HIGHWAY RESEARCH BOARD

B U L L E T I N No. 8

DESIGN OF FLEXIBLE PAVEMENTS

USING THE

TRIAXIAL COMPRESSION TEST

STATE HIGHWAY COMMISSION

KANSAS

P^"^""""""" VF,

m 21 m/

1947

The Highway Research Board it not responsible for the statements made or opinions expressed in its publications.

HIGHWAY RESEARCH BOARD

BULLETIN NO 8

JJ3ESIGN OF FLEXIBLE PAVEMENT

USING

THE TRIAXIAL COMPRESSION TEST^

Reported by

STATE HIGHWAY COMMISSION OF KANSAS

R C KEELING, State Highway Engineer

Developed and Prepared by

SOILS DIVISION OF THE MATERIALS DEPARTMENT

under the d i r ec t i on of

R D FINNEY J ARNDT Engineer of Materials Assis tant Engineer of Materials

Soils Div i s ion Personnel i n charge of work

D L LACEY C R FRICKE F i e l d Engineer Laboratory Engineer

HERBERT E WORLEY Laboratory Research Engineer

HIGHWAY RESEARCH BOARD D I V I S I O N OF ENGINEERING AND INDUSTRIAL RESEARCH

NATKMAL RESEARCH COUNCIL

Washington 25, D C September, 1947

NATIONAL KESEARCH COUNCIL

The N a t i o n a l Research C o u n c i l i s a coope ra t ive o r g a n i z a t i o n o f the s c i e n t i f i c men o f A m e r i c a . I t s members i n c l u d e , however , no t o n l y s c i e n t i f i c and t e c h n i c a l men b u t a l s o b u s i n e s s men i n t e r e s t e d i n eng inee r ing and i n d u s t r y . I t was e s t ab l i shed i n 1916 by the N a t i o n a l Academy o f Sc i ences .

The Cha r t e r o f the N a t i o n a l Academy o f Sciences passed by Congress and approved by P r e s i d e n t L i i ^ o l n i n 1863 p rov ides t h a t " t h e Academy s h a l l , whenever c a l l e d upon by any Department o f the Government, i n ­ves t i ga t e , ' examine, experiment , and repor t upon any s u b j e c t o f science or a r t . "

D I V I S I O N OP ENGINEERING AND INDUSTRIAL RESEARCH

OFFICERS

Chairman F r e d e r i c k M. Fe iker

Vice Chairman Hugh L . Dryden

EXECUTIVE COMMITTEE

Chairman F r e d e r i c k M. Fe iker Vtce-Chairman Hugh L . Dryden

Lyman J . B r i g g s , W i l l i a m B . Kouwenhoven, Thomas H . MacDonald

I

HIGHWAY RESEARCH BOARD The Highwagr Research Board i s o rgan ized under the auspices o f the

D i v i s i o n o f E n g i n e e r i n g and I n d u s t r i a l Research o f the N a t i o n a l Re­search C o u n c i l . I t s purpose i s t o p rov ide a n a t i o n a l c l e a r i n g house f o r h i g h w a y r e s e a r c h a c t i v i t i e s and i n f o r m a t i o n . The membership c o n s i s t s o f 36 t e c h n i c a l , e d u c a t i o n a l , and i n d u s t r i a l a s s o c i a t i o n s o f n a t i o n a l scope. Assoc ia tes o f the Board are f i r m s , c o r p o r a t i o n s , and i n d i v i d u a l s who a re i n t e r e s t e d i n highway research and who d e s i r e t o f u r t h e r i t s work . ^

I n i t s p r a c t i c a l workings the Board p rov ides a f o r u m f o r the d i s ­cuss ion and p u b l i c a t i o n of the r e s u l t s ob ta ined by i n d i v i d u a l research workers ; organizes committees o f exper t s t o p l a n and suggest research work and t o s t udy and c o r r e l a t e r e s u l t s ; publ i shes and o therwise d i s ­seminates i n f o r m a t i o n ; p r o v i d e s a r e sea rch i n f o r m a t i o n s e r v i c e ; and c a r r i e s on f a c t f i n d i n g i n v e s t i g a t i o n s . W i t h the c o o p e r a t i o n o f the highway departments o f the s t a t e s and t e r r i t o r i e s and the P i i > l i c Roads A d m i n i s t r a t i o n , the Highway Research Board conducts a Highway Research C o r r e l a t i o n S e r v i c e . I t i s the f u n c t i o n o f t h i s s e r v i c e t o a i d the many highway r e sea rch agencies t o c o r r e l a t e t h e i r work th rough per ­sona l v i s i t s , confe rences , committee work , and d i s t r i b u t i o n o f p e r t i ­nent i n f o r m a t i o n .

1 1

HIGIT-VAY RESEiVRCH BOARD

1947

O F F I C E R S

Chairman R. L . Mor r i son Vice Chairman F . V. Reagel Director R. W. Crum Associate Director Fred Burggraf

E X E C U T I V E CC»JMITTEE

Ex-Officio, Thomas H . MacDonald, Commiss ioner , P u b l i c Roads Ad­m i n i s t r a t i o n

Ex-Officto. F r e d e r i c k M. F e i k e r , Chairman, D i v i s i o n of E n g i n e e r i n g and I n d u s t r i a l Research, N a t i o n a l Research C o u n c i l

Ex-Officio, H a l H. Ha le , E x e c u t i v e S e c r e t a r y , American A s s o c i a t i o n of S t a t e highway O f f i c i a l s

R. H. Ba ldock , S t a t e Highway Eng inee r , S t a t e Highway Commission of Oregon

Pyke Johnson, P r e s i d e n t , Automot ive S a f e t y Founda t ion Bur ton W. Marsh, D i r e c t o r , Sa fe ty and T r a f f i c Engineer ing Department,

American Automobile A s s o c i a t i o n R. L . M o r r i s o n , P ro fe s so r o f Highway E n g i n e e r i n g and Highway Trans ­

p o r t , Department o f C i v i l E n g i n e e r i n g , U n i v e r s i t y of Mich igan

R. A. Moyer, Research Assoc ia t e P r o f e s s o r o f Highway E n g i n e e r i n g , Iowa S ta te C o l l e g e

F. V. Reagel, Engineer of M a t e r i a l s , M i s s o u r i State Highway Department Charles M. Upham, E n g i n e e r - D i r e c t o r , American Road B u i l d e r s ' Assoc i ­

a t i o n S t a n t o n W a l k e r , D i r e c t o r o f E n g i n e e r i n g , N a t i o n a l Sand and Grave l

A s s o c i a t i o n

DEPARTMENT OF ECONOMICS, FINANCE AND ADMINISTRATION

H . S. Fai rbank, Chairman

Committee on A c q u i s i t i o n and Legal C o n t r o l o f R i g h t - of -Way, Highway Access and A d j a c e n t Areas

Frank C. B a l f o u r , C h i e f R i g h t - o f - W a y Agent , C a l i f o r n i a D i v i s i o n of Highways

J , M. Devers , C h i e f Counse l , Oregon S t a t e Highway Commission J . L . D i c k s o n , E n g i n e e r - M a n a g e r , San A n t o n i o - U r b a n Expressways H . E . H i l t s , D e p u t y Commiss ione r , Depar tment o f D e s i g n , P u b l i c

Roads A d m i n i s t r a t i o n L , W. Kern , R i g h t - o f - W a y Engineer , Maryland S ta t e Roads Commission Theodore M. Matson, D i r e c t o r , Bureau o f Highway T r a f f i c , Yale U n i ­

v e r s i t y H. J . Nea le , Landscape E n g i n e e r , V i r g i n i a Department o f Highways F l a v e l S h u r t l e f f , Counse l , American P l a n n i n g and C i v i c A s s o c i a t i o n

TABLE OF CONTENTS

Page

FOREWORD v i

SUMMARY AND CONCLUSIONS 1

U N D E S I R A B I L I T Y OF STATE LEGISLATION OF SPECIAL AND 2 LOCAL CHARACTER 2

EXTENT OF SPECIAL PARKING LEGISLATION 3

S u g g e s t e d p o l i c y 4

DECLARATION OF POLICY 4

D e s i r a b l e e l e m e n t s o f p o l i c y 6

DESIGNATION OF PARKING F A C I L I T I E S 6

ADMINISTRATIVE AUTHORITY AND J U R I S D I C T I O N 7

S t a t e 7 S p e c i a l d i s t r i c t s 7 C i t y 7 C o u n t y 9 T o w n , v i l l a g e o r o t h e r l o c a l u n i t 9 A d m i n i s t r a t i o n o f s p e c i a l p r o j e c t s 9

PLANNING AND PRELIMINARIES 9

I n d i c a t e d p o l i c y 10

FINANCING 11

S t a t e 11 S p e c i a l d i s t r i c t s 11

Page

C i t y 12 C o u n t y 14 T o w n , v i l l a g e o r o t h e r l o c a l u n i t 14 S u g g e s t e d p o l i c y 15

LAND A C Q U I S I T I O N 15

S t a t e IS S p e c i a l d i s t r i c t s . . . 15 C i t y 15 C o u n t y 16 T o w n , v i l l a g e , o r o t h e r l o c a l u n i t 16 D e s i r a b l e p o l i c y 16

CONSTRUCTION 16

S t a t e 16 S p e c i a l d i s t r i c t s 17 C i t y 17 C o u n t y 17 T'own, v i l l a g e o r o t h e r l o c a l u n i t 18

MAINTENANCE AND OPERATION 18

S t a t e 18 S p e c i a l d i s t r i c t s ' 18 C i t y 18 C o u n t y 19 T o w n , v i l l a g e , o r o t h e r l o c a l u n i t 19

BASIC TABLES ON STATE LEGISLATION 19

LEGISLATION OF 1946 DEALING WITH PARKING F A C I L I T I E S . . 19

APPENDIX. BASIC L E G I S L A T I V E DATA BY STATES 21

FOREWORD

This ana lys i s o f s t a t e enab l ing l e g i s l a t i o n of a s p e c i a l and l o c a l charac ter d e a l i n g w i t h automobile p a r k i n g f a c i l i t i e s has been rev iew­ed by the Committee on Land A c q u i s i t i o n and C o n t r o l of Highway Access and Adjacent Areas, Department of Economics, Finance, and A d m i n i s t r a ­t i o n , the Committee on Park ing , Department of T r a f f i c and Opera t ions , b o t h of the Highway Research Board , and o t h e r s i n t e r e s t e d i n the problem of automobi le p a r k i n g f a c i l i t i e s . The comments submit ted by these committees and i n d i v i d u a l s have been h e l p f u l i n the p r e p a r a t i o n o f t h i s monograph.

