DEVELOPMENT AND USE OF A VOLUMETRIC TRANSDUCER FOR STUDIES OF PARAMETERS UPON SOIL COMPACTION By J o se p h Der H o v a n e sia n AN ABSTRACT Subm itted t o th e S c h o o l f o r Advanced Graduate S t u d i e s o f M i c h i g a n S t a t e U n i v e r s i t y o f A g r i c u l t u r e and A pplied S c ie n c e in p a r t ia l f u l f illm e n t th e req u irem en ts f o r the degree of DOCTOR OF PHILOSOPHY Departm ent o f A g r i c u l t u r a l E n g in e e r in g Approved of JOSEPH DER HOVANESIAN AN ABSTRACT L a r g e m a c h i n e s and r e p e a t e d t r a f f i c a re com pacting our a g r i c u l t u r a l s o i l s * o f modern f a r m i n g The l a c k o f i n f o r ­ m ation c o n c e r n in g th e b e h a v io r o f c u l t i v a t e d so ils pered a ra tio n a l b a sis rem ed ial e f f o r t s . fo r the so lu tio n , In order to c r e a t e h a s ham­ an e m p i r i c a l s t u d y was c o n d u c t e d in w hich b u lk d e n s i t y o f s o i l was measured a t v a r i o u s m e a n - s t r e s s load in gs* A ccordin g t o a co-w ork er, to the m ean -stress in s o i l . bulk d e n s it y P h y sica lly , found by t a k i n g th e a l g e b r a i c is rela ted the m ean -stress mean o f s o i l stress is in th r ee m u tu a lly p erp en d icu la r d ir e c t io n s at a p o in t. In e x p e r im e n ts perform ed h e r e , d ifferen t v a l u e s w e r e a p p l i e d b y means o f h y d r o s t a t i c d e n s i t y w a s m e a s u r e d i n tw o d i f f e r e n t w a y s . placed m ean-stress pressure. F ir st, B ulk s o i l was i n a s m a l l r u b b e r b a l l o o n w h i c h was c o n n e c t e d t o n o n - co lla p sib le p la stic tu b in g. B ulk d e n s i t y c h a n g e s in s o i l w e r e t h e n a c c o m p a n i e d by a i r d i s p l a c e m e n t tubing* in the p l a s t i c The d i s p l a c e m e n t was m e a s u r e d b y movement o f a m er­ cury bubble in a c a lib r a t e d c a p illa r y tube. Second, a stra in - g a g e t r a n s d u c e r w as u s e d w h i c h was d e s i g n e d and c o n s t r u c t e d for t h is purpose. tu b in g. Its The t r a n s d u c e r was c o n n e c t e d t o t h e a b ility t o r e c o r d s m a l l c o n t i n u o u s volum e c h a n g e s w as a n i m p o r t a n t c o n t r i b u t i o n t o w o r k p r e s e n t e d On t h e b a sis v a rio u s m oisture p la stic of te sts contents, perform ed w i t h t h r e e in t h i s so il th esis. types at a g e n e r a l m ath em atical e q u a tio n iii JOSEPH DER HOVANESIAN AN ABSTRACT r e l a t i n g m e a n - s t r e s s w i t h b u l k d e n s i t y , w as d e v e l o p e d . e m p i r i c a l e q u a t i o n , w hich i s d ep en d s on i n i t i a l co n d itio n s are: b a s e d on l a b o r a t o r y t e s t s , c o n d i t i o n s and t w o c o n s t a n t s . 1 ) The i n i t i a l i n i t i a l m ean-stress sta te The The i n i t i a l s o i l bulk d e n s i t y , in the s o i l . 2) The The t w o c o n s t a n t s d e p e n d on s o i l p a r a m e t e r s . The e m p i r i c a l l y d e v e l o p e d r e l a t i o n s h i p c o n n e c t i n g mean s t r e s s w i t h b u l k d e n s i t y was a d a p te d f o r s p e c i a l may a i d in the d e s ig n , fo r a given so il. s e l e c t i o n and u s e o f f a r m m a c h i n e r y Some o f t h e a p p l i c a t i o n s o f th e adapted m ea n -stress v e rsu s b u lk -d e n sity eq uation s are: mine change in b u lk d e n s ity A X o ccu rrin g m e a n - s t r e s s a p p l i c a t i o n from G o to t o CT0 u s e s w hich l) in a s o i l To d e t e r ­ due t o a CTmaX} t h e n r e l i e v e d back 2 ) To d e t e r m i n e t h e maximum m e a n - s t r e s s ^max l o a d t h a t may be a p p l i e d to a given s o i l p e r c e n t change in bulk d e n s i t y is if AT/ Toe given . > the c r i t i c a l DEVELOPMENT AND USE OP A VOLUMETRIC TRANSDUCER FOR STUDIES OF PARAMETERS UPON SOIL COMPACTION By J o s e p h Der H o v a n e s ia n A THESIS S u b m itted t o th e S c h o o l f o r Advanced G raduate S t u d i e s M ichigan S t a t e U n iv e r sity of A g ricu ltu re A p p lied S c ie n c e in p a r t i a l f u l f i l l m e n t the req u irem en ts fo r th e degree o f DOCTOR OF PHILOSOPHY Departm ent o f A g r i c u l t u r a l E n g in e e r in g Year 1958 and of ProQuest Number: 10008606 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. uest ProQuest 10008606 Published by ProQuest LLC (2016). Copyright of the Dissertation is held by the Author. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code Microform Edition © ProQuest LLC. ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 48106 - 1346 V J o s e p h Der H o v a n e s i a n can did ate fo r the degree of D octor o f P h ilo so p h y F i n a l e x a m i n a t i o n , A p r i l 2 9 , 1 9 5 8 , 8 : 0 0 A . M . , Room 2 1 8 A g r i c u l t u r a l E n g in e e r in g Departm ent D isserta tio n : D e v e l o p m e n t and U s e o f a V o l u m e t r i c T r a n s d u c e r f o r S t u d i e s o f P a r a m e t e r s Upon S o i l C o m p a c t i o n O u tlin e o f S tu d ie s M ajor S u b j e c t : M in o r S u b j e c t : A g r ic u ltu r a l E n g in eerin g M athem atics B io g r a p h ic a l Item s Born, August 14, 1 9 3 0 , D e t r o i t , M ichigan U ndergraduate S t u d i e s , M orn in gsid e C o l l e g e , S io u x C i t y , 1 9 4 9 - 5 0 , M ichigan S t a t e U n i v e r s i t y 1 9 5 0 -5 3 ( B . S . ) M ajor S u b j e c t : A g r ic u lt u r a l E ducation M in o r S u b j e c t s : P h y s i c a l S c i e n c e and Shop G raduate S t u d i e s , M ichigan S t a t e U n i v e r s i t y , (M.A. i n E d u c a t i o n ) and 1 9 5 4 - 5 8 E xp erien ce: 1953-54 T r u c k M e c h a n i c , Reo M o to r Company, L a n s i n g , M ic h ig a n , 1 9 5 1 - 5 4 , Graduate T e a c h in g A s s i s t a n t , M ic h ig a n S t a t e U n i v e r s i t y , 1 9 5 4 - 5 6 , G raduate R esearch A s s is t a n t , 1956-58. Member o f A m e r i c a n S o c i e t y o f A g r i c u l t u r a l E n g i n e e r s ; Sigma P i S i g m a , P h y s i c s H o n o r S o c i e t y ; P i Mu E p s i l o n , M a t h e m a t i c s Honor S o c i e t y ; S o c i e t y o f t h e Sigma X i . Vi TABLE OF CONTENTS page I. INTRODUCTION ............................................................................................ 1 ................... 6 I I . REVIEW OF LITERATURE ........................ ’.............................................. 8 D efin itio n III. o f t e r m s and s y m b o l s used DESIGN AND DEVELOPMENT OF A RECORDING VOLU?*ETRIC TRANSDUCER AND AN INDICATING VOLUMETER ................ 12 ...................* ..................... 12 The I n d i c a t i n g V o l u m e t e r The R e c o r d i n g V o l u m e t r i c T r a n s d u c e r ................... 16 ..................... 16 ........................................ 17 .......................................... 17 C a l i b r a t i o n and S e n s i t i v i t y o f T r a n s d u c e r s IS T e m p e r a t u r e C o m p e n s a t i o n and E f f e c t s o n T r a n s d u c e r s .................................................................. 21 B asic P r in c ip le s of Transducer Two M o d e l s o f T r a n s d u c e r s L in e a r ity of Transducers Com parison o f V o lu m e ter w i t h T r a n sd u c e r .... IV . DEVELOPMENT OF A LABORATORY TECIP’IQ/JE FOR THE STUDY OF THE EFFECTS OF PARAMETERS UPON SOIL COMPACTION ............................................................................................... The G e n e r a l T e c h n i q u e Impact L o a d in g ......................................... ................................................. V . PRESENTATION AND ANALYSIS OF LABORATORY DATA . . . . 26 26 28 31 T ests of C lay S o i l T ests of S i l t y Loam S o i l T ests of S a n d y Loam S o il Impact T e s t s ....................................................... 52 A d a p ta tio n o f E q u a tio n s R e l a t i n g B ulk D e n s i t y ( X ) and Mean S t r e s s ( C ) t o F i e l d P r o b l e m s and S p e c i a l C a s e s ................... 55 R epeated .............................................................. 23 ................................... ..................... 31 36 45 v ii Case 1 : Case 2 : C a s e 3: F i n a l b u lk d e n s i t y change o c c u r r i n g i n a s o i l due t o a l o a d a p p l i c a t i o n f r o m Go t o CTma x ( f i n a l ) t h e n t h e l o a d r e l i e v e d b a c k t o G*0 .............. 57 T r i n t e r m s o f G* when "jfor i s n o t known ................................ 58 D e t e r m i n a t i o n o f G*max f o r a p r e s c r i b e d A T / T 0 c when Kr = Kc = 0 .............................................. 58 .......................... 59 Exam ples o f a d a p ted eq u ation s V I . SUMMARY AND CONCLUSIONS.......... .................................. 60 Summary . . .................................................................................... 60 C on clu sion s ............................................................................... 63 SOIL DATA CF THREE TYPES USED IN EXPERT TENTS ..................................... 65 VOLUME CHANCE A V VERSUS PRESSURE ( p s i ) DEVELOPED IN SOIL SAT.RLES ................................... 66 TEST DATA FROM 3 2 . 6 $ SILTV LOAM S O I L ........................................ 67 TEST DATA FROM 1 3 . 3 $ SILTY LOAM SOIL .................................................. 68 TEST DATA FROM 2 0 $ SILTY LOAM SOIL .................................................. 69 TEST DATA FROM 1 6 $ SILTY LOAM S O I L .................................................. 70 APPENDIX G: TEST DATA FROM S $ CLAY SOIL . . . 71 APPENDIX H: TEST DATA FROM 3 0 . 9 $ CLAV SOIL. 72 APPENDIX I : TEST DATA FROM 1 . 3 $ SANDY LOAM S O I L .................................................. 73 TEST DATA FROM 8$ SANDY LOAD SOIL.................................................................... 74 TEST UAmA FROM 2 0 $ SANDY LOAM SOIL .................. 75 V I I . APPENDICES APPENDIX A: APPENDIX B: APPENDIX C: APPENDIX D: APPENDIX E: APPENDIX F: APPENDIX I : APPENDIX K: v iii LIST OF TABLES T ab le 1 Page A p p lied load ( G ) v e r s u s bulk d e n s i t y (T) f o r c l a y s o i l a t t w o m o i s t u r e l e v e l s .................... 32 A p p l i e d l o a d (CT) v e r s u s bulk d e n s i t y ( T ) f o r s i l t y loam s o i l a t f o u r m o i s t u r e l e v e l s ............................................................................................ 38 A p p lie d load { C ) v e r s u s b u l k d e n s i t y ( "T) f o r san dy loam s o i l a t t h r e e m o is t u r e l e v e l s ...................................................... 