an ge bolts (Fig ure B -1). 2. Remove the leve ling disk fr om the top of the shaf t and place the load ce ll and jack betwee n the top of the shaf t and the bottom of the static fr ame ( Fig ure B -2). Run the loa d c e ll w ir e to t he int e nd e d d a ta a c qu isi tio n d e vic e a nd c on ne c t. 3. Attach the hy draulic hose from the ha nd pump to the jack. 4. Posit ion at least two L VDT’s on e ither side of the shaft with the plung ers r esting on the surfa ce of the load ce ll alignment plate (F igur e B -2). 5. Attach the L VDT wire s to the transduce rs then to the intended da ta ac quisiti on device

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182 App e ndix B: (C ont inue d) 6. Pum p th e ja c k h a nd le a nd mon ito r t he loa ddis pla c e me nt r e a din g s a s th e te st prog resse s (Fig ure B -3). Onc e the maximum l oad or displac ement is attained, close the supply valve a nd allow the ac quisiti on device to rec ord suffic ient data. 7. After a fe w sec onds (appr ox imately 15 seconds) slowly open the va lve and a llow pressure to bleed fr om the jack. Attempt to re lieve pre ssure slowly so that enoug h data c an be c ollected to def ined an unload c urve. 8. On c e the te st i s c omp le te r e mov e a nd sto re a ll d e vic e s. B.4 St at nam ic Loa d Te st and C ali br at ion Te st ing 1. Prior to setup, estimate the maximum desired loa d to obtain during the test. Using the fu e lfo rc e c ur ve s a nd the op e ra tor g ra ph s, de te rm ine the mos t a pp ro pr ia te te st config uration. 2. I f n e c e ssa ry to c ha ng e ma ss c on fi g ur a tio ns f oll ow the ste ps be low I f t he ma ss config uration is sufficie nt for the test, proc eed to step 16. 3. Using a lifting sy stem, remove the masses fr om the catc h fra me (F igur e B -4). 4. Remove both shock absor bers f rom the slide ca rriag es. To do this, remove the upper c otter pin and wa sher, then pull the top of the shock absor ber of f of the mounting stud (F igur e B -5). B efor e re moving the top of the sec ond shock, plac e one hand unde r the slide ca rriag e. Pull the upper c otter pin and re move the washe r of the r emaining shock absor ber. Pull the top of the shock a way from the masses and of f of the mounting stud. The ca rriag e should slide down and of f of the ca rriag e ra ils. P erf orm the same ope ration to the other side

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183 App e ndix B: (C ont inue d) 5. Un bo lt t he c a rr ia g e ra ils fr om t he top ma ss, bu t on ly loo se n th e bo tto m f ou r b olt s of ea ch ra il (Fig ure B -6). 6. Rest the mass stack on the g round or some othe r supporting device taking car e not to allow debris to enter the cy linder. 7. Unscre w the muffle r lid then attac h a cha in to the opposing pick e y es of the top mass. L ift the mass off of the stack a nd place aside (F igur e B -7). 8. At ta c h a c ha in t o th e pic k e y e s o f t he low e st m a ss t o b e re mov e d. Th e e nti re ma ss stack c an be lifte d with any two opposing pic k ey es, so the streng th of ea ch pick s h o u l d n o t b e a n i s s u e. I f t h e a l i gn m en t d o we l s o f t h e m as s es b i n d d ri v e a we d ge betwee n the masses to sepa rate 9. Remove the de sired amount of ma sses and plac e in a sa fe loc ation. 10. I f masses a re to be added instea d of re moved, pick the de sired amount of additional mass and lower onto the mass stack. 11. Wit h the top mass suspended, bolt the ca rriag e ra ils onto t he to mass and tig hten the bottom four bolts of eac h side (F igur e B -8). 12. Screw the muffler lid back onto the top of the silenc er a nd pick the mass stac k. 13 At tac h t he car ri age sl id es i n rev ers e ord er t han ho w t hey were r emo ved (Figur e B9). 14 L oc k th e te e th i n th e do wn po sit ion by pu lli ng the loc kin g c ha ins of e a c h to oth and plac ing the locking wire throug h the cha in. 15. L ift the mass stack, a lign, a nd lower throug h the ca tching fra me.