I t i s the second o f a s e r i e s of s t u d i e s of l e g i s l a t i o n d e a l i n g w i t h the p r o v i s i o n of au tomobi le p a r k i n g f a c i l i t i e s . The f i r s t i n ­v e s t i g a t i o n concerned s t a t e general e n a b l i n g a u t h o r i t y of s t a t e -wide or area-wide a p p l i c a t i o n . * This second p r e s e n t a t i o n i nc ludes s t a t e e n a b l i n g l e g i s l a t i o n o f a s p e c i a l and l o c a l c h a r a c t e r , a p p l i c a b l e only t o s p e c i f i c p laces or s p e c i a l p r o j e c t s . Both monographs should be rev iewed t o g e t h e r , i n order t h a t the i n t e r e s t e d reader may v iew the f i e l d o f s t a t e p a r k i n g l e g i s l a t i o n i n i n t e g r a t e d f a s h i o n . ^

•^See AN ANALYSIS OF GENERAL STATE ENABLING LEGISLATION DEALING WITH AUTOMOBILE PARK­ING F A C I L I T I E S , Highway Research Board, Bu l l e t in No. 2, Revised 1947.

^ I t should be noted that these studies include only State l eg i s la t ion that i s spe­c i f i c a l l y appl icable to automobi le parking f a c i l i t i e s . Add i t i ona l ly , there may be some state legis la t ion which is generally applicable to public improvements, and by administrative or j u d i c i a l interpretation may relate to parking f a c i l i t i e s . No attempt has been made to include th is type of state l e g i s l a t i o n i n e i ther inves t igat ion .

DESIGN OF F L E X I B L E PAVEMENT

, USING

THE T R I A X I A L COMPRESSION TEST

Kansas has had extensive experience during the past six years with the use of the t r i a x i a l ceopression apparatus and method of testing.1 Engineers of the State Highmy Ceonission of Kansas fee l that this test is par t icu lar ly we l l adapted to use in the design of f l ex ib le paveoent. Tr iax ia l tests may be conducted upon each ceopenent of both the road surface and the foundation indiv idua l ly and calcula­tions made to determine the thickness of each material which is required over the sub-grade.

This manual describes the equipoent and procedure for preparation and testing used i n Kansas. I t defines the problem of f l ex ib l e pavenent design and shows in d e t a i l how the t r i a x i a l test is used for the purpose of design. Sample calcula­t ions , derivations, and convenient tables and charts are included.

ANALYSIS OF THE PROBLEM OF DESIGN OF FLEXIBLE PAVEMENTS

An accurate method o f des ign f o r f l e x i b l e p a v e m e n t s i s r e q u i r e d w h i c h w i l l e v a l u a t e the q u a l i t y o f a l l p o r t i o n s o f the roadway f o r each c o n d i t i o n t h a t occurs over a g i v e n l o c a t i o n . The de s ign metnod d e s c r i b e d i n t h i s manual makes use o f the t r i a x i a l compres s ion t e s t . E s s e n t i a l l y t h i s t e s t p r o v i d e s l a t e r a l suppor t t o a specimen wh ich a t the same t ime i s s u b j e c t e d t o a v e r t i c a l l oad . I t a l l ows e x p u l s i o n o f water f r o m the specimen as the t e s t p rogresses i n a manner s imu­l a t i n g the l o s s o f wa te r f r o m ma­t e r i a l under f i e l d c o n d i t i o n s . The s t r e s s c o i n c i d e n t w i t h s t r a i n i s obta ined at r egu la r i n t e r v a l s . From these data a s t r e s s - s t r a i n curve i s d rawn w h i c h , i n t u r n , i s used f o r d e t e r m i n i n g the modulus of deforma­t i o n .

Samples o f the m a t e r i a l s t o be used are t a k e n and such t e s t p r o ­cedure adop ted as i s necessary t o

report of ea r l i e r work i n Kansas on th is Ridiway Research Board, p.109-116, (1943).

determine the q u a l i t y and th ickness o f each component f o r the pavement under c o n s i d e r a t i o n . The t e s t r e ­s u l t s a r e a p p l i e d b y t h e use o f p r o v e n t h e o r e t i c a l f o r m u l a s and c o r r e l a t e d w i t h s e r v i c e records o f s p e c i f i c c o n d i t i o n s . The method used i s s u f f i c i e n t l y f l e x i b l e t o be a p p l i c a b l e t o any c o n d i t i o n s of t r a f f i c , c l i m a t e , and ma te r i a l s i n ­v o l v e d . S u f f i c i e n t t e s t s should be made on a p r o j e c t t o f u l l y eva lua te the e x i s t i n g v a r i a b l e roadbed con­d i t i o n s . N o r m a l l y s e v e r a l d i f f e r ­en t s o i l s and c m d i t i o n s o f s o i l s occur over a l o c a t i o n o f moderate l e n g t h . Since sampling and t e s t i n g a re b o t h per formed w i t h reasonable ease and speed, i t i s p o s s i b l e t o f u l l y e v a l u a t e the t o t a l w o r t h o f the l e n g t h o f the p r o j e c t , w i t h o u t n e g l e c t i n g i n v e s t i g a t i o n s o f u n ­u s u a l l o c a l i z e d a r e a s .

DEVELOPMENT OF T R I A X I A L TESTING

The t r i a x i a l con5)ression method

subject appears in V o l . 23, Proceedings,

o f t e s t has been used f o r research and d e t e r m i n a t i o n o f c e r t a i n char ­a c t e r i s t i c s of mix tures by a number o f o rgan iza t ions f o r seve ra l years . I t i s a d a p t a b l e t o t e s t i n g a l l t ypes or c l a s s i f i c a t i o n s o f s o i l s and r e l a t e d m a t e r i a l s . Subgrade s o i l s may c o n v e n i e n t l y be t e s t e d w i t h t h e i r n a t u r a l o r e x i s t i n g s t r u c t u r e i n t a c t , or b y i n d u c i n g s t r u c t u r a l f o r m a t i o n .

The e q u i p m e n t f o r t h e Kansas H i g h w a y C o m m i s s i o n was d e s i g n e d e s p e c i a l l y w i t h t h e s e needs i n mind. The complete bas i c u n i t was cons t ruc t ed a t a l o c a l machine shop. A d d i t i o n a l items "have been added t o the u n i t as the need f o r them be­came a p p a r e n t .

About 1,000 sq f t o f f l o o r space i s needed f o r c o n d u c t i n g t h i s work w i t h equipment desc r ibed l a t e r when 100 or more t e s t s pe r month are t o be conduc t ed . When i n s t a l l e d , i n 1941. t h i s - e q u i p m e n t cos t a p p r o x i ­mate ly 2,000 d o l l a r s , e x c l u s i v e o f the compression machine. An aver ­age o f one t e s t per hour may be run w i t h t h i s equipment . The a d d i t i o n o f a second compression machine f o r load a p p l i c a t i o n would pe rmi t more t e s t s t o be r u n i n a g i v e n t i m e w i t h o u t i n c r e a s i n g the other equip­ment.

The t e s t t echn ique as desc r ibed l a t e r has been developed t o the ex­t e n t t h a t i t may be e a s i l y adopted by any o r g a n i z a t i o n w i s h i n g t o de­s i g n f l e x i b l e pavements by t h i s method.

D u r i n g t h e past s i x years over 6,000 t r i a x i a l t e s t s have been con­ducted by the s o i l s d i v i s i o n o f the M a t e r i a l s Department o f the Kansas Highway Commission. Most of these t e s t s have been made i n connec t ion w i t h f l e x i b l e pavement s t u d i e s . These have i n c l u d e d r e s e a r c h t o c o r r e l a t e t e s t r e s u l t s w i t h se rv ice b e h a v i o r o f h ighways w h i c h have been i n s e r v i c e f o r a number o f y e a r s . The p r o c e d u r e has been d e v e l o p e d t o s u c h an e x t e n t t h a t f o r the pas t two yea r s t e s t s have

been co/iducted t o evalua te the con­d i t i o n s which e x i s t on each p r o j e c t f o r the des ign of new c o n s t r u c t i o n . T h i s i s now r o u t i n e f o r a l l p r o ­j e c t s r e q u i r i n g f l e x i b l e s u r f a c e s .

UTILIZING THE TRIAXIAL TEST METHOD

The t r i a x i a l compression t e s t i s r e a d i l y u s a b l e and p r a c t i c a l f o r de te rmin ing s t r e n g t h values of each component o f the roadbed s t r u c t u r e i n c l u d i n g the subgrade, sub-base , base, and su r face c o u r s e . Each o f t hese w i l l be d i s c u s s e d b r i e f l y .