46 Summary o f p a r a m e t r i c a n d o t h e r c o n s t a n t s f o r s o i l s s t u d i e d ................................................................... 61 BIBLIOGRAPHY .............................................................................................................. 76 2 3 4 ix LIST OF FIGURES igu re Page 1 V olum eter photo 2 V o lu m e tr ic t r a n s d u c e r photo 3 I n d i c a t i n g V olum eter ........................................................................ 13 ......................................... 13 ........................................................... 14 4 Means f o r c a l i b r a t i n g v o l u m e t r i c t r a n s d u c e r . 14 5 The v o l u m e t r i c .............................................. 15 6 Volum e c h a n g e m e a s u r e m e n t s by v o l u m e t e r a n d v o l u m e t r i c t r a n s d u c e r .......................................... 24 7 G eneral view o f t e s t 27 8 Impact m echanism 9 A n a l y s i s o f im pact l o a d i n g a p p l i e d by a tractor tir e .................................................................. 30 B ulk d e n s i t y X v e r s u s m e a n - s t r e s s CT f o r 8$ m oisture co n ten t c la y s o i l ( a ir d ried ) 33 10 11 12 13 14 15 transducer equipm ent ................................. ............................................. 30 . B ulk d e n s i t y I f v e r s u s m e a n - s t r e s s CT f o r 3 0 .9 $ m oistu re c o n ten t c la y s o i l (low er p la stic lim it) .................................. 34 B ulk d e n s i t y I f versu s m ean-stress C fo r c l a y s o i l a t 3 0 .9 $ (low er p l a s t i c l i m i t ) and a t 8 . 0 $ ( a i r d r i e d ) m o is t u r e c o n t e n t s - s e m i - l o g p l o t - ............................................................... 35 B ulk d e n s i t y X v e r s u s m e a n - s t r e s s CT f o r 1 3 . 3 $ m o i s t u r e c o n t e n t s i l t y lo a m s o i l ( a i r d r i e d ) ............................... , .............................................. 39 T B ulk d e n s i t y v e r s u s m e a n - s t r e s s G" f o r 1 3 .3 m oisture con ten t (a ir d r ie d ) s i l t y l o a m s o i l - s e m i - l o g p l o t - .................................. 40 T B u lk d e n s i t y v e r s u s m e a n - s t r e s s G* f o r 20$ m oisture c o n ten t ( t y p ' c a l f i e l d con­ d i t i o n ) s i l t y l o a m s o i l ................................................ 41 X Figure 16 17 18 19 20 21 22 23 24 25 26 Page B u l k d e n s i t y X v e r s u s G- ( c o r r e c t e d t o s t r a ig h t l i n e ) fo r 20# m oisture co n ten t s i l t y l o a m s o i l - s e m i - l o g p l o t - ............................ 42 Bulk d e n s i t y T v e r s u s CT m e a n - s t r e s s f o r 16# m o istu r e co nten t ( t y p i c a l f i e l d c o n d i t i o n s ) s i l t y l oa m s o i l ....................* .............. *. 43 Bulk d e n s i t y X v e r s u s m e a n - s t r e s s CT(corr e c t e d t o s t r a i g h t l i n e ) f o r 16# m o is t u r e c o n t e n t s i l t y l o a m s o i l ..................................................... 44 Bulk d e n s i t y X v e r s u s m e a n - s t r e s s 1*3# moisture conten t (a ir dried) l oa m s o i l • • *• 47 Bulk d e n s i t y X v e r s u s m e a n - s t r e s s CT f o r 8 # m o i s t u r e c o n t e n t s a n d y l oam s o i l ........................ 45 Bulk d e n s i t y X v e r s u s m e a n - s t r e s s CT f o r s a n d y l oa m s o i l a t 3 2 . 6 # ( l o w e r p l a s t i c l i m i t ) and 1 . 3 # ( a i r d r i e d ) m o i s t u r e le v e ls - sem i-log plot - ................................................ 49 Bulk d e n s i t y X v e r s u s m e a n - s t r e s s G"* f o r 3 2 . 6 # m o i s t u r e c o n t e n t s a n d y l oa m s o i l ( l o w e r p l a s t i c l i m i t ) .......................................................... 50 G* f o r sandy X Bulk d e n s i t y v e r s u s m e a n - s t r e s s (j f o r 8 # m o i s t u r e c o n t e n t s a n d y l oa m s o i l - s e r a i - l o g p l o t - ................................................................... 51 R e p e a t e d impact a p p l i c a t i o n s o f m e a n - s t r e s s v e r s u s bulk d e n s i t y X f ° r 20# m oisture c o n t e n t ( f i e l d c o n d i t i o n s ) s i l t y loam s o i l .................................................... 53 O' R e p e a t e d i m p a c t a p p l i c a t i o n s o f m e a n - s t r e s s Gv e rsu s bulk d e n s it y X fo r moisture c o n t e n t ( f i e l d c o n d i t i o n s ) s a n d y l oa m s o i l ....................................................................................................... 54 A t y p i c a l c o m p r e s s i o n and r e l a x a t i o n c u r v e f o r a g r i c u l t u r a l s o i l s r e l a t i n g X and CT • • • • 56 xi ACKNOWLEDGMENT S The a u t h o r w i s h e s t o e x p r e s s to: h is s i n c e r e acknow ledgm ents . D o c t o r W. F . B u c h e l e , a s major p r o f e s s o r f o r h i s g u i d a n c e and a s s i s t a n c e throughout the e n t i r e in sp irin g course of t h is endeavor. D o c t o r D. J . M ontgom ery f o r h i s t i m e l y s u g g e s t i o n s and encouragem ent. D o c t o r s M. L . Esmay and H. S t e l s o n f o r s e r v i n g on t h e g u i d a n c e c o m m i t t e e and f o r t h e i r i n t e r e s t Mr. G. E. V a n d e n B e r g f o r h i s to in the p r o j e c t . im m easurable c o n t r i b u t i o n th e c o m p le t io n o f t h i s work. P r o f e s s o r s A. W. F a r r a l l who a p p r o v e d t h e r e s e a r c h a s s i s t a n t s h i p and.H . F . M cC olly f o r h i s v a l u a b l e du rin g th e e a r l y phases o f t h i s M essers F. su g g estio n s in v e stig a tio n . J . M ortimore f o r h i s a s s i s t a n c e in e d i t i n g and Y i l r a a z T o k ad f o r h e l p i n p r e p a r a t i o n o f f i g u r e s . Mr. and M r s . C h a r l e s D e r H o v a n e s i a n , t h e w r i t e r t o whom m o s t l o v e and l i f e - l o n g d e d i c a t e d t o them . in d eb ted n ess is owed. parents o f the For t h e i r f a i t h f u l encouragem ent, t h i s d i s s e r t s t i o n ' i s I. The d e c l i n e INTRODUCTION of v ir tu a lly a l l h is t o r ic a l n ation s of im portance has c o in c id e d w it h problem s o f s o i l c o m p a c tio n . I n many o f t h e cases, for M e s o p o t a m i a , and o t h e r s , of in ten siv e p ra ctices* e x a m p l e , The Roman E m p i r e , B q y p t , th e problem s a r o se as a c o n se q u en ce i r r ig a t i o n w ithou t proper s o i l More r e c e n t l y , C a lifo rn ia management has su ffe r e d th e lo ss o f 2 , 0 0 0 ,0 0 0 a c r e s o f C la s s I land b ecau se o f e x c e s s i v e com paction, w ith another 2 , 0 00 ,0 0 0 a c r e s d e stin e d same f a t e w i t h i n a s h o r t p e r i o d o f t i m e p e r so n can r e a d i l y d e t e c t i n o u r own s t a t e symptoms o f (5)*. e x c e s s i v e com paction c o m p a c t i o n a r e somewh at d i f f e r e n t t o d a y from t h o s e w h ich p la g u ed h i s t o r i c a l some o f t h e same c a u s e s may s t i l l p a r ticle-siz e knowledge about d istrib u tio n , be f a c t o r s , causes. but b ecau se of im pact, these The b a s i c causes in creased mecha­ W h i l e b i g g e r t r a c t o r s and i m p l e m e n t s a p p e a r t o produ ction e f f i c i e n c y , th eir long-run e f f e c t s o i l c o m p a c t i o n may be m o s t d i s a s t r o u s . exam ple, to Of c o u r s e , and d r a i n a g e , energy of d rop let o f m o d e r n - d a y c o m p a c t i o n may be r e l a t e d in crease n a tio n s. irrig a tio n p r a c t i c e s a r e no l o n g e r t h e b a s i c n iza tio n . An i n f o r m e d o f M ichigan. The c a u s e s o f e x c e s s i v e more s c i e n t i f i c to the t h e t r e n d t o w a r d more t r a f f i c of sp ec ia lize d on In M ichigan f o r and b i g g e r m a c h i n e s farm ing has p r e sen ted a s e r i o u s oroblem . T h ese problem s are d em o n stra ted by i n a d e q u a t e s o il a ir m ov e- *Numbers i n p a r e n t h e s e s r e f e r t o t h e "BIBLIOGRAPHY*1 on p a g e s 76 t o 7 7 . 2 m e n t , r e d u c e d we t e r in filtr a tio n , low ered c a t i o n exchange c a p a c i t y and u l t i m a t e l y by r e d u c e d c r o p y i e l d s . At t h e p r e s e n t tim e t h e r e a r e e x p e r i m e n t a l t r a c t o r s t h a t w eigh over 1 6 ,0 0 0 pounds. I n t h e thumb a r e a o f M i c h i g a n , bean c o m b in e s h ave b een c o n s t r u c t e d by m o u n tin g o l d t h r e s h i n g m a c h i n e s on a i r p l a n e w h e e l s . These com bines are p u l l e d l a r g e t r a c t o r s and t h e c o m b i n a t i o n a p p l i e d l o a d s on t h e so il. by concentrated A r e d u c tio n o f d a ir y farm ing in t h i s area has caused th e rem oval o f a l f a l f a , p a s t u r e and o t h e r so il resto rin g f u r t h e r adding to the problem . c r o p s from t h e r o t a t i o n , In a n o t h e r a rea o f M ic h ig a n , a d e f i c i e n c y o f n it r o g e n has been d e t e c t e d have r e p e a t e d l y t r a v e l e d track s, at l o c a t i o n s where t r a c t o r w h e e l s on muck s o i l s . no d e f i c i e n c y was o b s e r v e d . among o t h e r t h i n g s , ^etween th e t r a c t o r T h is in d ica tes com paction a f f e c t s n u t r i e n t Many a t t e m p t s h a v e b e e n made t o a l l e v i a t e co n d itio n s. p u lv erize Some p e o p l e h a v e t r i e d so il, p ra ctices. lim ited o r "minimum" t i l l a g e . efforts because th ey lacked b a sic fo r the ju stific a tio n a v a ila b ility . compacted t o t h r o u g h l y m i x and w h i l e o t h e r s ha v e r e s o r t e d c h i s e l i n g and r e l a t e d to deep t i l l a g e , A gain o t h e r s have proposed They have a l l en g in eerin g fa iled these and e r r o r " t y p e . It in t h e ir in form ation o f t h e i r proposed s o l u t i o n s . w riter c la s s i f ie s that The proposed s o l u t i o n s as o f th e " tria l s h o u l d be p o i n t e d o u t h e r e h o w e v e r , some a s p e c t s o f t h e a b o v e p r a c t i c e s may u l t i m a t e l y become accepted in form ation . on t h e b a s i s of s c ie n t if ic that But f i r s t 3 th is i n f o r m a t i o n m ust be s o u g h t and d i s c l o s e d . The l a c k o f a d e q u a t e a g r i c u l t u r a l s o i l m e c h a n i c s in fo r­ m a t i o n h a s f o r some t i m e h a n d i c a p p e d w o r k e r s who h a v e a t t e m p t e d to fin d the so lu tio n (6 ). th eo retica