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184 App e ndix B: (C ont inue d) 16. Place a long boa rd (2" x 4") on top of the mass stack a nd use to lift the catc hing fra me. 17. Remove four bolts from the top flang e of the Fr ustum (eac h bolt removed must be 90 deg ree s apar t). 18 Al ig n th e re ma ini ng bo lt h e a ds wi th t he la rg e r h ole s in the ba se of the c a tc h f ra me and lower the statnamic de vice on top of the Fr ustum. Bolt the fra me down using the four long er F rustum bolts (Fig ure B -10). 19. L ower the mass stack a nd remove the boar d from the top of the mass stack. 20. Place the loa d cell on top of the sha ft and wire to the data a cquisition device. 21 L oa d th e pis ton wi th 0 .5 0 g of ri fl e po wd e r t he n th e de sir e d a mou nt o f f ue l pe lle ts (F igur e B -11 and B -12). Scr ew the de sired vent pin to the vent lid, then scr ew the vent lid to the top of the piston. 22. Attach the g low plug w ire to the g low plug situate d in the bottom of the piston. Gre ase the vent pin and the top inch of the piston sides to ease the inse rtion of the piston int o the cy linder (F igur e B -13). 23. Tilt and tap the piston such that the rifle powder within is compacted a g ainst the g low plug ( Fig ure B -14). 24. Place the piston inside of the c y linder and lowe r the mass stac k (F igur e B -15). En su re tha t th e g low plu g is p oin te d in a sa fe dir e c tio n. Af te r t he sta c k is l o w e r e d r e l e a s e t h e c a t c h t e e t h a n d m o v e t h e o v e r h e a d l i f t o u t o f t h e w a y.

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185 App e ndix B: (C ont inue d) 25. Attach the a cce leromete r wire to the acc eler ometer a nd the data a cquisition device 26 Pe rf or m a ny ne c e ssa ry op e ra tio ns fo r t he da ta a c qu isi tio n p or tio n o f t he te st. 27. When rea dy to perfor m the test, chec k to make sure that the ar ea is c lear and by sta nd e rs a re a la rm e d. At ta c h th e g low plu g wi re to a DC po we r s up ply to commence ignition. 28. Repea t the proce ss outlined above whe n perf orming calibra tion tests, but disreg ard step 17 a nd 18. I nstead of mounting the ca tch fra me to the top of the Fr ustum, lower and bolt it to the rig id concr ete ba se. 29 Sin c e no fo un da tio n d isp la c e me nts a re to b e mon ito re d in the c a lib ra tio n te st, dis re g a rd ste p 2 5. Th e on ly re qu ir e d tr a ns du c e r i s th e loa d c e ll.

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186 App e ndix B: (C ont inue d) Fig ure B -2 Placing load ce ll and jack ( left) a nd L VDT’s ( rig ht). Fig ure B -1 Taking bolts out of Frustum (left) and plac ing sta tic fra me (rig ht).

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187 App e ndix B: (C ont inue d) F ig ur e B -3 Pe rf or min g the sta tic te st. Fig ure B -4 Removing the mass stack.

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188 App e ndix B: (C ont inue d) Fig ure B -5 Removing the shocks (le ft) and the slide car riag es (r ight) F ig ur e B -6 Un bo lti ng the c a rr ia g e ra ils

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189 App e ndix B: (C ont inue d) F ig ur e B -8 At ta c hin g the top ma ss. Fig ure B -7 Remove the top mass ( left) a nd the desire d mass stack (r ight)

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190 App e ndix B: (C ont inue d) Fig ure B -9 Re-a ttaching the ca rriag e slides (lef t) and locking the teeth ba ck (r ight) Fig ure B -10 B olting the c atch f rame to the F ru stu m.

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191 App e ndix B: (C ont inue d) Fig ure B -12 Placing the rifle pow der ( left) a nd the statnamic fue l (rig ht) into the piston. Fig ure B -11 Weig hing out the r equire d rifle powde r (0.5 g ).

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192 App e ndix B: (C ont inue d) F ig ur e B -1 4 T a p th e pis ton on sid e to pack r ifle powde r. Fig ure B -13 Gre ase the vent pin and the piston.

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193 App e ndix B: (C ont inue d) Fig ure B -15 Seat the piston and lowe r the ma sse s.

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194 Fig ure C-1 Statnamic Mini Tester Append ix C: Statnam ic Mini Tester Drawings