Subgrade s o i l s a r e p r e f e r a b l y t e s t e d w i t h t h e i r s t r u c t u r e i n t a c t . T h i s i s a c c o m p l i s h e d b y c u t t i n g specimens f r o m r e l a t i v e l y u n d i s ­tu rbed m a t e r i a l s , commonly r e f e r r e d t o as und is tu rbed samples. I n sons cases , i t i s d e s i r a b l e t o o b t a i n d i s t u r b e d samples p r i o r t o e a r t h ­w o r k c o n s t r u c t i o n . Specimens o f t h i s d i s t u r b e d m a t e r i a l are molded and t e s t e d t o p r o v i d e t e n t a t i v e de s ign va lues which are cons ide red as an e s t i m a t e o n l y . The a c t u a l d e n s i t y w h i c h i s o b t a i n e d d u r i n g e a r t h w o r k c o n s t r u c t i o n has a v e r y c r i t i c a l e f f e c t upon the s t r e n g t h o b t a i n e d and , s i n c e t h i s d e n s i t y cannot be p r e d i c t e d a c c u r a t e l y , un­d i s t u r b e d samples a r e o b t a i n e d a f t e r c o n s t r u c t i o n is complete f o r f i n a l e v a l u a t i o n on wh ich t o base the d e s i g n .

Bases or sub-bases are ob ta ined and t e s t e d as a f i n i s h e d m i x t u r e o r t he i n d i v i d u a l m a t e r i a l s are combined i n p r o p o r t i o n s t o p rov ide the d e s i r e d m i x t u r e . The t r i a x i a l compress ion t e s t i s a u s e f u l t o o l f o r o b t a i n i n g c o m p a r a t i v e v a l u e s o f v a r i o u s types of m i x t u r e s such as s o i l - a g g r e g a t e o r b i t u m e n -a g g r e g a t e , f o r d i f f e r e n t i a t i n g between c o m p a r a t i v e s t r e n g t h s ob-t a i h e d w i t h round agg rega t e s and a n g u l a r c r u s h e d a g g r e g a t e s , and a,lso f o r comparing combinat ions o f these m a t e r i a l s . I t i s a l so u s e f u l i n e v a l u a t i n g t h e e f f e c t on m i x -

t u r e s o f v a r i a t i o n s i n g r a d a t i o n and p r o p o r t i o n o f b i n d e r , and i n comparing the s t r e n g t h s o f d i f f e r ­e n t b i n d e r s . I t i s p o s s i b l e t o t e s t m i x t u r e s h a v i n g a l a r g e pe r ­centage o f coarse m a t e r i a l t o ob­t a i n an e v a l u a t i o n o f the m i x t u r e as a w h o l e . T h i s e l i m i n a t e s t h e p r a c t i c e of t e s t i n g o n l y tha t por ­t i o n w h i c h passes a c e r t a i n s i z e o f sc reen t h a t i s common tor o the r methods u t i l i z i n g s m a l l specimens.

F l e x i b l e s u r f a c e s , c o n s i s t i n g o f b i t u m i n o u s m a t s , s o m e t i m e s c a l l e d dense graded surface courses, may a l s o be e v a l u a t e d by the t r i -a x i a l t e s t . These m i x t u r e s may be combined and handled i n the labora­t o r y i n any manner ( t e m p e r a t u r e , e t c . ) t ha t w i l l assure tha t the re ­s u l t s w i l l be the same as those obta ined d u r i n g f i e l d c o n s t r u c t i o n .

The methods of t e s t are e x p l a i n ­ed under LABORATORY TESTING. The load d i s t r i b u t i n g medium i n a road s t r u c t u r e may c o n s i s t of a s u r f a c e course and a base course combined or e i t h e r one used s e p a r a t e l y . The f o u n d a t i o n may c o n s i s t o f a sub-base and a sil>grade combined or may be o n l y a subgrade. A f t e r a l l o f t h e components w h i c h a p p l y t o a g i v e n p r o j e c t have been e v a l u a t e d , the u n i f i e d s t r u c t u r e may be d e -'s i g n e d .

COMPOKEHT PARTS OF ROADBED STRUC­TURE DEFINED Terms used i n t h i s manual may be d e f i n e d as f o l l o w s :

Subgrade - The e x i s t i n g s o i l s w h i c h occur on a p r o j e c t , e i t h e r as s o i l s i n c u t s e c t i o n s or as ma­t e r i a l d e r i v e d from b u l k borrow and p l a c e d i n f i l l s w i t h o u t s p e c i f i c s e l e c t i o n . These are the ma te r i a l s u p o n w h i c h t h e o t h e r component p a r t s o f the roadbed s t r u c t u r e are p l a c e d .

Sub-base - A l a y e r or l a y e r s o f m a t e r i a l placed between the sub-grade and the base course h a v i n g g rea te r s t a b i l i t y than the subgrade bu t u s u a l l y l e s s s t a b i l i t y than a base c o u r s e . The sub-base may be

s p e c i a l b o r r o w m a t e r i a l w h i c h i s placed on the subgrade or i t may be c r e a t e d by m o d i f y i n g the t o p p o r ­t i o n of the e x i s t i n g subgrade by t h e a d d i t i o n and i n c o r p o r a t i o n o f s u i t a b l e aggrega te s .

Base Course - A l a y e r w h i c h has h i g h i n t e r n a l s t a b i l i t y . Ma­t e r i a l s f o r aggregate b i n d e r base cou r se may be any c o m b i n a t i o n of crushed s tone, g r a v e l , sand, sand-g r a v e l , c h a t , o r l i m e s t o n e - g r a v e l w i t h s o i l or other q u a l i f i e d b inde r m a t e r i a l mixed i n such a manner as t o be u n i f o r m l y graded and of u n i ­form p l a s t i c i t y throughout . Kansas S t a n d a r d S p e c i f i c a t i o n s g i v e the requirements of grading and p l a s t i ­c i t y f o r v a r i o u s types o f c o n f i n e d m a t e r i a l s .

Surface Course or Pavement -A r e l a t i v e l y w a t e r p r o o f top course composed of an aggrega t ion of i n e r t p a r t i c l e s h e l d t oge the r by a b i t u ­minous b i n d e r . The m i x t u r e should be p l a c e d at such t h i c k n e s s as t o impar t added s t r e n g t h t o the road s t r u c t u r e and be h i g h l y r e s i s t a n t t o wear .

EVALUATION Of ROADBED - Before con­s i d e r i n g t h e d e s i g n o f f l e x i b l e pavement i t i s f i r s t necessary t o u n d e r s t a n d t h e f u n c t i o n s o f the component p a r t s o f the c o m p l e t e s t r u c t u r e . By comple te s t r u c t u r e i s meant t he s u r f a c e cou r se , base c o u r s e , s u b - b a s e , and s u b g r a d e t a k e n as a u n i t . I t i s sometimes p o s s i b l e t o d e s c r i b e e m p i r i c a l l y t h e r e q u i r e m e n t s o f a base course f o r a g i v e n subgrade s u b j e c t e d t o o r d i n a r y t r a f f i c . However, i t i s n o t p o s s i b l e t o d e s i g n an economi­c a l b a s e c o u r s e b y e m p i r i c a l methods f o r adverse c o n d i t i o n s such as e n c o u n t e r e d over muck s p o t s , f r o s t heave areas , and weak s t r u c ­t u r e d sha les or s o i l s over which many f a i l u r e s o c c u r even u n d e r n o r m a l road t r a f f i c . Hence f o r heavy loads on poor subgrades one o r more sub-bases may be economi­c a l l y r e q u i r e d . Sub-bases o f f e r an

improvement over e x i s t i n g sii>grades but are not g e n e r a l l y of s u f f i c i e n t s t r e n g t h t o a c t as t he main l oad c a r r y i n g c o m p o n e n t . They a l l o w more economica l c o n s t r u c t i o n t han t h e use o f a base c o u r s e o n l y .

A comprehensive method of des ign must be adequate f o r a l l subgrade c o n d i t i o n s encountered on the p r o ­j e c t , and i t must enable the e n g i ­neer t o e v a l u a t e each component s e p a r a t e l y and combine them t o de­s i g n a s u i t a b l e r o a d s t r u c t u r e .

Design va lues of the modulus o f d e f o r m a t i o n have been d e t e r m i n e d f o r some o f t he s t a n d a r d types of s t a b i l i z e d mixtures used i n Kansas. M a t e r i a l s which meet the s p e c i f i c a ­t i o n s f o r these s t anda rd m i x t u r e s must have m o d u l i at l e a s t equal t o these d e s i g n v a l u e s . Those whose c h a r a c t e r i s t i c s f a l l w e l l w i t h i n or about the midd le o f the s p e c i f i c a ­t i o n r equ i remen t s u s u a l l y p r o v i d e much grea ter s t a b i l i t y as evidenced b y c o n s i d e r a b l y h i g h e r m o d u l i o f d e f o r m a t i o n . The des ign modul i f o r the types of base course g e n e r a l l y used i n Kansas a t the present t ime are shown i n Table 1 .

4

TABLE 1

Kansas Type Material

Design Modulus of DeforuBtion

AB-1 Coarse Sand Gravel 7,000 bound wi th So i l

AB-2 Fine Sand Gravel 6,000 - 7.000 bound with So i l

AB-3 Crushed Limestone 10,000 bound with Line Dust

AB-4 Oiat 10,000 bound with S i l ica Dust

A l l o f these types have A A S H 0 p l a s t i c i t y i n d i c e s l i m i t s o f 1 t o 6) except AB-4 wh ich has l i m i t s o f 0 t o 6.