l resu lts, w i t h some m o d i f i c a t i o n s , ex p la in c e r ta in resu lts ph en o m en a. were d e r i v e d id e a liz ed Sin ce so il C i v i l e n g i n e e r s have en gin eers coarse tex tu red , homogeneous, a g ricu ltu ra l s o ils a r e lo w i n a p p a r e n t d e n s i t y , u ltim ate set state at ap p lied to betw een th e f o r c e r esu ltin g co m p letely . so il, stra in , it va ried to S in ce in lead to f a u lt y to s o i l s w ill i n t h e medium. and t h e r e s u l t i n g nor has s o i l F urther, if a certa in to The stress stress has not been p o s s i b l e state itse lf stress state p red ict the w h ich i s a measure o f s o i l c o m p a c tio n . To s e e how f o r c e s a r e a p p l i e d t o Lask use o f t h e s e t h e same s o l u t i o n s a fo rc e ap p lied e v er y poin t has n ot been c l e a r l y d e f in e d , is so ils, s o l u t i o n d e p e n d s on many a s p e c t s o f For exam ple, been d e f in e d and e l a s t i c . ( 1 2 ). r e s e a r c h work. up a s t r e s s i s an h a s b e e n s u c c e s s f u l t o some d e g r e e . r e a s o n i n g and f a i l u r e rela tio n sh ip iso tro p ic e n g i n e e r i n g work a r e l i k e l y Indeed the so il co n d itio n s, n o n - h o m o g e n e o u s and i n e l a s t i c , in c i v i l th eo retica l r e l a t i v e l y h o m o g e n e o u s and e l a s t i c th eo retica l resu lts used these p r e d i c t and u s u a l ly d e a l w ith h ig h ly com pacted, t h u s a p p r o a c h in g th e above i d e a l i z e d textu re, to under t h e a s s u m p t io n t h a t c o n tin u o u s m edia, c iv il U su ally, used c e r t a i n so il by f a r m e q u i p m e n t , ( 1 2 ) h a s i n s t r u m e n t e d a common t r a c t o r t i r e . ,Afi t h data 4 to be c o l l e c t e d from t h i s tire , it i s hoped t h a t in form ation c a n be o b t a i n e d w h i c h may be u s e d t o p r e d i c t w h at f o r c e s a tire a p p lie s to so il. With t h i s kind o f b a sic one may l a t e r be a b l e t o p r e d i c t w h a t s t r e s s expected in so ils due t o t r a c t o r - t r a f f i c . m en tation o f o th e r of so il a ll stress field (2 0 ) , stress of s o i l so il stress. req u ires a se t of q u a n tities in to v alu e. t e n s o r and t h e d e v i a t o r i c sim ila r to h y d ro sta tic is selectio n " tra ce” of the an i n v a r i a n t stress show t h a t v o l u m e t r i c stress M ath em atically i t ten sor. stra in VandenBerg in s o i l stress mean o f at a p o in t. b ein g ind ep en dent o f at the p o in t. mhe tensor. p r e s s u r e and c a n be m e a s u r e d i n s o i l by t a k i n g t h e a l g e b r a i c ex p ressio n in the two c o m p o n e n t s , n a m e l y , in th r e e m u tu a lly p erp en d icu la r d i r e c t io n s o f the He p o i n t e d o u t te n s o r r a th e r than a s i n g l e t e n s o r c a n be s e p a r a t e d The f o r m e r i s a x is p red ictio n u s i n g t h e m o d e l o f a c o n t i n u o u s medium t h e mean n o r m a l s t r e s s e a sily Further in s tr u ­ c a n be e x p e c t e d w i t h e s s e n t i a l l y was a b l e t o d e f i n e form o f a s t r e s s stress c a n be op eration s. so ils, that the states i m p l e m e n t s may r e n d e r a n a c c u r a t e s ta te s that VandenBerg for in form ation , T h is co o rd in a teis ca lled ( 2 0 ) was a b l e is rela ted stress the to to the tra ce tensor. In v i e w o f t h e im portance o f t h i s rela tio n sh ip , it was d e c id e d t o exam ine th e b u lk d e n s i t y v e r s u s m e a n - s t r e s s fu n ctio n to c a refu lly . Sin ce th is rela tio n sh ip be a c o m p l i c a t e d f u n c t i o n c a n be e x p e c t e d d e p e n d i n g on s o i l type, so il 5 m oisture c o n te n t, organic m atter p resen t a t w h i c h a g i v e n mean s t r e s s is ap p lied , many i n s t r u m e n t a t i o n p r o b l e m s w e r e to app ly v a r io u s m ea n -str ess in a h y d r o sta tic d escrib ed in s o i l , ra p id ity and o t h e r f a c t o r s , in volved . I t was p o s s i b l e s t a t e s t o a s m a ll sam ole o f s o i l medium by means o f a w a t e r - p r e s s u r e in s e c t i o n TV. cham be r ^ h e n e x t r e q u i r e m e n t was t o fin d a n a c c u r a t e m ea ns f o r c o n t i n u o u s m e a s u r e m e n t o f b u l k d e n s i t y in s o i l . problem , O r i g i n a l l y t h i s w as c o n s i d e r e d o n l y a s a m i n o r however, t h i s t h e work p r e s e n t e d S o il is phase, g rew i n t o in t h i s a m a jo r p o r t i o n o f d isserta tio n . a c o m p l e x medium w h i c h i s d ifficu lt to d e fin e . I t s many p h y s i c a l p r o p e r t i e s a r e n o t w e l l u n d e r s t o o d . g e n e r a lly recogn ized im p ossib le that it w i l l be v e r y d i f f i c u l t to form u late adequate a n a l y t i c a l b u l k d e n s i t y w i t h mean s t r e s s . is or even law s r e l a t i n g U ndoubtedly th e d e s c r i p t i o n o f b u l k d e n s i t y v e r s u s mean s t r e s s be It in term s o f a model w i l l ju st as d i f f i c u l t . The f i r s t s t u d y was t h e r e f o r e an e m p i r i c a l a p p r o a c h . The b u l k d e n s i t y was r e c o r d e d f o r v a r i o u s m e a n - s t r e s s a p p lica tio n s conten ts. fo r three d iffe r e n t type s o i l s at va rio u s m oisture The o b s e r v e d r e l a t i o n s h i p o f m e a n - s t r e s s v e r s u s b u l k d e n s i t y was t r i e d in v a r io u s e q u a tio n s u n til a general e x p r e s s i o n was f o u n d w h i c h w o u ld be s a t i s i f i e d a g r ic u ltu r a l s o ils by a l l the tested . ^he w r i t e r h o p es t h a t so il state the v a r io u s a s p e c t s c o m p a c t i o n may s o o n be c o o r d i n a t e d . o f work in ^he c o o r d i n a t i o n 6 of these r esu lts w ill so lu tio n to t h i s be e x t r e m e l y i m p o r t a n t p r e s s i n g problem . The e f f e c t s p a r a m e t e r s on c o m p a c t i o n c a n be more c l e a r l y d e a l t w i t h when b a s i c may s e r v e inform ation i s but a l s o of so il u n d e r s t o o d and presented. not o n ly as a guide t o t r a c t o r - t i r e ment d e s i g n , i n an o v e r a l l These r e s u l t s and f a r m - e q u i p - may f u r n i s h a b a s i s f o r r e n o v a t i o n o f a l r e a d y com pacted s o i l s . D e f i n i t i o n s o f Terms and S y m b o l s Used AGRICULTURAL SOIL N a t u r a l medium f o r p l a n t g r o w t h w h i c h c o n s i s t s p rim a rily o f the fo llo w in g fract io n s: 1 . Sand (lmm-O.lmm d i a . p a r t i c l e s ) 2 . S i l t ( 0 . 05mm- 0 . 005mm d i a . " ) 3 . C l a y ( 0 .0 0 2 m m - 0 . 0 0 0 0 5 m m d i a . ") SOIL TYPE: T e x t u r a l C l a s s i f i c a t i o n b a s e d on r a t i o o f above s o i l f r a c t i o n s . BULK DENSITY ( T ) Apparent d e n s i t y o f s o i l w hich i n c l u d e s a i r sp ace in i t ’ s c a l c u l a t i o n . B ulk d e n s i t y i s c o m p u t e d on a d r y w e i g h t b a sis. The t e r m i s u s e d i n t h i s w o r k a s an i n d i c a t i o n o f " v o l u m e t r i c s t r a i n . " MEAN STRESS ( O') May be c a l l e d t h e mean n o r m a l s t r e s s or the "trace" of th e s t r e s s t e n s o r . I t i s d e t e r m in e d e x p e r i m e n t a l l y by a v e r a g i n g measured s o i l s t r e s s a t a p o in t in th r e e m u tu a lly p e r p e n d ic u la r d irectio n . T h i s v a l u e i s an i n v a r i a n t b e in g independent o f c o o r d in a t e - a x i s selectio n . PARAMETRIC CONSTANTS C e r t a in m easurable c o n s t a n t s w hich are c h a r a c t e r i z e d by s p e c i f i c s o i l p a r ­ am eters. A param etric c o n s ta n t as u s e d i n t h i s w o r k may be a f u n c t i o n o f one o r s e v e r a l s o i l p a r a m e t e r s . INITIAL CONDITIONS: M e r e l y r e f e r s t o v a l u e s o f mean s t r e s s ( 6*0 )" a nd b u l k d e n s i t y ( Y o ) a t i n s t a n t wh en o b s e r v a t i o n i s b e g u n . 7 TRANSDUCER: An i n s t r u m e n t t h a t i s c a p a b l e o f c o n v e r t i n g a p h y s i c a l phen o m en o n i n t o m easurable e l e c t r i c a l r e s i s t a n c e or output* SOIL COMPACTION: A w i d e l y a c c e p t e d and som e w h a t i n a d e q u a t e word u s e d t o d e s c r i b e t h e many p h a s e s o f " a g r ic u lt u r a l s o i l m echan ics." The w or d must be t r a n s l a t e d i n c o n t e x t s i n c e i t may h a v e v a r i e d m e a n i n g s . SOIL MOISTURE CONTENT: P e r c e n t w a t e r i n s o i l c a l c u l a t e d on a dry w e ig h t b a s i s . C o il m o is tu r e was d e t e r m i n e d b y o v e n d r y i n g and w e i g h i n g f o r m oisture l o s s . 1 . Lower P l a s t i c L i m i t : A w i d e l y r e c o g n iz e d m oisture co n ten t d esign ation for s o i l . The l o w e r p l a s t i c l im i t i s th e m oisture c o n t e n t a t w h ich s o i l b e g i n s t o l o s e i t s c r u m b l y f e e l and sh o w s a t e n d e n c y t o become p l a s t i c . 2 . A ir D r ie d : E q u ilib ru m m o istu r e l e v e l o f s o i l w ith a i r . The c o n d itio n o f the a ir i s taken as a v e r a g e room c o n d i t i o n s and t h e s o i l i s s p r e a d i n s u c h a mann er t o a l l o w n o r m a l a i r movement t h r o u g h o u t t h e s o i l medium. 