IMPOSED TESTING CONDITIONS - One advantage o f t h i s method o f de s ign i s t h a t c e r t a i n c o n d i t i o n s may be imposed i n the l a b o r a t o r y s i m u l a t ­i n g those tha t are encountered dur ­

i n g c o n s t r u c t i o n i n the f i e l d . For example l a t e r a l pressure i s app l i ed t o the t e s t specimen which i s s i m i ­l a r t o the suppor t p r o v i d e d by the sur rounding m a t e r i a l when a load i s a p p l i e d t o a g i v e n p o r t i o n of the s t r u c t u r e . L i k e w i s e c o n d i t i o n s o f s a t u r a t i o n and s t r e s s are imposed which approximate those encountered

' i n t h e a c t u a l roadbed. These a re discussed more f u l l y i n the f o l l o w ­i n g paragraphs.

S a t u r o t t o n - T h i s p r o c e d u r e r equ i r e s tha t a l l sanples be t e s t e d i n a s a t u r a t e d c o n d i t i o n . Sa tura ­t i o n i s deemed d e s i r a b l e i n o rder t o o b t a i n a d i r e c t compar i son f o r a l l types o f m a t e r i a l s and a t the same t ime o b t a i n a measure o f the s t r e n g t l i when t h e m a t e r i a l i s i n i t s most c r i t i c a l c o n d i t i o n . Ma­t e r i a l s such as s o i l s and s t a b l e m i x t u r e s seldom f a i l when d r y , bu t u s u a l l y f a i l when q u i t e w e t . A s o i l mass i s considered t o be f u l l y sa tu ra ted when a l l o f the vo ids are f i l l e d w i t h wa te r l e a v i n g p r a c t i ­c a l l y no a i r spaces. T h i s c o n d i ­t i o n i s a t t a i n e d i n the f i e l d d u r ­i n g p r o l o n g e d p e r i o d s o f we t w e a t h e r o r i n u n d a t i o n due t o f l o o d s , or a t seepage a reas , t h e l e n g t h of t ime r e q u i r e d f o r sa tura ­t i o n depending upon the c h a r a c t e r ­i s t i c s o f the s o i l .

Und i s tu rbed samples of subgrade are o b t a i n e d and c o m p l e t e l y s a t u ­r a t e d i n the l a b o r a t o r y by means o f a vacuum. T h i s p r o c e d u r e makes p o s s i b l e a u n i f o r m c o n d i t i o n t h r o u g h o u t the spec imen .

For many areas o f low r a i n f a l l , s a t u r a t i o n p r o v i d e s a c m s i d e r a b l e f a c t o r of s a f e t y . I t proves t o be more o f a f a c t o r o f s a f e t y t h a n e c o n o m i c a l c o n s t r u c t i o n m i g h t d i c t a t e i n areas where f i e l d mois­t u r e c o n d i t i o n s are no t as severe as i s the s a t u r a t e d c o n d i t i o n i m ­posed on the sQmples t e s t e d . Th i s s i t u a t i o n i s c o a v e n i e n t l y and ac­c u r a t e l y d e a l t w i t h , however , b y u s i n g a s a t u r a t i o n c o e f f i c i e n t based on the average annua l r a i n -

f a l l ( T a b l e 2 ) . T h i s c o e f f i c i e n t i% not t o be cons t rued as be ing the percentage of s a t u r a t i o n . The t e s t c o n d i t i o n s and methods remain con­s t a n t , hence the t e s t values remain c o m p a r a t i v e and an economica l de­s i g n i s p o s s i b l e . Such p rocedure does n o t d i f f e r m a t e r i a l l y > f r o m t h a t used b y d e s i g n e r s o f o t h e r t y p e s o f s t r u c t u r e s .

TABLE 2

Saturation Coefficient

ft 1.0 0.9 0.8 0.7 0.6

Average Annua 1 RaiAfal l

in . 35.0 - 45.0 30.0 - 34.9 25.0 • 29.9 20.0 • 24.9 15.0 - 19.9

Table 2 may be extended t o make the method a p p l i c a b l e t o areas hav­i n g d i f f e r e n t r a i n f a l l ranges. The values shown i n the t a b l e have been c o r r e l a t e d w i t h a c t u a l c o n d i t i o n s i n Kansas. Other l o c a l i t i e s , w i t h d i f f e r e n t ra tes o f e v a p o r a t i o n , may r equ i r e o ther va lues of the c o e f f i ­c i e n t . Kansas has c o n s i d e r a b l e area w h i c h i s r e p r e s e n t e d by each o f the r a i n f a l l bands .

F l e x i b l e type sur faces are p l e n ­t i f u l i n the area o f each band thus our e x p e r i e n c e i s a d a p t a b l e t o o t h e r areas o f l i k e r a i n f a l l . A r e v i e w o f t h e " A t l a s o f Amer ican A g r i c u l t u r e " p u b l i c a t i o n on p r e ­c i p i t a t i o n t h r o u g h o u t t h e U n i t e d S t a t e s r e v e a l s t h a t f o r t y s t a t e s have r a i n f a l l bands c o v e r i n g a t l e a s t 50 p e r c e n t o f t h e i r a r e a w h i c h a r e t h e same as t h o s e i n Kansas. The except ions are F l o r i d a , Alabama, M i s s i s s i p p i , Oregon, Wash­i n g t o n , N e v a d a , A r i z o n a , a n d L o u i s i a n a . I n t he se s t a t e s more than SO percent of the areas under­go e i t h e r more o r l e s s r a i n f a l l t han Kansas, Thus , these c o e f f i ­c i e n t s ' a re a p p l i c a b l e t o a l a r g e p e r c e n t a g e o f t h e t o t a l a r e a o f

t he U n i t e d S t a t e s . Lateral Pressure - The l a t e r a l

p r e s s u r e w h i c h i s a p p l i e d t o t h e specimen s imula tes the l a t e r a l sup­po r t or h o r i z o n t a l r e s i s t ance which i s n o r m a l l y p r o v i d e d by the a d j a ­cent s i m i l a r m a t e r i a l i n the road ­b e d . F o r e x a m p l e , c o n s i d e r a

normal subgrade upon wh ich i s l a i d a p l a t e 9 i n . i n d i a m e t e r . I f a load of 5,000 l b i s a p p l i e d t o t h i s p l a t e r e s t i n g upon t h e s u b g r a d e , some se t t l emen t w i l l l i k e l y o c c u r . I f t h e l o a d i s r e l e a s e d , t h e ma­t e r i a l .removed f r o m the edge o f the p l a t e out f o r 6 i n . and t o a d e p t h o f a t l e a s t 18 i n . , and the 5 ,000-I b l o a d r e a p p l i e d , t h e c y l i n d e r w i l l s e t t l e t o a much g r e a t e r de­g r e e . The l o a d has no t been i n ­creased , b u t the h o r i z o n t a l r e s i s ­tance has been removed a l l o w i n g the s ides of the s o i l c y l i n d e r t o move o u t w a r d when u n s u p p o r t e d . When m a t e r i a l su r rounded the c y l i n d e r , such h o r i z o n t a l movement was r e ­s i s t e d . The l a t e r a l p r e s s u r e a p ­p l i e d t o a specimen i n a t r i a x i a l compression t e s t i s s i m i l a r i n e f ­f e c t t o t h i s h o r i z o n t a l r e s i s t a n c e .

A l a t e r a l pressure o f 20 l b per sq i n . i s used f o r f l e x i b l e pave­ment d e s i g n .

Stress - P ressure a p p l i e d a t the sur^faee produces s t resses w i t h ­i n the m a t e r i e l be low. The magni­tude o f the s t r e s s a c t i n g upon the roadbed s t r u c t u r e dec reases w i t h d e p t h below the p l ane o f l o a d a p ­p l i c a t i o n ; t h e r e f o r e the amount o f s t r e s s f o r each component ( l a y e r ) i s dependent upon i t s d i s t a n c e b e -l o v the road s u r f a c e . The decrease i n s t r e s s as d e p t h i n c r e a s e s r e ­s u l t s f r o m a d i s t r i b u t i o r t o f a load over an increased a rea .

I n t r i a x i a l compression t e s t i n g , two s t resses are evaluated: v e r t i ­c a l and l a t e r a l . The p r i n c i p a l s t r e s s d i f f e r e n c e i s the d i f f e r e n c e between these two s t r e s se s and i s expressed as ( v - Z ) . Data o b t a i n e d f r o m t r i a x i a l t e s t s p r o v i d e the

range of s t r e s s d i f f e r e n c e which i s used t o d e t e r m i n e t h e modulus o f d e f o r m a t i o n f o r t h e m a t e r i a l be ing t e s t e d . T h i s i n t u r n may be used w i t h the co r r e spond ing s t r e s s d i f ­f e rence found under wheel loads t o de te rmine the p rope r t h i c k n e s s o f any s p e c i f i e d t y p e o f s u r f a c e .

SAMPLING FOR LABORATORY TESTING

M a t e r i a l s wh ich are t o be t e s ted i n t r i a x i a l c o m p r e s s i o n s h o u l d p r e f e r a b l y be i n t h e f o r m o f u n ­d i s t u r b e d samples t a k e n f r o m the e x i s t i n g roadway or area w h i c h i s t o be i f l i p r o v e d . H o w e v e r , t h e method may be used on samples mold­ed f r o m b u l k s o i l . Extreme c a r e and e x p e r i e n c e d judgment a r e r e ­q u i r e d i n o b t a i n i n g s a m p l e s t o a ssure t h a t r e l i a b l e r e s u l t s may be ob ta ined . A c l e a r unders tanding o f t h e i n f o r m a t i o n needed and t h e e f f e c t o f t h i s da ta upon the f i n a l des ign and c o n s t r u c t i o n o f the p r o ­j e c t w i l l a i d c o n s i d e r a b l y i n ob­t a i n i n g p r o p e r r e p r e s e n t a t i v e s a m p l e s .