3* T y p i c a l E i e l d C o n d i t i o n s : A t y p i c a l m o istu r e c o n te n t a t w hich t i l l a g e o p e r a t i o n s may be p e r f o r m e d . II. REVIEW OF LITERATURE The i m p o r t a n c e o f t h e e f f e c t s of so il p a r a m e t e r s on c o m p a c t i o n h a s b e e n r e c o g n i z e d b y many p e o p l e . The r o l e o f some o f t h e s e in th e param eters is d e s c r i b e d by Soehne f o l l o w i n g m ann er: "An a r e a o f c o m p r e s s i v e s t r e s s i n t h e s o i l w h i c h h a s a r i s e n from th e r o l l i n g o f t r a c t o r o f f i e l d - w a g o n w h e e l s o v e r i t d e p e n d s upon t h e s i z e o f t h e l o a d , t h e s i z e o f t h e c o n t a c t s u r f a c e s b e t w e e n t i r e s an d s o i l , and t h e d i s t r i b u t i o n o f t h e s u r f a c e p r e s s u r e i n t h e s e c o n t a c t s u r f a c e s , a s w e l l a s on t h e k i n d o f s o i l , t h e m o i s t u r e , and t h e d e n s i t y o f t h e s o i l l a y e r s . " 117) A ccording to from an a p p l i e d Soehne, load , w ith sandy s o i l s com p ressive concen trate so il on m o i s t u r e c o n t e n t . that so il is O ther w r i t e r s so ils m oistu re, d e p e n d e n t on s o i l (2 ) h a v e p o i n t e d d e p e n d e n t on s o i l m o i s t u r e to being a fu n c tio n of p a r t i c l e that so ils. S e v e r a l i n v e s t i g a t o r s made e x t e n s i v e 14). p la stic ity and c o h e s i v e p r o p e r t ie s o f s o i l are dependent s t u d ie s d e a lin g w ith p r o p e r tie s of s o i l (1 0 , 13, r esu ltin g t o w a r d t h e l o a d a x i s more t h a n w i t h t h e more p l i a b l e C o h e s i v e and a d h e s i v e m oisture stresses, size and s h a p e . out in a d d it io n I t w as shown g e n e r a l l y b ecom e more p l a s t i c w i t h i n c r e a s i n g except f o r sand w h ich p o s s e s s e s few p l a s t i c p rop erties to begin w ith . so il A tterb erg (l) suggested p la stic ity . These are: t h r e e v a l u e s be u s e d t o d e s c r i b e a ) The u p p e r p l a s t i c m o is tu r e c o n te n t a t w h ich s o i l w i l l b a r e ly flow a p p lied load; b) The l o w e r p l a s t i c lim it, t e n t a t w hich th e s o i l w i l l b a r e ly r o l l lim it, u n d e r an th e m oisture out the con­ in to a w ire; 9 c) The p l a s t i c i t y n u m b e r , t h e d i f f e r e n c e an d l o w e r p l a s t i c ticity . lim its and i t is betw een th e used a s an in d e x o f p l a s ­ These above v a lu e s have gain ed w idespread a r e known a s t h e "A tterberg L im its." " p l a s t i c i t y number" a s d e f i n e d R u ssell (16) It is of exchangeable c a t i o n s a n d d) contrary, (3) Of more d i r e c t (19) O rganic m a t t e r . is sh o w e d t h a t in terest th e com p ression t o work p r e s e n t e d h e r e i n , is stra in He l o w when d e a l i n g w i t h s o i l s shows a v e r y d i r e c t P in t h i s n is rela tio n sh ip content. R u ssia n a g r i c u l t u r a l e n g in e e r s of lim it. In agreem ent w it h above f i n d i n g s , s i n k a g e and m o is t u r e z sin k age, low er p l a s t i c in crea ses , i n d o in g r e s e a r c h work d e a l i n g w i t h m i l i t a r y land l o c o m o t i o n , P = k z 11. To t h e r ep o rted th a t com p ression o f s o i l a t low m o i s t u r e c o n t e n t s . (4) c) N ature in creased . r a p id ly w ith m o istu re above the v eh icle a) N ature o f s o i l s h o w e d t h a t t h e p l a s t i c i t y number d e c r e a s e d as s o i l organ ic m atter Bekker (5 u p a r t i c l e s ) . b) C h e m i c a l c o m p o s i t i o n o f t h e c o l l o i d , Baver depen­ reported th a t a lin e a r r e la t io n s h ip e x i s t s O ther f a c t o r s t h a t have been g iv e n a r e : Terzaghi itse lf s o i l m oistu re. b e t w e e n p l a s t i c i t y number and c l a y c o n t e n t m in era ls, u s e and show n t h a t t h e by A t t e r b e r g i s d e n t on many o t h e r f a c t o r s b e s i d e s upper (7) A ccording t o B ekker, g en era lized exp ression rep resen ts th e form ula: "ground p r e s s u r e , " an e m p i r i c a l e x p o n e n t r e f l e c t i n g c h a n g e w i t h l o a d and k i s fu n c tio n of not on ly th e so il between the r a t io a c o n s t a n t w h ich i s bu t a l s o a th e nature o f load 10 a p p l i c a t i o n and a r e a . A c c o r d i n g t o R. R, P r o c t o r com paction e n e r g y , so il (15), bulk d e n s it y w i l l p r o p o r t io n a lly to m oisture c o n te n t where t h i s when t h e is in c r e a s e alm ost up t o a p o i n t . The p o i n t r e l a t i o n s h i p d e v i a t e s from p r o p o r t i o n a l i t y m oisture co n ten t approaches a " s a tu r a tio n T h is above r e l a t i o n s h i p It fo r a given a p p lied is known a s t h e m oisture t h a t a l lo w s a g iv e n com paction energy t o y i e l d ing sta n d p o in t, or s o i l th is d en sity. knowledge is p o in t." " P ro c to r C urve." used as a gu id e t o determ ine a s o i l com paction s t a t e is a maximum From a c i v i l im portant, lev el en gin eer­ but i t is eq u ally im p o r ta n t from an a g r i c u l t u r a l e n g i n e e r i n g s t a n d ­ p o in t. H o w e v e r , minimum c o m p a c t i o n i s a given f i e l d op eration sin ce problem in a g r i c u l t u r e . seek a s o i l m oisture u su a lly desired during e x c e s s i v e com paction i s a T hus an a g r i c u l t u r a l e n g i n e e r w o u ld l e v e l w hich w i l l resu lt i n minimum comr p a c tio n fo r a given energy in p u t. Spangler (16) was found t o e x i s t a p p lied pressure (a b scissa e) y ield ed m etric case rep orts th at a logarith m ic betw een a v o id s r a t i o (p )• He p l o t t e d the v e rsu s the v o id s r a t io a stra ig h t lin e of n eg a tiv e (e) of s o i l versus logarithm of p ressu re (o rd in a te). slop e, m oistu re c o n te n t, structure, type o f a p p lied lin e c o n d i t i o n s and s o i l s o il type, organic m atter load a r e a , e tc .). T h is curve ^ h e tw o p a r a ­ c o n s t a n t s t h a t accompany any s t r a i g h t d e p e n d e n t on i n i t i a l r ela tio n sh ip are in t h i s param eters in s o i l , {% so il In a g r i c u l t u r a l 11 en g in eerin g , bu lk d e n s ity ra tio (X ) (i. (© ) • e .,X c x an d l / e ) , thus (X ) is (e) are alm ost if (X ) ( p ) , the r e s u lt in g s tr a ig h t were lin e be p r e s e r v e d but w i t h d i f f e r e n t S p angler in d ica ted as w e ll as s tr e s s . param etric of so il However t h i s curve f l a t t e n s stra in if so ils, so il p e r m e a b ilit y o f the ( 8 ) in h is in d icated that relea sed , in d ica ted th a t the so il w ill d eform ation w i l l if For F or im perm eable f i n e ­ H is reason in th e v o i d s t h e volume c f the pore w a te r so il. d iscu ssion so ils load . i s req u ired The r a t e o f o u t f l o w o f t h i s f o r m d i f f e r e n t l y when s u b j e c t He f u r t h e r o f tim e tim e e l a p s e s . o n ly 1 second be s q u e e z e d o u t b e f o r e H oegentogler is c u r v e s sh o w e d t h a t some o f t h e w a t e r c o n t a i n e d v o i d s can d e c r e a s e . he s a i d may be a f u n c t i o n s e v e r a l s e c o n d s may be n e c e s s a r y . s o i l s has t o of T h is, su ffic ien t in order fo r th e curve to f l a t t e n . erties constan ts. in c r e a s e d w ith tim e f o r a g i v e n perm eable c o a r s e - g r a i n e d d e p e n d s on t h e type. H is tim e-co m p ressio n bulk d e n s it y f o r t h i s was t h a t pressure g e o l o g i c a l h i s t o r y and o t h e r f a c t o r s . A ccordin g to S p a n g le r , of p lotted versus t h a t t h i s r e l a t i o n s h i p may n o t a l w a y s due t o p r i o r l o a d i n g , so ils, in v ersely rela ted r e p o r t e d bv S p a n g le r would conform p e r f e c t l y to a lo g a r it h m ic grain ed used i n s t e a d o f v o i d s of structural prop­ may be e x p e c t e d t o per­ to m oisture c o n te n t v a r i a t i o n . an a p p l i e d load to so il is r e b o u n d s o m e w h a t , b u t some p e r m a n e n t rem ain s i n c e so il is not p e r f e c t ly e la stic . III. DESIGN AND DEVELOPMENT OF A RFCCRDING VOLUMETRIC TRANSDUCER AND AN INDICATING VOLUMETER The I n d i c a t i n g V o l u m e t e r The i n d i c a t i n g v o l u m e t e r F i g u r e 1 and F i g u r e 3 co n sists p r i n c i p a l l y o f a c a p i l l a r y tube c o n n e c te d t o a s p h e r i c a l shaped rubber b a llo o n n o n -co lla p sib le (a p p r o x im a te ly 3 c.m . p la stic tu b in g is located and b a l l o o n and c o n n e c t s t h e t w o . betw een th e tube When t h e b a l l o o n , w ith s o i l , is type t h e en co m p a ssed m inute volume so il, d iam eter). A surrounded w it h a la r g e q u a n t it y o f the in th e When t h e stress, o f v o l u m e a t t h e p o i n t m ass i s decrease s o i l medium i s d e t e r m i n e d by t h e d i s p l a c e m e n t ca p illa ry tube s i n c e of th e c a p i l l a r y tube is subjected to o f a mercury bu b b le the v o lu m e /lin e a r same balloon rep resen ts a p oin t. its filled e a sily in th e un it of d isp lacem en t kn own. The v o l u m e o f t h e c a p i l l a r y t u b e / c m d i s p l a c e m e n t w a s m e a s u r e d by two m e a n s . The f i r s t m eth o d, w h i c h p r o v e d un­ sa tisfa cto ry , o f d eterm in in g th e w eight the con sisted c a p illa r y tube, len g th . of w ater in and t h u s o b t a i n i n g v o l u m e / c m o f t h e A more a c c u r a t e means o f c a l i b r a t i o n w a s e m p l o y e d by u s i n g a o n e m i l l i l i t e r connected to the p ip ette c a p illa r y tube. (accurate A known v o l u m e o f w a t e r AV was n e x t t r a n s f e r r e d from th e p i p e t t e a t w h ich tim e A X , the displacem en t t o 0 . 01-m l) in to the c a p i l l a r y o f a c o lu m n o f w a t e r tube, in 13 J F ig , 1, V olum eter photo F ig , 2, V o lu m etric T ransd ucer photo 14 -AV, 'So,/ F ig . 3. I n d ic a t in g volum eter ?1 1 P2 1T1 1 lrS Tl 1 T2 E nlargem ent F ig . 4. Means f o r c a l i b r a t i n g v o l u m e t r i c t r a n s d u c e r 1000 F i g . 5. Tho V o l u m e t r i c T r a n s d u c e r 16 t h e t u b e , w as m e a s u r e d and r e c o r d e d . a r e kn o w n , t h e ca lib ra tio n ra tio is Now s i n c e AL and AV sim p ly A V /A T . The R e c o r d i n g V o l u m e t r i c T r a n s d u c e r The r e c o r d i n g v o l u m e t r i c t r a n s d u c e r w hich i s It is is an i n s t r u m e n t c a p a b l e o f r e c o r d i n g m i n u t e v o lu m e c h a n g e s more a c c u r a t e a n d s e n s i t i v e than th e v o lu m eter, has th e a d d it io n a l advantage o f b e in g ad ap tab le fo r co n ven tion al stra in -g a g e F igu re The s k e l e t o n of the 5 sh o w s how t h i s sk etc h o f F igu re s e n s i n g e l e m e n t and t h e B asic P r in c ip le s The s o i l in th e sam ple pressure sid e use w ith p ressu re-sen sin s e l e m e n t was c o n s t r u c t e d . 