SUBGRADES CREATED BY GRADIHG - When a l o c a t i o n has been s e l e c t e d f o r g r a d i n g and s u r f a c i n g w i t h a f l e x ­i b l e pavement , a s o i l s u r v e y i s c o n d u c t e d . T h i s i s a c c o m p l i s h e d by b o r i n g holes o r d i n a r i l y w i t h an o rchard type auger ( I on F i g u r e 1) t o a d e p t h a t l e a s t e q u a l t o t h e p lanned grade o f t h e d i t c h l i n e . The a r e a l d i s t r i b u t i o n o f a l l s o i l s i s a c c u r a t e l y d e t e r m i n e d . The i n t e r v a l s between t e s t holes should be s u f f i c i e n t l y shor t t i n t a l l s o i l changes may be d e t e r m i n e d . I t may v a r y f r o m less than one hundred t o s e v e r a l h u n d r e d f e e t , d e p e n d i n g upon the topography* A t l e a s t 60 l b d r y w e i g h t o f e a c h sample i s ob t a ined . When more than the regu­l a r number o f t e s t s as f l e s c r i b e d under LABORATORY TESTING a r e t o be pe r fo rmed , t h i s q u a n t i t y i s i n ­

creased. Samples r ep re sen ta t ive o f each s o i l type are submi t t ed t o t h e l a b o r a t o r y .

A f t e r r o u t i n e p h y s i c a l t e s t s have been c o n d u c t e d , samples are s e l e c t e d f o r t r i a x i a l compress ion t e s t s . Th i s s e l e c t i o n i s based on t h e p r o p o s i t i o n t h a t a l l types o f s o i l wh ich w i l l appear i n the f i n ­i shed subgrade t o any a p p r e c i a b l e e x t e n t w i l l need t o be e v a l u a t e d f o r s t r e n g t h . A l l l o c a l i z e d areas of ev ident weak s o i l s t r u c t u r e must be appra i sed i n o r de r t o de te rmine whether s p e c i a l t r ea tmen t o f a d d i ­t i o n a l th ickness or b e t t e r m a t e r i a l may be r e q u i r e d . M a t e r i a l s t h a t a r e b e t t e r t h a n t h e average b u t wh ich have a l i m i t e d a r e a l e x t e n t may not need t o be e v a l u a t e d .

EXISTING SUBGRADES - When an e x i s t ­i n g roadway i s t o be improved by the a d d i t i o n o r improvement o f a f l e x i b l e pavement, the c o n d i t i o n of the e x i s t i n g subgrade i s su rveyed . T h i s is" done by probe b o r i n g s ex­t e n d i n g i n t o t h e s u b g r a d e t o a d e p t h o f a t l e a s t one f o o t f o r h i g h w a y s . The d i s t a n c e b e t w e e n ho le s f o r these p robe b o r i n g s i s s t c h t h a t a l l changes i n s o i l type and c o n d i t i o n may be a s c e r t a i n e d . I n o r d e r t o a s s u r e t h a t t h i s i s accomplished the d i s t ance i s r a r e l y more than 500 f t f o r c o n d i t i o n s en­coun te red i n Kansas, and o f t e n i s somewhat l e s s .

Probe b o r i n g s may be made by hand equipment, bu t where t h e sub-grade i s q u i t e hard and conta ins an a p p r e c i a b l e q u a n t i t y o f aggrega te the use o f a power auger f a c i l i ­t a t e s the w o r k . S e v e r a l types o f power equipment have been found t o be f a i r l y s a t i s f a c t o r y .

A f t e r probe b o r i n g s have been c o n d u c t e d t h r o u g h o u t a p r o j e c t , r e p r e s e n t a t i v e m a t e r i a l s a r e se­l e c t e d and the l o c a t i o n s determined f o r o b t a i n i n g u n d i s t u r b e d t r i a x i a l samples. P resen t Kansas p r a c t i c e c a l l s f o r a t l e a s t two samples per

m i l e f o r each type and c o n d i t i o n - o f m a t e r i a l encounte red i n the upper one f o o t of the subgrade. I n t h i s way the s u r f a c e f o r an e n t i r e p r o ­j e c t i s not des igned on the b a s i s o f any one s m a l l l o c a l i z e d c o n d i -t i o n .

Samples a r e o b t a i n e d i n t h e i r e x i s t i n g s t r u c t u r a l c o n d i t i o n ( r e l ­a t i v e l y u n d i s t u r b e d ) b y use of a s p e c i a l sampler . One type o f such sampler c o n s i s t s of a c y l i n d e r and a d r i v i n g head w h i c h w i l l f a c i l i ­t a t e f o r c i n g t h e sampler i n t o the subgrade and p u l l i n g i t out w i t h t h e sample c o n t a i n e d t h e r e i n .

SAMPLING EQUIPMENT - The s amp l ing equipment used i n Kansas ( F i g . l ) has been developed f o r the purpose of o b t a i n i n g e s s e n t i a l l y u n d i s t u r b ­ed samples o f subgrade s o i l s . The i tems i n F i g u r e 1 are as f o l l o w s :

(A) Saupler - The barre l of the sampler is made of seamless s tee l tubing six (6") inches i n s i d e d iameter and ten (10") inches long. The d r i v i n g head i s made from larger s ized tubing with a one-inch plate welded in the top. P r o v i s i o n i s made in the driving head to permit driving to a depth of 12 inches. A 2- inr pipe 43 i n . long i s welded to th is s t e e l p la te for use as a drive pipe. Holes H i n . in diameter spaced at 2M-in. centers v e r t i ­c a l l y are d r i l l e d through the drive pipe to f a c i l i t a t e pu l l ing the sampler a f t e r i t i s dr iven . The sampler has a cut t ing edge with an inside diameter of 5.75 i n . to provide r e l i e f for the sample and to permit the use of a s p l i t sheet metal sleeve inside the b a r r e l . The outside of the c u t t i n g edge is beveled for a d i s ­tance of 1.25 i n . Detailed plans of this equipment are avai lable at the Materials Department of the Kansas Highway Com­m i s s i o n .

(B) Drive Bawuer - This hammer, which weigjis approDcimately 65 lb, was made from a piece of 4 - i n . outjtide diameter seamless s t e e l tubing 42 i n . long. I t i s c losed at one end with a s t e e l plate welded to the pipe and reinforced with heavy strap i ron bent over the end of the pipe and p la te and welded to the outside of the p ipe . The two handles made from 1 - i n . s t ee l rod are fastened to the outside of the pipe wi th four L-shaped p ieces of strap iron welded to the pipe and to each

rod. The handles are further reinforced with a l ight s t r a p iron from the end of each handle to the top of the pipe (One of these s trap irons has been broken and does not show in the p i c t u r e . ) . Power driving equipment may be used in place of the manual dr ive hammer.

( C ) Hydraulic Jacks - Two h y d r a u l i c jacks with 3-ton capacity and 6 - i n . l i f t are used to pul l the sampler a f t e r i t i s dr iven . Handles for the jacks are lying beside them in the p ic ture .

(D) Sanple Puller - Two 3 - i n . channels 3 f t long are fastened together 2.5 i n .

Figure 1. Sampling Equipment

apart by welding a 6- by 5- in . plate under one end of the pa ir , to form a device for pull ing the sampler.

( E ) Steel Plate - A s t e e l plate 6 i n . long and 2 i n . wide i s placed on one of the jacks under the end of the channels opposite from the welded stee l plate when pull ing the sampler.

( F ) Steel Rod - A s t e e l rod 7/16 i n . i n diameter and 12 i n . long i s inserted through the holes in the dr ive pipe for the channels to push aga ins t .

(G) Push-Out Block - A s t e e l cy l inder 5 i n . in outside diameter and 12 in . long with a round s t e e l plate welded over one

8 end. The sample is placed on th is plate and the sampler is pushed o f f the sample.

(H) Push-Ovt Cylinder-An open cylinder 6-3/8-in. inside diameter which is placed on top of the t tar re l of the sampler to f a c i l i t a t e forc ing i t downward from the sample.

( I ) Auger - An ordinary orchard type auger for making probe borings.

PROCURING TEE SAMPLE - I t i s ' neces­s a r y t o remove g r a v e l o r a s p h a l t s u r f a c i n g f rom the subgrade over an a r e a a p p r o x i m a t e l y 7 i n . i n d i ­ameter b e f o r e an u n d i s t u r b e d sub-grade sample can be o b t a i n e d . The s a m p l e r ( A ) w i t h t h e hammer ( B ) p laced on i t may be set i n a v e r t i ­c a l p o s i t i o n on the stibgrade i n the manner shown i n F i g u r e 1 . The hammer may t h e n be l i f t e d and a l l o w e d t o f a l l f r e e l y . The f o r c e o f t h e b l o w d r i v e s the sampler a s h o r t d i s t a n c e i n t o the subgrade . The d i s t a n c e wh ich the hammer must be r a i s e d and dropped may be v a r i e d a c c o r d i n g t o the c o n d i t i o n o f the subgrade. H i e nurdser o f blows may range f r o m about t e n f o r s o f t ma­t e r i a l s w h i c h are wet and a t l ow d e n s i t y t o more t h a n one hundred blows f o r d r y hard m a t e r i a l s w i t h h i g h d e n s i t y .

U n d i s t u r b e d samples s h o u l d be o b t a i n e d f r o m the p o r t i o n o f the roadway where f a i l u r e i s most l i k e ­l y t o occur . F a i l u r e s o f f l e x i b l e pavements u s u a l l y occur a l o n g the edges o f the pAvement; t h e r e f o r e i t i s p r a c t i c a l t o evaluate the c o n d i ­t i o n near the edge o f the pavement i n order t o determine the exis tence of p o t e n t i a l f a i l u r e s . For a road w h i c h n o r m a l l y c a r r i e s t r a f f i c f o r a w i d t h o f about 24 f t the weakest c o n d i t i o n s f o r which des ign va lues need t o be determined u s u a l l y occur a t a d i s t a n c e o f 11 f t f r o m the c e n t e r l i n e . I f any d i f f e r e n c e s are t o be made i n t r e a t m e n t r e l a t i v e t o the c r o s s - s e c t i o n o f a roadway, . sampj.es may be r e q u i r e d f r o m o ther p o s i t i o n s . When the subgrade be­comes a p p r e c i a b l y weaker as t h e depth increases , i t i s necessary t o

o b t a i n a sample of the weakest ma­t e r i a l a l t h o u g h i t may o c c u r s e v e r a l inches f r o m the s u r f a c e . Sometimes two v e r t i c a l und i s t u rbed samples may be ob ta ined a t d i f f e r ­e n t d e p t h s a t t h e same l o c a t i o n .