4 shows t h e w o r k in g f e a t u r e s s o i l sa m p le under t e s t . o f Transducer (encom passed w ith b a llo o n ) and t h e o f the tra n sd u c er are rep re sen ted w i t h Vp r e p r e s e n t i n g t h e F igu re 4. and i t r e c o r d in g equipm ent. The t r a n s d u c e r i s an e x t r e m e l y s e n s i t i v e elem en t. in s o i l . i n i t i a l volum e o f t h e space by V, system as in Thus: V = Vp - AV When AV o c c u r s i n t h e s o i l as a r e s u lt of CT And P = Pp + AP Sin ce = PV = (P I + A P ) (Vx - A P ) , AV = Vi A P / ( P i + AP) = fin a lly , (V x /P i) AP (l) 17 Hence, t h e a b o v e d e r i v a t i o n sh o w s a p r o p o r t i o n a l i t y b e t w e e n v o l u m e c h a n g e and p r e s s u r e system . S in ce th e c ircu la r th in p la te load (a ir pressure stra in is resu ltin g AV. S in ce the in th e in a r i g i d l y in t h i s case), supported u ltim ate the r e s is t a n c e changes gages are d i r e c t l y p ro p o rtio n a l g o a l was t o measure t r a n s d u c e r was used d i r e c t l y a s a " v o lu m e t r ic f o r m easurem ents transducer p rop ortion al to a u n ifo rm ily a p p lied o c c u r r i n g i n t h e SR-4 s t r a i n to change AV, t h i s transducer" in s o i l . Two M o d e l s o f T r a n s d u c e r s Two m o d e l s o f t h e in F igu re 2. to the The m o d e l on t h e one o n t h e a P le x ig la s t r a n s d u c e r w e r e c o n s t r u c t e d a s shown left rig h t except th at elem en t 0 .0 4 inch t h i c k , a s t a i n l e s s - s t e e l diaphragm 0 .0 0 7 is p ra c tic a lly its id en tica l s e n s i n g diaphragm i s ^h e o t h e r m o d e l e m p l o y e s inch t h ic k . p o r t i o n s o f th e t r a n s d u c e r were c o n s t r u c t e d The o t h e r from P l e x i g l a s . L in e a r ity of Transducers The l i n e a r i t y o f t h e t r a n s d u c e r s w e r e t e s t e d o f i m p o s i n g known v o l u m e c h a n g e s AV i n t o t h e w a s a c c o m p l i s h e d by u s e o f a 1 - m l p i p e t t e , By means o f t h e p i p e t t e , r esu ltin g AR o f t h e an im posed s t r a i n gages.. tim es fo r se v e r a l v a lu e s of sequent data were c o l l e c t e d by m eans system . T h is a c cu ra te to 0 . 01-m l. AV w as c o m p a r e d t o t h e T h i s w as r e p e a t e d AV r a n g in g from 0 t o several 1-m l. f o r volume c h a n g e s from 0 t o Su b­ 5-ml 18 b y m ean s o f a l a r g e r p i p e t t e . The r e s u l t s showed e x c e l l e n t AV v e r s u s range* lin e a r ity for I t was p o s s i b l e to p red ict 0 .0 1 - m l e r r o r from r e a d in g s o f of in terest. of th ese tests AH in th e above A ^ 's w ith in less A R Ts f o r t h e e n t i r e than range S e e APPENDIX B. C a l i b r a t i o n and S e n s i t i v i t y o f T r a n s d u c e r s The e x t r e m e l y h i g h rendered p o ssib le A P / AV r a t i o of the transducers th e measurement o f v e r y s m a ll s e n s i t i v i t y was u n n e c e s s a r y f o r m e a s u r e m e n t s o f range o f 0 .1 -m l i n tw o w a y s . S u ch A V f s in th e ( a s n e e d e d i n t h i s w o r k ) , and i t w a s r e d u c e d The f i r s t way was t o a i r volum e o f t h e p r e s s u r e s i d e t u b e s and s o i l . S in ce it is o f t h e t r a n s d u c e r and s o i l , enlargem ent to AV’s. in crease Vp, t h e in itia l o f the tr a n sd u c e r , d iffic u lt con n ectin g t o change th e volum es V]_ w as i n c r e a s e d b y a d d i n g an t h e c o n n e c t i n g t u b e a s shown i n F i g u r e 4* B ecause: AP An i n c r e a s e P-j_/Vi* ra tio Sin ce = (P i/V x) AV in Vi r e d u c e s the p r o p o r t i o n a l i t y c o n s t a n t AH i s (se n sitiv ity ) lin e a r ly rela ted AP, the AR w a s r e d u c e d when V^ w as i n c r e a s e d * s e co n d method o f r e d u c i n g th e s y s t e m was t o to se n sitiv ity / AV The of the tra n sd u cer m e r e l y r e d u c e t h e g a i n on t h e strain -gage a m p lifier. C a l i b r a t i o n was a c c o m p lis h e d p r o c e d u r e was a s f o l l o w s : bv a d i r e c t The i n i t i a l p reload m ethod. CT0 The 19 w as a p p l i e d to the sam ple in order t o betw een th e b a l l o o n w a l l and t h e s o i l a g a in m entioned here t h a t th e a p p lied to a l l sam p les e lim in a t e void sam ple* same p r e l o a d , in order t o in to th e s t r a i n - g a g e a m p l i f i e r was a d j u s t e d d e flectio n was some c o n v e n i e n t m u l t i p l e o f s u b s e q u e n t c h a n g e s i n volume w i l l c a lib r a tio n involved As a r e s u l t so il, = l on ly th ese of c o lle c tin g e a c h v a r y i n g somewh at i n covered th at very s l i g h t understood, Hence, the so th a t th e A V C. be r e c o r d e d lin ea r ly , i n i t i a l volum e, i t was d i s ­ in a m p lifie r gain in itia l T h i s was a i r volume o f t h e s o i l A P and AV. S i n c e Vp i s s t a n t volum e b e i n g a f f e c t e d v e r y s l i g h t l y betw een d i f f e r e n t n e a r ly unchanged. of v i the en large­ T h i s c a n be one l o o k s a t t h e p r o p o r t i o n a l i t y c o n s t a n t w hich r e l a t e s size pe n data from s e v e r a l sam p les o f m e n t , and p r e s s u r e c ha m be r o f t h e t r a n s d u c e r . if gain S in ce i s v e r y s m a l l c o m p a re d w i t h t h e v o lu m e o f t h e t u b e s , shown b e t t e r and steps. m od ification s in c e the tests) p ip ette a d j u s t m e n t was n e c e s s a r y from sam ple t o s a m p le . e a sily p s i was A v c was i n t r o d u c e d s y s t e m by means o f a 1 - m l c a l i b r a t i o n a b u b b l e o f m e r c u r y a s shown i n F i g u r e 4 . of the ( I t may be sta n d a r d ize the N ex t an im posed c a l i b r a t i o n volume chan ge spaces so il sam p les, alm ost a con­ by s m a l l v a r i a t i o n s t h e r a t i o Pp/Vp r em a in s U se was made o f t h i s b y a d j u s t i n g t h e {by a l t e r i n g t h e t u b e e n l a r g e m e n t ) s u c h t h a t t h e same c a l i b r a t i o n f a c t o r c o u l d be u s e d f o r t h e t r a n s d u c e r independent o f th e s m a l l a i r volume o f t h e so il. T h i s meant 20 th a t the p ip e t t e c a l i b r a t i o n m e th o d w a s u s e d o n l y o n c e , s u b s e q u e n t c a l i b r a t i o n s w ere a c c o m p lis h e d by a d j u s t i n g t h e a m p lif ie r g a in to the c a n be ju stified same p o s i t i o n f o r a l l = ( P i / v x ) AV (l) The r e a d e r w i l l be r e m i n d e d t h a t to AP i s on t h e r e c o r d e r a s a r e s u l t AP the of p h y s i c a l change AV. It is d esired r e s u l t i n g from C)Vp. T h is by s e l e c t i n g a Vp s u f f i c i e n t l y large in the m inim ize th e e r r o r accom p lish ed T h is as fo llo w s: A? in d ica ted sam p les. in is f o l l o w i n g m ann er: From e q u a t i o n I n AP r - (1) I n Vp + I n P]_ +I n AV (la) Thus*: ± S(AP)/AP If sam p les S v i, is d esira b le = -S (V l)/V ! t h e a i r volum e v a r i a t i o n known ( u s u a l l y much l e s s t o keep th e e r r o r in AP, (2) expected than 4 - m l) , i.e ., between s o i l and i t S (A P )/A P is less than say 1% then: S } /V-L < 0 .0 1 or Vl > S v i/0 .0 1 TTe n c e a c o n s t a n t p ra ctice, use the c a l i b r a t i o n f a c t o r mav be u s e d . g a in was a d j u s t e d o f a shunt c a l i b r a t i o n gage a m p l i f i e r . adjusted to =4 / 0 . 0 1 = 4 0 0 - m l o b t a i n 10 l i n e s t o t h e same v a l u e bv making r e s is to r b u ilt For exam ple, if In in to the stra in ­ o r i g i n a l l y t h e s a i n was r e c o r d e r d e f l e c t i o n f o r a 1-m l 21 A ^ c t on0 w ould d e p r e s s t h e a m p l i f i e r c a l i b r a t i o n (th is p l a c e s a 3 9 0 - K ohm r e s i s t o r the s t r a in gages w ill resu lt. in th e b rid ge) T h is l a t t e r t h e s y s t e m on t h e lon g as changes changes in in p a r a l l e l w i t h one o f t o o b s e r v e what d e f l e c t i o n d eflectio n a " s i m u l a t e d volum e c h a n g e ." can be c o n s i d e r e d a s T hereafter, b a s is o f the sw itch one may c a l i b r a t e s i m u l a t e d volume change a s i n Vj_ do n o t e x c e e d 4 - m l . If one e x p e c t s t o e x c e e d 4 - m l , a l a r g e r V i c a n be s e l e c t e d by t h e above m eans. T e m p e r a t u r e C o m p e n s a t i o n and E f f e c t s on T r a n s d u c e r I f th e r ea d er w i l l a g a in rev iew F igu re th a t the strain o f a b r id g e netw ork. is four gauges are a c tiv e Of c o u r s e t h i s stan d p oin t sin ce is components a d v a n ta g eo u s from f o u r t i m e s more s e n s i t i v i t y a tta in ed . T h is type o f c i r c u i t of he w i l l n o t i c e g a g e s a r e m ounted on t h e t r a n s d u c e r d i a p h r a g m i n s u c h a manner t h a t a l l a se n sitiv ity 5, Its is a d d itio n a lly d esirab le because in h e r e n t e l e c t r i c a l tem perature com p en sation s i n c e ( 3 R / QT) AT = A R w i l l be i d e n t i c a l f o r e a c h arm o f t h e b rid ge thus le a v in g th e balance u n c h a n g e d when t e m p e r a t u r e s flu e uate. A n oth er im portant c o n s i d e r a t i o n ature on a i r an alyzed exp an sion in th e system . is the e f f e c t T h is effect o f tem per­ may be i n t h e f o l l o w i n g way: A ? i = - |^ A V i *See F ig u re 4 + 5 1 = 1 . 2 * 22 S in ce: P±Vi = njR Ti and i f : A ^ A Pnet = ; i = 1, - 0, and AV2 A P i -A P g = when : AVg — ^ Pn e t = (P lA l)A V i If: 0, 2 ^ 0; i = 1, 2 (P i/V lJA V i and AT^ = AT2 - = AT ^ 0 R (n 2 /V s - n i A i ) A T P^_ = P g , t h e n n g / V g = n l A rl s i n c e T^_ = Tg Thus: A P net E quation the A = (P l/V l) (3) AVi sh o w s t h a t A P n 0 p i s p r o p o r tio n a lity constant V i on t h e pressure sid e o f tem perature change AT. *1 = (3) P i/lq and d e p e n d e n t o n l y on t h e v o lu m e c h a n g e o f t h e d i a p h r a g m and i n d e p e n d e n t Cf c o u r s e t h i s is o n ly true if P2 • W ith d a ta p r e s e n t e d effort in t h i s in v estig a tio n , no s p e c i a l o r p r o v i s i o n w as made t o make Pj_ = P g , t h u s t h e t e r m R ( n i / V i - n g / V g ) was n o t e q u a l t o c o llec ted zero. S in c e d ata were under l a b o r a t o r y c o n d i t i o n s where te m p e r a t u r e v a r i a t i o n s were n e g l i g i b l e , te m p e r a tu r e e f f e c t s were n ot con sid ered . T h is erature sectio n d e a lin g w ith tem perature e f f e c t s com pensation i s in clu d ed here to and t e m p ­ show t h a t t h e v o l ­ u m e t r i c t r a n s d u c e r may be u s e d s u c c e s s f u l l y w h e r e l a r g e r tem perature v a r ia t i o n s may be e x p e c t e d . few a d d i t io n a l e f f o r t s a s p o in ted however i n s u f f i c i e n t data T h is w i l l out above in volve rn a m « i v P]_ = p 2 ) » d e a lin g w ith tem perature effects 23 have been c o l l e c t e d to v e r ify th is p r e d ic tio n ex p erim en ta lly . A P r e s s u r e s D eveloped A ir p ressu re in n a tu ra l s o i l a tm o s p h e r ic v a l u e , nam ely about d esira b le to m aintain s o i l a i r in S o i l is of course 1 4.7 p s i. A "7. If natural v a ria tio n s w i l l not r e s u lt in t h e measurement o f in th e s o i l error. error AV. (4 = 1/3 p si A P fflai w a s f o u n d t o be o n l y a b o u t b e c a u s e V^ w as l a r g e r t h a n 4 0 0 - m l . d evelop ed a seriou s ( P l A i ) A V max E x p erim en ta lly , the serio u s w i t h volume change pressure, = (1 4 .7 /4 0 0 )(9 ) 1/4 p si o f the th a n t h o s e v a l u e s e x p e c t e d from in atm ospheric - therefore in tera ctio n (p r e s su r e change A P ) A P i s held l e s s is p r e s s u r e com parable t o n a t u r a l c o n d i t i o n s s o t h a t t h e r e w i l l be l i t t l e means o f m e a s u r e m e n t It eq u a l to the Thus, p r e s s u r e s sam ple w i l l p r o b a b ly n o t c r e a t e any The l a r g e s t # e r r o r i s CT*ma x xlOO - 1 . 