When rock or g r a v e l i s p r e s e n t and und i s tu rbed samples of the sub-grade can not be ob t a ined , d i s t u r b ­ed samples may be o b t a i n e d . These may be sampled as p r e v i o u s l y de s ­c r i b e d under SUBGRADES CREATED BY GRADING. U n d i s t u r b e d samples o f subgrade as f o u n d i n t h e roadbed a r e p r e f e r a b l e and s h o u l d be used when p o s s i b l e .

SURFACE COURSE OR PAVEMENT MATERI-lALS - M a t e r i a l s w h i c h are t o be used f o r c o n s t r u c t i o n o f t he s u r ­f a c e cours .e a r e sampled by any means whereby r e p r e s e n t a t i v e p o r ­t i o n s m a y b e o b t a i n e d . When t h e y occur i n a bank d e p o s i t , t e s t holes o r p i t s a re dug t o de termine t h e ex ten t and v a r i a t i o n of the m a t e r i ­a l i n the d e p o s i t . I f the d e p o s i t i s c o n s i d e r e d s u i t a b l y u n i f o r m , a composite sample may be obta ined t o represent such m a t e r i a l .

When two or more m a t e r i a l s are conbined f o r any s p e c i f i c component o f t h e pavement t h e y a re mixed i n t h e p r o p e r p r o p o r t i o n s i n t h e l a b o r a t o r y f o r t e s t i n g . S u f f i c i ­e n t l y l a r g e samples a re o b t a i n e d f o r a l l - o f t he n e c e s s a r y t e s t s . T h i s o r d i n a r i l y r e q u i r e s about 100 l b o f m a t e r i a l unless s p e c i a l t e s t s a r e t o be conducted w h i c h r e q u i r e more m a t e r i a l . D u r a b i l i t y t e s t s on m a t e r i a l s w i t h w h i c h p o r t l a n d cement i s t o be i n c o r p o r a t e d r e ­q u i r e a b o u t 300 l b o f m a t e r i a l .

CARE AND TRANSPORTATION OF SAMPLES - Samples w h i c h a r e o b t a i n e d i n t h e i r u n d i s t u r b e d s t a t e must be h a n d l e d i n s u c h way t h a t t h e i r s t r u c t u r e w i l l not be d i s t u r b e d . Many m a t e r i a l s w h i c h a re e i t h e r q u i t e d r y or v e r y wet and which are a t a l o w r e l a t i v e d e n s i t y may e a s i l y be d i s t u r b e d and t h e i r char-

a c t e r i s t i c s a l t e r e d . P a r t i c u l a r c a r e must be t a k e n i n h a n d l i n g samples o f these types o f m a t e r i ­a l s .

Samples have been s a t i s f a c t o r i l y packed i n damp sawdust i n boxes w h i c h h o l d f r o m f o u r t o e i g h t samples. The sawdust i s moistened so t h a t v e r y l i t t l e change occurs i n t h e m o i s t u r e c o n t e n t of t h e samples d u r i n g s h i p m e n t . These boxes have been shipped by f r e i g h t s a t i s f a c t o r i l y . I n d i v i d u a l samples are sometimes p laced i n ga lvan ized

and t r a n s p o r t e d by any means which w i l l i n s u r e t h e i r a r r i v a l w i t h o u t l o s s o f m a t e r i a l .

V ' LABORATORY TESTING

T e s t s a r e c o n d u c t e d i n t h e l a b o r a t o r y t o determine the p h y s i ­c a l c h a r a c t e r i s t i c s of each m a t e r i ­a l w h i c h i s s ampled . The number and charac ter o f these t e s t s d i f f e r , d e p e n d i n g upon the n a t u r e o f t he samples submi t ted and the use which

F i g u r e 2 . T r i a x i a l Equipment Asseirbled f o r Tes t

m e t a l cans 8 i n . i n d i a m e t e r and 12 i n . h i g h us ing a m a t e r i a l s i m i ­l a r t o t h e sample f o r p a c k i n g . M o i s t u r e c o n t e n t i s m a i n t a i n e d f a i r l y cons tan t by s e a l i n g the can w i t h adhesive t a p e .

No p a r t i c u l a r ca re i s r e q u i r e d i n h a n d l i n g d i s t u r b e d s a m p l e s . These may be o b t a i n e d by any con-

/ v e n i e n t method , p l a c e d i n sack^ .

i s t o be made of the r e s u l t s . Some o f t hese t e s t s a r e o f a r o u t i n e cha rac te r and the methods are s t an ­d a r d i z e d and may r e a d i l y be found elsewhere. Therefore on ly the t r i ­a x i a l compression t e s t i s descr ibed i n f u l l . The others are designated i n t h i s s e c t i o n under the heading Routine Physical Tests f o r each o f the types of samples and m a t e r i a l s

d i scussed . ' " > '

EQUIPMENT - D e t a i l e d p lans o f t he t r i a x i a l compression equipment are a v a i l a b l e a t the M a t e r i a l s Depa r t ­ment o f the Kansas Highway Com­m i s s i o n . Seve ra l photographs are shown t o a s s i s t i n d e s c r i b i n g the equipment and the var ious steps i n ­v o l v e d i n the p r e p a r a t i o n of spec i ­mens and conduct o f the t e s t . F i g ­ure 2 shows a specimen i n the com­pres s ion chamber ready f o r t e s t i n g .

mens - Specimens 2 . 8 i n . i n d i ­ameter and 8 i n . h i g h are prepared f r o m samples i n e i t h e r an u n d i s ­t u r b e d o r a d i s t u r b e d c o n d i t i o n . The type most used i s designated as an u n d i s t u r b e d specimen. Th i s i s c u t f r o m a r e l a t i v e l y u n d i s t u r b e d sample w h i c h i s o b t a i n e d as des­c r i b e d p r e v i o u s l y . The other type , d e s i g n a t e d as a d i s t u r b e d or r e ­molded specimen, i s p repa red f rom m a t e r i a l o b t a i n e d i n a d i s t u r b e d c o n d i t i o n . The equipment used f o r

F i g u r e 3 . Equipment f o r P repa r ing Specimens

A h y d r a u l i c compression machine i s used f o r app ly ing the l o a d . L a t e r a l support i s p rov ided th rough g l y c e r ­i n around the specimen. Pressure i s a p p l i e d by means of the g l y c e r i n r e s e r v o i r shown on the l e f t of the p h o t o g r a p h as a p a r t i a l l y f i l l e d t a l l c y l i n d e r . An e l e c t r i c motor and compressor i n s i d e the c a b i n e t s u p p l y a i r p r e s su re t o the r e s e r ­v o i r . The mercury manometer, a s p i ­r a t o r b o t t l e , p i p e t t e s , va lves and e l e c t r i c s w i t c h are mounted on the manometer board near the r e s e r v o i r . V a r i o u s p o r t i o n s of the equipment a re shown more i n d e t a i l i n e t h e r p h o t o g r a p h s and d e s c r i b e d more f u l l y i n l a t e r pa ragraphs .

Equipment for Preparing Sped-

p r e p a r i n g b o t h types of specimens i s shown i n F i g u r e 3 . The methods o f p r e p a r i n g specimens a re des ­c r i b e d l a t e r . Items shown i n F i g ­ure 3 are as f o l l o w s :

( A ) Timer - A Kodak t in ier c l o c k used for t iming molding o p e m t i o n s .

( B ) Push-Out Blocks - Two w o o d e n b l o c k s 2 . 8 i n . i n d i a m e t e r ; one about 7 i n . l ong and the o t h e r 5 i n . l o n g .

( C ) Upper Piston - A b r a s s p i s t o n 2 . 8 i n . i n d i a m e t e r , 2 i n . h i g h w i t h a f lange M i n . t h i c k and 4 i n . i n d i a m e t e r .

( D ) Mold - A c y l i n d r i c a l mold 2 . 8 i n . i n i n s i d e d i a m e t e r and 1 1 . 2 5 i n . h i g h .

( E ) LovDer Piston - A b r a s s p i s t o n 2 . 8 i n . i n d i a m e t e r and 1 . 5 i n . h i g h w i t h a f l a n g e ^ i n . t h i c k and 5 i n . i n d i a m e t e r . I n c l u d e d w i t h t h i s a r e two s p a c e r s each 1 i n . t h i c k c u t from a r i n g w i t h a n i n ­s i d e d iameter of 2 . 8 i n .

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( F ) Undisturbed Sample - T h i s shows Sample No. 314 a f t e r i t has been removed from i t s packing ready for p r e p a r a t i o n of a s p e c i m e n . I t i s e n c a s e d i n the s h e e t m e t a l s l e e v e t h a t i s p l a c e d i n s i d e the s p e c i a l s a m p l e r b e f o r e i t i s d r i v e n .

( G ) Pressboard Disc - One d i s c 2 . 8 i n . i n d i a m e t e r and one d i s c 4 i n . i n d i ­ameter cut from pressboard 1/4 i n . t h i c k . I t i s convenient to have a number of d i s c s s i m i l a r t o e a c h of t h e s e a v a i l a b l e f o r use .