1 %m C o m p a r i s o n o f V o l u m e t e r and T r a n s d u c e r F i g u r e 6 s h o w s a c o m p a r i s o n o f m e a s u r e m e n t s made w i t h t h e v o l u m e t e r and t h e v o l u m e t r i c transducer. com p ression c y c le load in g, of m ean-stress r e l a t i o n s h i p was p r a c t i c a l l y a marked v a r i a t i o n AV v e r s u s CT i d e n t i c a l f o r b o t h m ea ns o f m e a s u r e m e n t s a s may w e l l be e x p e c t e d . phase, the During th e D uring the r e l a x a t i o n in r e a d in g s between th e v o lu m e ter a nd t r a n s d u c e r w a s o b s e r v e d . T h i s c a n be e x p l a i n e d by n o t i n g 6. change measurements by in o o co in 02 o 02 isd in - (£ ) o SSEiLLS iMVSM o o volumeter B Volume and v o lu m e tric o Fig. transducer 24 ~o CO 25 a ch a ra cteristic o f the volu m eter. D esp ite the f a c t that \ t h e c a p i l l a r y t u b e o f t h e v o l u m e t e r w as m o u n t e d h o r i z o n t a l l y , a slig h t c o n s t a n t p r e s s u r e was n e c e s s a r y f o r t h e d i s p l a c e ­ m ent o f t h e m e r c u r y b u b b l e . a maximum and r e v e r s e s , v e r s e s w hich r e s u l t s la g , When t h e v o l u m e c h a n g e h a s r e a c h e d the s l i g h t constant p ressu re a lso r e ­ i n a l a g a s s e e n on F i g u r e the volum eter in d ic a t e s does not p o ssess t h is p ro p erly . ch a ra cteristic, Since th is 6. A fter th is the tr a n sd u c e r l a g w a s a b s e n t and a c c u r a t e m e a s u r e m e n t s o f end c o n d i t i o n s w e r e r e c o r d e d . The v o l u m e t e r i s so il con sid ered a v a lu a b le c o m p a ctio n r e s e a r c h work d e s p i t e Much o f t h e w o r k i n s o i l th e com p ression c y c l e , thus being w e ll w ith in th e a ccu ra te ^h e i n d i c a t i n g v o l u m e t e r the advan tages o f being sim p le, to op erate. in ex p en siv e, and e a s y Some d i s s a d v a n t a g e s o f t h e v o l u m e t e r a r e : cu ra cy d u r in g r e l a x a t i o n m easurem ents, dynamic m e a s u r e m e n t s , The v o l u m e t r i c lin ea rity , work p r e s e n t e d in Inac­ u n su ita b ility for n o n - r e c o r d i n g , and so m ewhat b u l k y . t r a n s d u c e r w a s an e x c e l l e n t p a r t i c u l a r i l y f o r work i n t h i s ness, one c h a r a c t e r i s t i c . com paction r e s e a r c h d e a ls o n ly w ith o p e r a tin g range o f the v o lu m eter, offers th is instrum ent f o r in v estig a tio n . instrum ent, Its com pact­ s e n s i t i v i t y and r e c o r d i n g f e a t u r e s made t h e th is th esis p ossib le* IV . DEVELOP’fFNT OF A LABORAmORY TECHNIQUE FOR THE STUDY OF THE EFFECTS OF PARAMETERS ON SOIL COMPACTION The G e n e r a l T e c h n i q u e Data were o b ta in e d w it h th e r e c o r d in g v o lu m e t r ic t r a n s ­ ducer d escrib ed in the p reviou s s t a t e s were a t t a i n e d pressure q u ite t o a s m a l l sam ple o f s o i l The h y d r o s t a t i c V arious m e a n -str e ss s i m p l y by a p p l y i n g h y d r o s t a t i c in a sm all rubber b a llo o n as ( a b o u t 15 gm) c o n t a i n e d shown i n F i g u r e 2 and F i g u r e 4 . p r e s s u r e s w e r e c o n t r o l l e d b y means o f a r e g u l a t o r v a l v e and p r e s s u r e sure sectio n . in d ica tin g in d ic a t in g system c o n s is te d p r e s s u r e s from 1 t o 10 p s i , system . The p r e s ­ o f a m e r c u r y m a n o m e ter f o r and a d e a d - w e i g h t c a l i b r a t e d b o u r d o n t u b e g a g e f r o m 10 t o 30 p s i . It must be p o i n t e d o u t h e r e t h a t t h e s o i l " d istu rb ed d esirab le s o i l as sib le sam p les." if data Of c o u r s e i t w o u l d h a v e b e e n e x t r e m e l y c o u l d h a v e b e e n t a k e n on u n d i s t u r b e d n a t u r a l in th e f i e l d , bu t a t t h e p r e s e n t s i n c e no a d e q u a t e at a poin t tra ffic in u n d istu ib ed s o i l o f t h e plow c a u s e s it recen tly -p lo w ed is has been d e v i s e d . undisturbed Even r e c e n t l y because th e S in ce land c o n t r i b u t e s t o e x c e s s i v e was d e c i d e d t o a p p r o x im a te c o n d i t i o n s so il. im pos­ volume con sid erab le d istu rb an ce. over recen tly-p low ed com paction, tim e t h i s means o f m e a s u r i n g s p e c i f i c p l o w e d l a n d c a n n o t be c o n s i d e r e d a s action sa m p le s were Modern f a r m i n g i s b a s e d on t h e of growth - i a . 7. General view of test equipment 28 of p lan ts in d istu rb ed , S o ils (cu ltiv a ted ) t h a t were t e s t e d so ils. were crum bled to a d e n s i t y s t a t e ap p roxim ately equal to fr e sh ly -p lo w e d then preload ed to sam p les t o th e same s t r e s s were e lim in a t e d 1 p si to by t h i s shape o f th e e n c lo s e d to 1 p si, and t h e the stan d ard ize t e s t s state. s o i l m ass. v o lu m e a t 1 p s i w as d e t e r m i n e d . of w eigh in gs w e r e c o n t i n u e d f r o m 1 t o 30 p s i . have unnatural a i r pockets took the A f t e r t h e s o i l was p r e l o a d e d t h e s a m p l e was r e p l a c e d i n t o so ils large by b r in g in g a l l s a m p l e was rem ov ed f r o m t h e p r e s s u r e cha m be r in itia l was s e l e c t e d The s a m p l e was p r o c e d u r e and t h e b a l l o o n s a c c o m p l i s h e d by a s e r i e s N ext, so il. sin ce m ean-stress the i n and o u t o f w a t e r . chamber and t e s t s An u p p e r l i m i t o f 30 p s i states seldom been found t o T h i s was in a c t u a l a g r i c u l t u r a l exceed t h i s valu e (21). Impact L o a d in g The a p p a r a t u s used f o r e l e m e n t s o f th e equipm ent T ith t h i s constant impact l o a d i n g c o n s i s t e d u tiliz ed phase o f th e w ork, p reload a p p lica tio n s. ^ general tech n iq u e. i t was d e s i r e d t o m a i n t a i n a o f 1 p s i b e f o r e and a f t e r T h i s was done a s shown a b o v e m a i n t a i n i n g a c o n s t a n t w a t e r head the p r e ssu re fo r the o f many impact i n F i g u r e 8 by (eq u ivalen t to 1 p si) cham ber c o n t a i n i n g t h e s o i l sam p le. above TTe a n - s t r e s s i m p a c t - l o a d i n g was a c c o m p l i s h e d by i m m e d i a t e a p p l i c a t i o n and rem oval of a i r F ig u re S. p r e s s u r e above t h e w a t e r head a s shown i n 29 TJpon i n s p e c t i o n o f t h e d a t a graph, r e c o r d e d by t h e o s c i l l o ­ i t was s e e n t h a t t h e a v e r a g e d u r a t i o n o f lo a d app­ lic a tio n from 1 t o 27 p s i t o o k a b o u t 1 / 2 1 / 2 o f a s e c o n d was r e q u i r e d t o r e l i e v e 1 p si. the H ence, load the (im pact) F igu re A-& d e g r e e s the L ik ew ise, l o a d f r o m 27 t o t o t a l t i m e r e q u i r e d t o a p p l y and r e l i e v e was eq u a l t o 1 s e c o n d . 9 sh o w s how a t r a c t o r t i r e load s to s o i l . second. The t i m e may a p p l y i m p a c t AT r e q u ir e d f o r th e t i r e to r o ta te may be t a k e n a s an a p p r o x i m a t e d u r a t i o n o f lo a d in g ap p lied b y t h e t r a c t o r w h e e l when A0 con tact an gle. Then in term s A T c a n be e x p r e s s e d TT, t h e f o r w a r d s p e e d o f t h e t r a c t o r , w h e e l and h , the A6 h eig h t of the t i r e = (V /r)A T r, the is the s o i l A0, ra d iu s o f the lug: = 20os-1 r /(r + h) F o r a t y p i c a l c a s e w h e r e r = 2 4 tT, h= 1" and V = 5mph: AT = 0 .15 The a b o v e a n a l y s i s sh ow s t h a t i m p o s e d by a t r a c t o r t i r e by t h e im pact second im pact c o n d i t i o n s a s were a p p r o x im a te d t o load in g techn iqu e used in th e some d e g r e e la b o ra to ry . (5) 30 A ir p ressu re (0-27 p si) r a p i d l y a p p l i e d and r e lie v e d here TV a t e r head e q u i v a l e n t t o CT0 = 1 p s i F ig . 8. Impact l o a d i n g m echanism . V AB V F orw ar d s p e e d o f tr a c to r wheel A ngle o f s o i l contact h Lug h e i g h t r T ire radius -A9 So il F ig . 9. A n a ly sis of tir e . impact- l o a d i n g a p p l i e d by a t r a c t o r V. PRESENTATION AND ANALYSIS OF LABORATORY DATA T e s t s o f C lay S o i l T a b l e 1 s h o w s how b u l k d e n s i t y c h a n g e s w i t h a g i v e n m eanstress CT a p p l i c a t i o n f r o m 1 t o 30 p s i . Data w ere c o m p ile d from a c l a y s o i l a t two m o i s t u r e c o n t e n t low er p l a s t i c lim it; and 8 . 0 # , lev e ls; 3 0 .9 # , the the a ir -d r y eq u ilib riu m p o in t. The r e a d e r w i l l n o t e a r e m a r k a b l e s i m i l a r i t y b e t w e e n F i g u r e 10 and F i g u r e 1 1 . The f o r m e r i s a c u r v e o f th e a ir - d r y s o i l , w h ile so il 12. both m oisture l e v e l s is Here c o n s t a n t a s shown on F i g u r e Th us we may e x p r e s s versus of ^f CT w i t h 12, it in term s o f naner. is certain i f the reader CT w as p l o t t e d on s e m i - l o g a r i t h m i c lo garith m ic fu n ctio n cla y lim it. s i m i l a r i t y c a n be more r e a d i l y s e e n w i l l lo o k at F ig u re CT f o r t h e l a t t e r r e p r e s e n t s t h e same a t i t s low er p l a s t i c T h is '"'jf v e r s u s for 'd T S i n c e ^— ------- B ( in cr; seen th at i is a param etric c o n s t a n t s . CT i n the follow in g, manner: X = To + B ln TCc ( ^ ?—~' oCO t>i !>} P CD •H r—1 00 O d © P f© d © M P IQ •H d d o CQ O cac- fx 05*1 lO o gino/sniS - IQ CQ O CQ (J ^ ) A i l S N a a x i n e Fig, 11. f= 3 & CO o in o guio/sras - (j^) Aiis'Naa Hina mean s t r e s s ( C ) for plastic lim it) o, versus (l o we r CQ (T) w soil o Balk: d e n s i t y c o n t e n t clay 30. 