( H ) Cutting fool ~ A s t e e l c y l i n d e r 8 i n . long w i t h a n i n s i d e d i a m e t e r a t the c u t t i n g edge of 2 . 8 i n . , t h e n r e l i e v e d throughout the remainder of the c y l i n d e r t o a n i n s i d e d i a m e t e r of 2 . 9 i n . The o u t s i d e diameter i s 3 . 1 5 i n . The c u t t i n g edge i s b e v e l e d f o r a d e p t h of 0 . 6 i n .

r o d or s t e e l b a r a b o u t 5 / 8 i n . a m e t e r and a b o u t 1 8 i n . i o n s .

i n d i •

Unassembled Triaxial Test Equipment - The equipment which i s necessary f o r a s s e m b l i n g the c o m p r e s s i o n chamber comple t e w i t h a specimen enc losed f o r t r i a x i a l compress ion t e s t a f t e r i t has been prepared i s shown i n F i g u r e 4 . Th i s equipment i s d e s c r i b e d s u f f i c i e n t l y here t o i d e n t i f y the p ieces ; the manner i n w h i c h t h e y are used i s d e s c r i b e d l a t e r i n the e x p l a n a t i o n of t he t e s t p r o c e d u r e . I t e m s shown i n F i g u r e 4 a re as f o l l o w s :

F igu re 4 . Unassembled Test Equipment

( I ) Knives - An a s s o r t m e n t of k n i v e s r a n g i n g f r o m l o n g b u t c h e r k n i v e s t o s m a l l e r ones s i m i l a r t o h e a v y p a r i n g k n i v e s .

( J ) Hire Saw - A c o p i n g saw or h a c k saw w i t h the b l a d e removed and r e p l a c e d w i t h a f i n e p i a n o w i r e or g u i t a r s t r i n g .

( K ) f i n Snips - Used for c u t t i n g w i r e s on u n d i s t u r b e d s a m p l e s .

( L ) Straight Bdge - A s t a i n l e s s s t e e l s t r a i g h t edge 12 i n . long.

(M) Calipers - C a l i p e r s f o r measuring d i a m e t e r s to the n e a r e s t 0 .01 i n .

(N) Rule - A s t a i n l e s s s t e e l r u l e 12 i n . long, graduated i n 0 . 0 1 - i n . increnents .

(O) Paper Discs - T h i n paper d i s c s 2 . 8 i n . i n d iameter .

( P ) Tamping Sod - A s t a n d a r d tamping

A d i a 1 w i t h 1 - i n . d i v i s i o n s mounted on

( A ) ^ mes Dial -t r a v e l and 0 . 0 0 1 - i n . a p o s t . •

{B) D ial Arm ( C ) Piston ( D ) Bead Plate - An aluminum c a s t i n g

10 i n . i n d i a m e t e r , 1 i n . t h i c k , w i t h a g l y c e r i n t r o u g h , a i r v e n t p r o v i d e d w i t h a v a l v e and c o n n e c t i o n for an a i r h o s e , and a thuirib screw f o r s e c u r i n g the d i a l p o s t . I t a l s o has an o p e n i n g f o r the p i s t o n equipped w i t h a bronze bush ing , and h o l e s for t h r e e t i e r o d s .

( E ) forming Core - A wooden b l o c k 2 . 8 i n . i n d iameter and 10 i n . l ong .

( F ) Base Plate - An aluminum c a s t i n g 10 i n . i n d iameter and 1 i n . t h i c k w i t h a base p e d e s t a l 2 . 8 i n . i n d i a m e t e r , 1 i n .

12

h i g h w i t h a s m a l l v e r t i c a l h o l e i n t h e c e n t e r i n t e r s e c t i n g a s m a l l h o l e i n a r a d i a l d i r e c t i o n through the main p o r t i o n of the base to w h i c h i s a t t a c h e d a w a t e r v a l v e . A g l y c e r i n v a l v e i s a t t a c h e d to a s m a l l r a d i a l ho le i n t e r s e c t i n g a v e r t i c a l ho le outs ide the base p e d e s t a l and i n s i d e a groove made f o r the compres s ion c y l i n ­d e r .

( G ) C o m p r e s s i o n Cylinder - A l u c i t e c y l i n d e r 4 . 7 5 i n . i n s i d e dia iheter and 13 i n . h i g h .

(H) Can of Pander - Used for c o n d i t i o n ­ing rubber s l e e v e s .

( I ) liner - A Kodak t i m e r c l o c k . A •s top w a t c h may be u s e d .

( J ) nuhher Bands ( K ) Rubber Sleeve - A s l eeve 2 . 8 i n . i n

greater than 3/8 i n . are molded i n ­t o specimens S i n . i n d iameter and 14 i n . h i g h f o r t r i a x i a l compres­s i o n t e s t s . This requi res some ad­d i t i o n a l equipment such as a mold and compression chamber. The load­ing dev ice may be a h y d r a u l i c com­press ion machine w i t h 18 i n . c l e a r ­ance be tween p o s t s and a maximum v e r t i c a l opening of 36 i n . Figure 5 shows equipment needed f o r t e s t s on large specimens. Items shown i n F igu re 5 are as f o l l o w s :

( A ) C o m p r e s s i o n Cylinder - A s t e e l c y l i n d e r 8 i n . i n i n s i d e diameter and 19 .5

Figure 5 . Equipment f o r Large Specimens

d i a m e t e r and 10 i n . long made of rubber a p p r o x i m a t e l y 0 . 0 1 7 i n . t h i c k .

( L ) Sample Cap (M) Porous Stones - Manufactured s t c n e s

2 . 8 i n . i n d iameter hi i n . t h i c k w h i c h a l ­low f r e e p e r c o l a t i o n of w a t e r .

( N ) Calipers - C a l i p e r s f o r measuring d i a m e t e r s to the n e a r e s t 0 .01 i n .

( O ) Kuts and Washers ( P ) Rule - A s t a i n l e s s s t e e l r u l e 12

i n . long, graduated i n 0.01 i n . increments . ( 0 ) Ifrench ( R ) Feeler Gauge - An a d j u s t a b l e gauge

a p p r o x i m a t e l y 13 i n . long f o r a l i g n i n g h e a d and b a s e p l a t e s .

Equipment for Large Spec imens M a t e r i a l s such as base courses

w h i c h have maximum s i z e p a r t i c l e s

i n h i g h . ( B ) A*es Dial - D i a l w i t h 1 - i n . t r a v e l

and 0 . 0 0 1 - i n . d i v i s i o n s mounted on a p o s t . ( C ) Dial Arm ( D ) Piston ( E ) Head Plate - Aluminum c a s t i n g 12

i n . i n d i a m e t e r , 1 i n . t h i c k w i t h a g l y c e r i n t r o u g h , a i r vent provided w i t h a v a l v e and connec t ion for an a i r hose , and a thuni) screw for s e c u r i n g the d i a l p o s t .

• I t a l s o h a s an o p e n i n g f o r t h e p i s t o n equipped w i t h a bronze bush ing , and ho les f o r t h r e e t i e rods .

( F ) Base Plate - An aluminum c a s t i n g 12 i n . i n d i a m e t e r , 1.25 i n . t h i c k w i t h a b a s e p e d e s t a l 5 i n . i n d i a m e t e r , 1 i n . h i g h , w i t h a s m a l l v e r t i c a l h o l e i n the c e n t e r i n t e r s e c t i n g a s m a l l h o l e i n a r a d i a l d i r e c t i o n through the main p o r t i o n

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of the base to which i s attached a water valve . A glycerin valve is attached to a s n a i l radia l hole intersecting a v e r t i c a l hole outside the base pedestal and inside a groove nade for the compression cyl inder.

( G ) Mold - A s t e e l cy l inder 5 i n . in ins ide diameter by 14 i n . h igh , f i t t e d with a removable c e l l a r extending 2 i n . higher.

(H) roruing Jacket - An aluminum sp l i t cylinder 5.075 i n . inside diameter, 16 in . long, provided with three c l a o ^ .

( I ) forming Core - A wooden block 5 i n . in diameter 16 i n . long.

( J ) Compaction Bammer - A haniner which w i l l de l iver a blow equal to the force of a 5M-lb hammer dropping 12 i n . This is a m o d i f i c a t i o n of the s t a n d a r d AASHO ( P r o c t o r ) hammer w h i c h may be u s e d .

( K ) Push-Out Block - A wooden block 5 i n . i n diameter by 5 i n . h i g h . Three blocks s i m i l a r to t h i s are required .

( L ) Sample Cap (U) Parous Stones - Manufactured stones

5 i n . i n d iameter , M i n . t h i c k , which a l low f r e e p e r c o l a t i o n of w a t e r .

(N) Calipers - Calipers for determining the diameter of 5 in . specimens.

(O) Straight gdge - A s t a i n l e s s s t ee l straight edge 12 i n . long.

( P ) Rule - A s t a i n l e s s s t e e l rule 12 in . long, graduated in 0.01-in. Increments.

(Q) Subber Sleeve - A sleeve 5 i n . in diameter and 17 i n . long made of rubber approximately 0.03 i n . t h i c k .

PROCEDURE FOR PREPARATIOH AMD TEST-ISG - Subgrade samples a r e sub ­m i t t e d t o the l a b o r a t o r y i n e i t h e r an und i s tu rbed c o n d i t i o n or as d i s ­t u r b e d m a t e r i a l t o be molded f o r t r i a x i a l t e s t i n g . Specimens are a l s o prepared i n the l a b o r a t o r y f o r t e s t i n g base m a t e r i a l s and a spha l t m i x t u r e s .