9 *f m o i s t u r e 34 -- o to CO 35 o to 3 3 4 -5 +3 ca co •r' r- J O f~ f o 00 *o o CV2 CD t>. »H 00 f— r-J <3 - n O 3 f-i *«"H O to -V -. ” *=> o G — OJ CO CO 4-5 -- Sh CD CD CD - P 'O CO c CD — cs CO CO C3 00 K -- <£> fE (D 4-5 Eh £ * n ' CO CQ*H UO S3 3 iH -— f <3 CD c-i o CD * H - - ^ f> 4-5 -— — to CQ 00 3 i> . CD 4-5 *5 •t-4 O CO i— I 3 —- co CD 4-5 'O'SR- C CD -1^ 0 5 - p — CVi *H • 3 30 0 3 to o w Sf •H s ujo/sui5 - ( j u i i i s i i a a jiiiia 36 values of Xo and F were determ ined a c c o r d i n g l y . ' T T oe “ "Refers t o t h e i n i t i a l b u l k d e n s i t y p r io r to com p ression or a p p lic a t io n of G Tor - d e f e r s t o the i n i t i a l bulk d e n s i t y d u r i n g r e l a x a t i o n , b u t i t must be remembered t h a t Xor c o r r e s P ° n d s to (To> t h e m e a n - s t r e s s s t a t e b e f o r e X l o a d was a p p l i e d . versus G fo r -c la y 6 so il a t a ir - d r y m oisture c o n ten t Xr = 1.40 * 0 .0 2 Xc - 1 .2 9 + 0.0 5 3 versus CT f o r I n G7 C 0 lnCT/CTo c la y s o i l at the low er p l a s t i c Xr = 1 .5 2 + 0 . 0 7 4 I n C / (T0 T c = 1 .0 4 + 0 .2 3 In C / Co lim it: T e s t s o f S j l t y Loam S o i l T ab le 2 s h o w s how b u l k d e n s i t y v a r i e s w i t h d i f f e r e n t m e a n - s t r e s s a p p l i c a t i o n s f r o m 1 t o 30 p s i . from f o u r d i f f e r e n t a ir-d ry m oisture l e v e l s . e q u ilib r iu m m oisture w etted to the low er p l a s t i c content lim it mhe f i r s t was a t an 1 3 . 3 % , t h e s e c o n d was 32.6 % , w h i l e t h e t h i r d a nd f o u r t h w e r e m o i s t e n e d t o t y p i c a l f i e l d a n d 16% w h e r e b y f i e l d s T ata were ta k e n m i g h t be t i l l e d at c o n d i t i o n s 20% such m o istu re con ten ts. F igu re c lo sely 1 3 and F i g u r e resem ble a X 14 y i e l d e d versus (T f u n c t i o n The r e a d e r w i l l n o t e t h a t t h e s e air-d ry silty loam s o i l . c u r v e s w h ich v e r y for cla y s o i l s . cu rv es are ta k en from the On s e m i - l o g c o o r d i n a t e paper, 37 the a ir - d r y lin e s o i l as shown i n F i g u r e 1 4 , thu s behavin g s im ila r ly F igu re to th e yield ed cla y s o i l s . 15 f o r a 2 0 % m o i s t u r e c o n t e n t som ew h at d i f f e r e n t l y a stra ig h t than e x p e c te d . sam ple p l o t t e d did not d e c rea se 'bC w ith CT a s r a p i d l y a s w i t h o t h e r s o i l s , t h u s a curved l i n e F igu re resu ltin g on s e m i - l o g p a p e r a s shown on F i g u r e 16 a l s o sh o w s how t h i s in 16. c u r v e was s t r a i g h t e n e d on s e m i - l o g p a p e r by i n c o r p o r a t i o n o f a s e c o n d p a r a m e t r i c c o n s t a n t tfKTt i n s u c h a manner t h a t X versus t h e new e x p r e s s i o n for CT w as c h a n g e d t o : (7) It w ill order to T of be n o t e d t h a t sa tisfy T o- 1 + K was ad d ed in itia l con d itio n s, O bvi o u s l . y e q u a t i o n eq u ation (6) sin ce the (7) thus a is la tter w ill T herefore, the d escrib e X versus CT b e h a v i o r o f a t of s o il by t h e c la sse s if CT z (7) (7 0 > g en era lized reduce to th e wh en K = 0 . the in e q u a t i o n form form er same e q u a t i o n c a n be u s e d t o proper s e l e c t i o n lea st tw o g e n e r a l o f param etric con­ stan ts . T ests of silty lo a m s o i l a t 1 6 % m o i s t u r e r e s u l t s v e r y s i m i l a r t o t h o s e found f o r th e m oistu re c o n te n t. F igu re rela ted to s o i l sin ce m oistu re. same s o i l a t 20% 17 and F i g u r e 1 8 e x e m p l i f y t h e s e r e s u l t s w h ich obey e q u a tio n con stan t are d iffe r e n t conten t y ield ed (7), but o f c o u r s e th e they are at lea st param etric p a r tia lly 38 TABLE 2 A p plied A p plied load (p si) 1 load ( O ') v e r s u s b u l k d e n s i t v (If) s o i l a t fo u r m oisture l e v e l s for s i l t y loam M oistu re c o n te n t o f s o i l __________________________ .____________ _____ 13.3% w a t e i * 16% w a t e r * 20% w a t e r * * 32.6 % w a t e r * * * (gm s/cm 3) 1.16 ( gms/cm3) {gms/cm3) 1.17 1.29 ferns / c 1.37 2 1.19 1.20 1.32 1.41 4 1.21 1.23 1.38 1.44 6 1.23 1.26 1.42 1.44 8 1.25 1.28 1.47 1.44 10 1.26 1.30 1.50 1.44 15 1.28 1.33 1.57 1.45 20 1.30 1. 36 1.64 1.46 25 1.32 1.38 1.67 1.47 30 1.33 1.40 1. 7 1 1.47 25 1.33 1.40 1 . 71 1.47 20 1.33 1.40 1. 71 1.47 15 1.32 1.39 1 . 71 1 . 47 10 1.32 1.38 1. 71 1.47 8 1.31 1.37 1.69 1.47 6 1.31 1.36 1.68 1.46 4 1.30 1.35 1.66 1.45 2 1.28 1.33 1.64 1.44 1 1.25 1 . 31 1.61 1.43 * A ir dry eq u ilib ru m p oin t of s o i l ** T y p ic a l t i l l a g e m oisture c o n te n ts *** Low er p l a s t i c l i m i t ) 39 o to © f -i r*. 4-> 03 •H O e in °, y to CVi to u o e — - CO t>>43 + 3 rH •»H **H © © G © 43 rO G © -V 43 rH — in CO I—\ cj) •H in to o m gWO/SUJg - o a> a j^ lsn b g x i a a G G O PQ O rri r-4 giDo/euiS - *-l ( j ^ ) A j is ja a a x i a a 41 CO ® fn to i- •H o in w £ o •rH to 04 1 . lO »-- CO CP K CO S3 m -- IO rH O «H CV2 o © *H o £ Sh © o -—- tH fc>; -P *H CO*H CO TO © U +3 C © o •H O +3 CO •H © TD £ O o TO O 3 © rO fn «H © © •rH

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o ^r H v—'H O fc>> TO P ^ •rH £3 TO CD a o © rH rCf Ad ncf 3 TO PQ TO C CVJ e»C •H o> rH £uio/sm 2 - f—I ( J ) illS N H G XTAS 49 i cO • CJ to o +3 o © *H 4 3 •«—1 o to 4 3 d £ o o CO o rH d d T J 43 © d CO CO content) a © % m oisture CJ © CO •*H CO o E d o © *— . •H O *H b d © ©3 Cki* - —■ (32.6 vh d CO iH CO © b> © f-l CO CO CO • to iH E *«H i— ( O •rH CO 43 © *«H © CO iH CJ a © ©5 O, id £ O rH d © 3 «— I CJ so pH in CO £m o / s w 2 - (j^j AjjSNaa xnns 50 o to > < .—' © *=5 E •rH •H O *H P © © r—1 D- P © t>> £ •P •rH r— 1 © P © -P o c ID © •«—W p > 1c 3 o CQ o w CV2 o ID CN £mo/sui3 - ( 0 ) AJiSNaa 3103 ID CO A - o t£ C*o R ig. 23. — kO (CT) for CM O i—I «o gi oo/ suj s - (j^) a JiI s n s g aina LO O B $ m oisture CM stress o mean content to versus ( CT) - p s l o Bulk d e n s i t y ( X) sandy loam s o i l — to MEAN STRESS 51 52 Because the s a t u r a t i o n l i m i t w a s r e a c h e d when t h e was m o i s t e n e d t o t h e l o w e r p l a s t i c content at 8 . 0 $ was s e l e c t e d . lim it, a third moisture This rep resen ted the l e v e l at which f i e l d o p e r a t i o n s c o u l d be p e r f o r m e d . a n d 2 3 show t h a t T soil at Xn t h e this the Bfc m o i s t u r e content case of equation particular versus moisture ^ i ^ u r e s 20 6” f u n c t i o n f o r s a n d y l o a m obeys equations (7), soil it is (6) and/or (7). obvious that F - 0 fo r soil. X v e r s u s G* f o r a i r - d r y s a n d y l o a m s o i l : Tc = 1.41 + 0.056 lnCT/CTo Tr = 1-53 + 0.020 lnC/CTo T v e r s u s (Tfor s a n d y l o a m s o i l a t 8 $ m o i s t u r e c o n t . Tc = 1.48 + 0 . 1 3 8 I n CT/ (T0 Tr = 1.92 + 0 . 0 0 9 I n d / (T0 have p r e v i o u s l y on pages 31 and 3 6 . Kc - Parametric constan t during compression Kr - Parametric constant during r ela x a tio n 57 G^max ~ “F i n a l (max) mean-stress ap p lication T max - F i n a l (max) b u l k- d e n s i t y r e s u l t i n g f r o m (Traax “E q u a t i o n s (7a) and ( 7b) o f above have been adapted f o r the follow in g cases: CASE 1: F i n a l b u l k d e n s i t y change A T o c c u r r i n g i n a s o i l d u e t o a l o a d a p p l i c a t i o n CT0 t o G~ma x l o a d r e l i e v e d back t o C o. s ince T' max = T o e + B0 I n [( G"max/Go + K0 ) / ( l + Kc )"] (7c) T 0 r + ^r l*1 [( ^ m a x / C o + Fr ) / ( l ■+ Fr )"^ ( 7 d) and Tmax = s u b tr a c tin g Equation 0 = (T )r"T cc) + Br (7c) f r o m (7d) we g e t : I n [ ( CTj^ax/^o *+ Kr ) / ( l + F r )] - Bc I n [( CTmg x /C7o ■+ Fc ) / ( 1 + Kc )] or A T- (T or-T oc)= Bc I n [( (Tm a x /(T0 + Kc ) / ( l + Fc ) ] - B r I n [( C'm ax /CT0 + Kr ) / ( 1 + Kr ) ] Equivalently: A T = B~ I n if; (8) ^ ^ ^ m a x / ^ n + Fc \ / l + F~ 1 + I UTjjbx/CTo ” Kc = F r = 0 , (9) then: A T = (Br - B q ) I n ^ m a x / ^*o (10) 58 CASE 2 . '^fr in terms o f (T when ^or i s n° t known s ince T or ^oc t Bc I n - ^max/^o ^ K o)/(l + Kc )"] Br l n [ ( CTmax/(To + Kr ) / ( 1 + Kr ) ] then Tr ^oc ~ Bc I n [( G“max/Cro + Kc ) / ( l t TCc ) ] •h Br I n ^(G'/C’q + Kr ) / ( ^*max/Q) + ^/r)"] . ( H ) CASE 3: Determination of CT ax for a prescribed AT/ Toe - P and when Kr * Kc = U d i v i d i n g Equation P = (Bp - B e ) / T o e ] P CTmax CT/ The r e a d e r w i l l the r e v is e d Toc, we g e t : ^max/ oc / (Be “Bp ) e (12) immediately r e a l iz e equations of cases Eor exam p le, to (10) by equations ( 9) and problems t o which 1 t h r o u g h 3 c a n be a p p l i e d . (10) o f Cas e 1 c an be u s e d p r e d i c t a b u lk d e n s i t y change r e s u l t i n g from a change m e a n - s t r e s s ACT= lement t r a f f i c . Equation ( G*ma x ” in G*o) t h a t may be c a u s e d b y imp­ S e e Exampl e 1 . (11) o f Ca s e 2 w i l l e n a b l e one t o predict a b u l k d e n s i t y v a l u e r e s u l t i n g f r o m an a p p l i e d l o a d n o t t o t a l l y relieved to its i n i t a l value p articu larly useful Equation (12) CT0 , under t h i s thus Equation ( l l ) is circum stance. i s a u s e f u l r e l a t i o n s h i p w h i c h c a n be 59 used to AT/ p rescrib e Toe* G*max f o r c e r t a i n F o r exam ple, if p erm issib le o n e k nows t h e v alu es of c r i t i c a l v alu e A T / T oc f o r a g i v e n s o i l , t h e r e s u l t i n g c r i t i c a l v a l u e ^~max determined fo r th a t p a r t ic u la r c r i t i c a l v alu e guide fo r soil* This ( T max c a n c o n s e q u e n t l y be u s e d a s a of implement s e l e c t i o n a n d / o r d e s i g n . S e e Exampl e 2 . Examples o f Adapted E q u a t i o n s Example 1 Known: CT0 = 1 p s i , ^ m a x = 20 p s i Be - 0 . 0 9 8 , (then r e l i e v e d to Kc = 2 , Kr = - 0 . 6 , T oc = 1 . 1 7 , 1 psi) Br = 0 . 0 2 3 * Required: AT r e s u l t i n g f r o m a l o a d a p p l i c a t i o n 20 p s i , then r e lie v e d from 1 p s i t o to 1 psi Solution: From E q u a t i o n A T : (9) ^ „ 0.023/0.098 I 0 . 0 9 8 i n [ ( 2 0 j — ) ( g 0: o-;— -) • 0 . 1 1 g ms / c m3 Ex a mp l e 2 Known: CT0 = 1 p s i , Bc = 0 . 1 3 8 , Br = 0 . 0 0 9 , Kc = Kr = 0 Yo c = 1 .4 8 Required: CTma x s u c h t h a t A T / T o e Solution: (From E q u a t i o n < 1* e ^ 0*2 ( 12 ) ( 0 . 2 ) ( 1 . 4 8 ) / ( 0 . 1.36 - 0.009) __ ^ ^ VI. SUMMARY AND CCNCTUSIONS Summary While have l a r g e r m a c h i n e s and more i n t e n s i v e in c r e a se d production markedly, of excessive evaluated. implement t r a f f i c The c o i n c i d e n c e cultivation long-run consequences ha v e n o t been c o m p l e t e l y o f t h e t r e n d toward i m p l e m e n t w e i g h t and t r a f f i c w i t h e x c e s s i v e i n d i c a t e s a need to s c r u t i n i z e t h i s increased compaction trend. A t t e m p t s t o s o l v e c o m p a c t i o n problems i n t h e p a s t have b e e n o f a t r i a l - a n d - e r r o r n a t u r e and h a v e f a i l e d any g r e a t success-. n o t be b a s e d Most o f . t h e a t t e m p t e d s o l u t i o n s could on s o u n d e n g i n e e r i n g i n f o r m a t i o n s i n c e t h i s i n f o r m a t i o n wa s n o t a v a i l a b l e . have t r i e d t o me e t Other r e s e a r c h w or ker s t o adapt form ulae a c ce p ted to agricultural s o ils , b u t me a s u r e d in c i v i l engineering results fa iled to agree w ith predicted v a lu e s. VandenBerg at a point His th e o r y medi um. (20) in s o i l is sh owe d t h a t t h e mean n o r m a l s t r e s s simply r ela ted to bulk d e n s i t y . was b a s e d on t h e m e c h a n i c s o f a c o n t i n u o u s The s t u d y p r e s e n t e d h e r e d e a l t w i t h t h e r e l a t i o n ­ s h i p b e t w e e n b u l k d e n s i t y and mean s t r e s s . important ment o f soil. It i n v o l v e d an i n s t r u m e n t a t i o n problem o f the a c c u r a t e measure­ sp ecific volume c h a n g e s o c c u r r i n g a t a p o i n t The p r o b l e m was s a t i s f a c t o r i l y in solv e d by the d e v e l o p ­ me n t o f a r e c o r d i n g v o l u m e t r i c t r a n s d u c e r . This instrument 61 Vto • oC *J**w o stu d ied £ O so ils CO © co CD QC o* CO CD •* CO* a CO to CJ OS CJ CO to o o o CJ o other constants for •* r— t to o c* o o • o o* CJ* o to £ CD O tO * rH * l-l and param etric CO • rH O o to o o CO* CJ to • o 00# o 1 C O CJ i~H • o • o to rH •H • fH o CJ to •H C D rH to • iH CJ C O • o rH to • o 1 C O • O O CJ iH CJ O • • o rH • fH fH • O CJ CO p © •H* £ P ^ G o CO of to CO 0> CO Summary Os CJ C2 6 © o h-3 © o i— 4 o> p • CJ o o CO o CO CJ o • o o o to o •H to o p p •H 4J •H -p * ©p «*H G O © r p© e CO CTi lO CJ o CJ o o © Pc o o ©p © o cx © rH •H CXiH •pH p OT © <0 P O P © P a •fH w p a >0 © c © -P c o o • • CM to to £ o o TVPFS OF TFRFF DATA IO i>> CO CD i— l SOIL to CT> CO *iH to o E -p « CD to to o- to CM o CD CM CD Pi 3 -p -p CQ •rH *rl O O CQ * H P O IO CM 73 © •1— ! tO CM C O Pi 9 P C O CD t3 •rH O CO Pi O <+-t a 0 O N •H •H Pi O -— . P to CM c CO O ”— t C! o | ^ © P O I rH I s rH O ® m co 0 a t>> -p rH © «jH GO Jh M I t P C O© rH -rH C O*rH O to P> P CO s © o p »rH Jx] © o —* ® to <1 o 13 o eO rH CO is d - (d ) a id p iv s o ni a a d o ia A a a a a a s s a a a o 67 -P •iH 80 > a p ^ © \to p ^ «w .« en rH II to B to 6 w> il W >° €> €> ♦> > C0C3 *fe: ^ rH ^ <3 I CD CM to» CO ^ • • to to to to to to to to to to tD ID tO CO CO tO fcO CM CM CM CM CM CM CM CM CM • • • • • • 9 m 9 9 CO O- O D- t>- O tO CM£N IO IO IO in in in IO O o in o«o rH £> M O t IS 6 6 6 6 6 O > tO C || l| *jH ft| £> ♦ to • o • * • • • • • S < o i-l o « Q 25 W (X 5* > o p> < E-* t-3 M CO C ' - O O O C M t n O C M C M C M C M C M C M C M a n t O C M l O r H S O t O t O t O t O ^ ^ ^ ^ ^ ' ^ ' ^ , <3 to 04 (D SC © « K CO .n o © in in if) in id 10 id to in to o OOOOOOOOOOOOOOOOOOO o IO CM O > lO in eMCMCMCMCMCMCOCOEOtOCOCQtOtOtnCMCMCM , » « » » • * * • • • • * * • • • • OOOOOOOOOOOOOOOOOOO (X © (X o H t o c o t Oint o ^ io ^tniCiin^ioiOin^^cow . * • « • • • • * * • • * • • • • * OOOOOOOOOOOOOOOOOOO V Pi tn cj © 00 s- CQ © -p !s CO m ^ HW^OCCOlfiOinOlOOlflOflO^^NH f— IHWWtOWNHH 68 >3 p r ft © f t CO in • © ^ rH p f t M f t fl II to E © a H l O l O O f f i O W l D t O t O C V J W H H O O C l O f t f t W C \ . i C V 2 C \ 2 e v i C O t O C O t O C O f c O l O C O t O C O C < 2 C V I © • • • • • • • • • • • • • • • • « E CUT f t H f t rH rH f t f— I » H f t r— 1 r H rH rH i— I f t H • • » H r— 1 <— I ft >0 ^ © © f> ft ft CO CD • f t rf t <3 < O 1 1 ft QCU')WW©CDOl>(COIMMncOH©HISCO ft>t>tO'*tOOCOC?> O C\2 * * » * • • * • • ♦ * » « • « CD* o f t• ft ft « • 4 « Ch CTi C CTj Ql O' CTi CO 00 QT) Q) 00 CT CTj CO CD 00 f t CT- ft". C II II CD pi m o CO ft ft ft f t > C >- O IO © O • t O • O O O H t Q ^ O O C • O ' - f t > O • O • • O f t O C t O f t f t f t O • f • t f • t f • t f t • • t i —I f IO • • • • • O O O O O ft; m fx © C£ r^o ft ft p O * p K to* £2) to s ft p ft ft O C \ i ^ * O CO ft <*; C\ J C - W^lDM^OSHWWtOWWWHHOOi^ © t — I f t O • O •— I • O * rH C O <0 • • i-H O O Id {OLOCDOHWtQ^lfllDlOlO^tOCOWOCD toE • • • • • • « • • • • • * • • • • O O O O rH r— I f t rH rH rH rH rH rH rH rH rH rH • rH O o in r-i^lOLDE>CTiHW«^Hi n n c a ^ H O cn O O O O O O O H r H H H H H H H H H H O inr'QDOOwco^intntn^tocowrHoc^ • • • • * • • • • • • • • • • • • • O © O O O f t f t <— I H H H H H H H H H H H C ft W^lfilDOCPOHWWWHHrlHHOffi , Cl, o © O « O • O • O • O • O • H • r • l r * l H « » i —I r H • * rH i— I r H r H r H O • • • ft © CQ CJ © CD © Ci P ^ CO CQ ft H W ^ ^ C O lfiO in O lfiO lO O ffliO ^ M H H N W I Q N W H H * 69 •p TOt> O' C ^ O © ^ • P O rH M H « > II It CO e o © £ W) a > 0 2 GO 0 2 CN O ES O *H rH rH r H rH O'- CO t o H* rH 0 2 CO t o IO IO tD tO O ' O O ' O O tO t o t o t o tO • » • • • • • • • • • • • • • • • 9 • rH r H rH i H rH r H *H *H rH r H r—i rH rH rH H r H rH r H rH ^ ©© > > eo cd aQ aotooiGOtnfcOoicommiQtna: tocctoh to 02OC‘-tOC2rHGDc0'«tf0202020202C0e0^»Oe0 • fc> . £ > r H -<1 < \ O | I > 00 * • • ♦ • • • • • • • • • • • * • • * 002 rH £ » 03 • 00 0j || II p«h > *iH P M O CO % c V t> < o O W © O lfilfl© IO C Q tQ tQ tO O IO O tnO IO o i i n o O r H ^ t o c c o o o o o a ' . o>acoto O O o o O O H H H H H W W C ^ W W H H H H H p CD Eh P © M CO o rH 0 2 i n C " rH 02 tO a: c <1 p © PC > © w Eh W o Eh • cc c! 03 -c! CO h p o g o to 03 cc pH o PC o §3 W©C7iHtQ©C5HCOtOtOtONWHHOOi P • CO E o o p o o 03 04 *> • rH 02 02 02 02 02 i—1 t—1 • • • • • • • • 02 02 o 02 02 02 02 02 02 © O o O O O cr. cr. 0 0 • • • • • • • • 4 02 02 02 02 02 rH r—1 *— oa CO O CO m O CT> rH rH rH r H O O cr.• CT• • • • • ♦ • • « • • • * o r H r H r H t—1 ■—1 02 02 02 02 02 02 i H r H 02 02 <44 in in in in in in • CO• t o C" 00 o • • • • • • • • • • * • rH r—1 rH rH rH rH rH rH rH rH rH o o o © K 04 r H in C" cr • • • • * rH rH rH rH iH o » © p rH • i—I rH • o CO © • • rH r H to TO a © © Ct ® 40 S co rn Q, rn c\w < o cD O tn o ii)O ir} o m o cc< o ^cv ! HHWWtQWWHH h 70 -P •iH © ! < © ^: • P rH rH i: i-4 n n rH o C" O to to CDO to to CTj O o o cr CO£Nto I P r - l CM CM CM CM tO to to to to to t o to to to to # • • • • • • • • • • • • • « • • • • © E r H <—1 * H r H r H r H r H r H r H i H Hi r H i H r H i H i H i H r H * H tlC P >® © © fc> f> P> ©£>© • £> OtNtOOlPtOOtOlOtOtOlPOCsOfcOOoeK W O C D t Dt f l t D H O t t O O i ^ O O H W C v ] ^ r H -<3 ^ O I I fc> o oto rH £> © • • • « • • • • • • • • • • » • • • ♦ c r c r cr) c r c d a c r c n gt. c n i > c - o a : a ) c o c r c r . cr • CT- G tl II p ► > O t> < CO CM ^ • © > < o o o • • • to PI to r H O - o CO CO cn o tr­ I P O O - ip rH CO CM O E> CD O s CM -sf to LO to IP -sP • • • • • • • • • • • • c o c c rH rH rH r H iH rH rH rH rH rH iH r H r—I to o- o io io * to • o > CD iH t o CO C\2 CV2 «H i H O a • • • • # • • ♦ • ♦ • • • r H rH r H iH rH r H *H rH iH i H o o O o M p CO © p g P P < ID to to IO tO CD GO CO CO D- O i> t o • • • • • « • • * • • • • i—{ r H rH fH rH P <3 © © P © to P © P Ci£ C -a o 6 rs #H O *> t o CQ QQ rH O O O CQ CO • • ♦ • * • • « • « • * • i—1 «—1 i H r H i—1 rH rH H i H rH i—1 r H o to^ E o tO CO t o IO tO c n CO CO CD CD O C• • * • « ♦ • • • * • • • rH i H rH r H r H H i H rH rH • — i i—1 r H iH CM in in t o 6 0 CO CV2 •H O CD • • • • • • + * • « • • • H r H rH iH H i H rH 4---1 r H iH rH rH o CV2 • P © P C OCM i n tO t o tO to m to in • • • • • • • • + • • © rH #H H r—1 i H rH i H rH rH i H r—1 i H r H CQ * P © P © m a © ©fHb ^ co © Oh H N ^ , o f l D o i o o i n o i n o i n o c o c i ’# W ' H h h m n c o n n *h h 71 n n rH »>° > tto 1 © E C' O CM t o to t o m M4 M4 to CM o to M4 Mi M4 M< M4 M4 Ml M4 M4 M1 M* • • « • • • # « • • • • * • * * * rH rH rH rH rH rH f-- 1fH rH r ^ rH o M4CN cr, to to to to 1 • e o 1 p »o ©^ to 1 00 f t 'r H 1 t> 1 -p ?g C 0> • >■ <1 *h cm M4 cr; M< cn to o h n - cm c> c - to cr- c - cn i n c o o o ^ c r . 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O O O O O O O O O O O O O O O O O O O © P£ CE o > © O ue E~< CO a M E-« m in tn in in o to m in O O O O O O O O O O O O O O O O O O O © ca CO ^r* pr o g ©<2 ft ss & O O O O O O O O O O O O O O O O O O O 'tf* CD GO CD CO' C D C D C D C O G O O O C D G O C O C O C D C O C D » » # ♦ . « • * • • » • » ♦ , s v • • co £ o CO .C o a, © O O O O O O O O O O O O O O O O O O O fr. © e 3 r—I (S i O f> ft commtnminmininininininininin^^ . O O O O O O O O O O O O O O O O O O O © cc ft O O O O O O O O O O O O O O O O O O O © C£ w co © ft CO ra ft .h w 'n tM o c o o i o o i n o i o o « g © « ^ w H H N W t O W W H H BIBLIOGRAPHY 1* A t t e r b e r g , A . , D i e E o n s i s t e n g und d i e B i n d i e k e i t d e r Boden. Intern. M itt. Bodenk., 2 :1 4 9 -1 3 9 , 1912. ________________ » D i e P l a s t i z i t a t B o d en k ,, 1 : 1 0 - 4 3 , 1911. der t c n e . Intern. T' i t t 3. B a v e r , L. D. , S o i l P h y s i c s , J o h n W i l e y and S o n s , E d it io n , 1956. 3rd 4* B e k k e r , U. S . , T e r r a i n E v a l u a t i o n i n A u t o m o t i v e O f f ^he Road O p e r a t i o n s , Or dnanc e C o r p s . , D e t r o i t A r s e n a l , Report No. 1 3 . , 1957. 5. E d m i n s t e r , T. T'E , P r o g r e s s R e p o r t o f C o m m i t t e e on S o i l Compaction, Paper p resen ted at Winter m eeting of A . S . A . E . , C h ic a g o , 1 1 1 . , Dec. 9 - 1 2 , 1956. 6. G i l l , T7. R. and R e a v e s , C, A . , C o m p a c t i o n P a t t e r n s o f S m o o t h Ru b b e r T i r e s , A g r i c u l t u r a l E n g i n e e r i n g , October, 1956. 7. G - o r i a t c h k i n , B. P . ( C o l l e c t i v e Work) " T e o r i a i p r o i s v o d s t n o s i e l s k a h o s i a y n i h m c s h i n " , Government P u b ­ l i s h i n g O f f i c e , Moscow, 1 9 3 6 . Q. H o g e n t o g l e r , C. 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S c i . , 1929. studies of , ^ e th o d s of R esea rch in S o i l Dynamics., A l a . A gr. Exp. S t . B u l l e t i n 2 2 9 , 1 929. 77 15. P r o c t o r , R. R. , " F u n d a m e n t a l P r i n c i p l e s o f S o i l Com­ p a c t i o n " , E n g i n e e r i n g N e w s - R e c o r d , A u g . 31 and S e p t . 7, 2 1 a nd 2 8 , 1 9 3 3 . 16. R u s s e l l , J . C . , and Mehr, F . M. , The A t t e r b e r g C o n s i s ­ t e n c y C o n s t a n t s , I . Am. S o c . A g r o n . 2 0 : 3 5 4 - 3 7 2 , 1 9 2 8 . 17. S o e h n e , W a l t e r , D r o c k v e r t e i l u n g i n Boden und B o d e n verformung unter S c h le p p e n e ifsn ( D i s t r ib u t i o n o f P r e s s u r e i n t h e S o i l and S o i l D e f o r m a t i o n unde r T r a c t o r T i r e s ) , E r d l h n D. L a n t e c h n 5 : 4 9 - 6 3 , 1 9 5 3 . 18. S p a n g l e r , U. 18:265-279, 19. T e r z a g h i , C. 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