Undisturbed Subgrade Samples 1 . Rout ine P h y s i c a l Tests - R e f e r ­ence was made at the b e g i n n i n g o f t h i s s e c t i o n t o the v a r i o u s t e s t s which are conducted on each sample s u b m i t t e d t o t h e l a b o r a t o r y ' f o r e v a l u a t i o n i n connec t ion w i t h f l e x ­i b l e pavement des ign . A l l of these t e s t s except the t r i a x i a l compres­s i o n t e s t s are regarded as of r o u - , t i n e charac ter i n t h i s work. These t e s t s c o n s i s t o f p l a s t i c i n d e x , mechanica l a n a l y s i s , and s p e c i f i c g r a v i t y . The procedures f o r these

t e s t s a re g i v e n i n t h e book o f s t a n d a r d p rocedu re s " H i g h w a y Ma­t e r i a l s " , pub l i shed by the American A s s o c i a t i o n o f S ta t e Highway O f f i ­c i a l s . T'hey a r e a l s o g i v e n i n s p e c i f i c a t i o n s o f t h e • A m e r i c a n S o c i e t y f o r T e s t i n g M a t e r i a l s S t a n d a r d s . "

2 . T r i a x i a l C o m p r e s s i o n T e s t -P r e p a r a t i o n - The u n d i s t u r b e d sample i s removed f rom the c o n t a i n ­er and the metal l i n e r removed f r o m around the specimen. The sample i s n o m i n a l l y 6 i n . i n d i a m e t e r and 10 i n . i n h e i g h t . A specimen 2 . 8 i n . i n d iameter by 8 i n . i n he igh t i s c u t w i t h k n i v e s and w i r e saws. H i g h l y p l a s t i c c l a y s hav ing a h i g h m o i s t u r e c o n t e n t are more r e a d i l y c u t w i t h a w i r e saw, whereas most o t h e r m a t e r i a l s and t h o s e i n a d r i e r c o n d i t i o n are more r e a d i l y c u t w i t h k n i v e s . M a t e r i a l s w h i c h a r e r a t h e r d r y o r c r u m b l y a r e trimmed v e r y c a r e f u l l y a l i t t l e a t a t ime t o prevent l a rge chunks f rom b e i n g b r o k e n out o f the specimen. A c u t t i n g t o o l ( H , i n F i g . 3 . ) c y l i n d r i c a l i n f o r m , hav ing i n s i d e d imens ions e q u i v a l e n t t o t h a t de­s i r e d f o r t he specimen enables the o p e r a t o r more e a s i l y t o o b t a i n a specimen o f the p r o p e r dimensions and shape. The c y l i n d r i c a l c u t t e r i s p l aced on t o p o f the sample t o mark the c i r c u m f e r e n c e o f the de­s i r e d specimen and when most of the excess m a t e r i a l has been t r immed o f f , the c u t t e r i s pushed down as the f i n a l t r i m m i n g proceeds. Very l i t t l e m a t e r i a l can be l e f t on the spec imen t o be t r i m m e d w i t h t h e c u t t e r or t h e specimen may be un­d u l y d i s t u r b e d . The c u t t e r i s f o r c e d down u n t i l i t enc loses the d e s i r e d p o r t i o n of the specimen. The excess m a t e r i a l on each er»d i s t h e n t r i m m e d o f f f l u s h w i t h the ends o f t h e c u t t e r . I t i s q u i t e e s s e n t i a l t h a t b o t h ends of t h e specimen be t r immed p e r p e n d i c u l a r t o t he a x i s of t h e specimen. The t o p o f the specimen i s planed w i t h

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a s t r a i g h t k n i f e or s t r a i g h t edge, t h e n a l a r g e d i s c (G, i n F i g . 3 ) i s p laced on top and the specimen i n v e r t e d . The o t h e r end i s t h e n t r i m m e d c a r e f u l l y . Most o f t h e excess m a t e r i a l i s removed b e f o r e t h e f i n a l p l a n e i s c u t t o a v o i d p u l l i n g out too much m a t e r i a l f r o m the specimen. I f t oo much m a t e r i a l i s removed, a s m a l l d i s c i s p laced on t h e o t h e r end o f the specimen i n s i d e the c u t t e r by the f o l l o w i n g d o u b l e i n v e r t i n g p r o c e d u r e . A l a r g e d i s c i s p u t o n t o p , t h e specimen i s i n v e r t e d , a s m a l l d i s c i s placed next t o the specimen, the l a r g e d i s c i s r e p l a c e d , and the specimen i s i n v e r t e d a g a i n . Then the p l a n i n g process i s c o m p l e t e d , r e s u l t i n g i n a s h o r t e r spec imen .

The e n t i r e t r i m m i n g process r e ­qu i r e s from less than one-ha l f hour t o severa l hours depending upon the type o f m a t e r i a l and the s k i l l o f the o p e r a t o r .

I f samples have not been p r e v i ­ous ly obta ined f o r r o u t i n e p h y s i c a l t e s t s , t h e y a r e t a k e n f r o m t h e c u t t i n g s o b t a i n e d d u r i n g t h e t r imming process . The specimen i s we ighed as i t i s encased i n the^ c u t t i n g t o o l and t h i s w e i g h t r e ­corded a l o n g w i t h the t a r e w e i g h t o f the c u t t i n g t o o l .

Some o f the items r e f e r r e d t o i n the nex t few paragraphs are shown i n F i g u r e 4' and were d e s c r i b e d t o some extent i n connec t ion w i t h t h a t p i c t u r e .

The base p l a t e ( F ) i s prepared f o r use on the s a t u r a t o r shown i n F i g u r e 6. The water hose i s c o n ­n e c t e d t o the base p l a t e a t t h e water v a l v e . The base pedes t a l i s f i l l e d w i t h wa t e r f r o m the w a t e r f l a s k , making sure t h a t no a i r i s en t r apped i n the water hose.

The rubber s leeve ( K ) i s powder­ed , s l i p p e d over the wood f o r m i n g core ( E ) , placed on the base pedes­t a l and secured w i t h rubber bands. The r u b b e r s l e e v e i s r o l l e d down o f f the forming core on t o the base p e d e s t a l . One porous s tone (M) i s

p l aced on the t o p of the specimen w h i l e i t i s i n t h e c y l i n d r i c a l c u t t e r w i t h the c u t t i n g edge down. The specimen i s t hen i n v e r t e d and placed on the base pedes ta l and the c y l i n d r i c a l c u t t e r i s s l i p p e d down u n t i l i t touches the rubber s l eeve . G l y c e r i n i s spread on the c u t t e r t o f a c i l i t a t e s l i p p i n g t h e r u b b e r s l e e v e , and the rubber s leeve un ­r o l l e d on t h e c u t t e r . The wood f o r m i n g core i s p l aced on the t o p of the specimen t o hold i t i n place and the c u t t e r s l i p p e d up, l e a v i n g the rubber sleeve around the s p e c i ­men. T h i s p r o c e s s i s p e r f o r m e d more e a s i l y by u n r o l l i n g the rubber s l e e v e a l i t t l e a t a t ime as the c u t t e r i s s l i p p e d up , c a r e b e i n g e x e r c i s e d not t o p u l l t h e c u t t e r beyond the u n r o l l e d p o r t i o n of the rubber s l e e v e . I t may be manipu­l a t e d w i t h the hands when necessary t o improve the l u b r i c a t i n g e f f e c t o f t he g l y c e r i n .

A second porous s tone and the sample cap ( L ) a r e p l a c e d on t h e t o p o f the specimen and the t o p o f the rubber s leeve i s secured w i t h rubber bands. The rubber hose con­n e c t e d t o t h e vacuum l i n e i s a t ­t a ched t o the sample cap and the vacuum i s a p p l i e d .

The d iameter of the specimen i s o b t a i n e d by measur ing w i t h a p a i r of c a l i p e r s two d i a m e t e r s each at the t o p , m i d d l e , and bo t tom o f the specimen. These s i x measurements are recorded on the data sheet and averaged . Twice the t h i c k n e s s o f t h e r u b b e r s l e e v e i s s u b t r a c t e d f r o m the average o f the s i x r ead ­ings t aken t o g i v e the average net diameter of the specimen. The area of the specimen i s computed or ob­t a i n e d by r e f e r r i n g t o a Tab le o f Areas such as g i v e n i n Appendix A, Table A - 3 .

A 1 2 - i n . r u l e d i v i d e d i n t o hun­d r e d t h s o f an i n c h i s used t o de­te rmine the d i s t a n c e f rom the b o t ­tom o f the base pedestal t o the top o f the sample cap a t th ree p laces e q u a l l y spaced around the specimen.

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These t h r e e measurements a r e r e ­corded and the average taken. This i s the he igh t of the specimen p lus a constant c o n s i s t i n g o f the he ight o f the base p e d e s t a l , two porous s tones , and the sample cap. This cons tant i s s u b t r a c t e d t o g i v e the net he igh t o f t he specimen.

The net volume o f the specimen i s c a l c u l a t e d b y m u l t i p l y i n g the area o f t he s p e c i m e n b y t h e ne t he igh t and i s recorded on the da ta sheet .

mercury i s a p p l i e d t o the t o p of the specimen u n t i l water i s p u l l e d t h r o u g h the specimen and c o l l e c t s i n the wa te r t r a p p r o v i d e d i n the s u c t i o n l i n e nea r the s p e c i m e n . The volume o f wa t e r c o l l e c t e d i n the w a t e r t r a p i s s u b t r a c t e d f r o m the volume o f water go ing i n t o the s p e c i m e n t o d e t e r m i n e t h e net volume of water taken d u r i n g s a t u ­r a t i o n .

The l e n g t h o f t ime r e q u i r e d f o r s a t u r a t i o n may range f r o m a few

k f

Figure 6. Sa tu ra to r

Specimens which are t o be s a t u r ­a t ed have water made a v a i l a b l e t o the b o t t o m o f the specimen f r o m a f l a s k c o n t a i n i n g water at a p p r o x i ­m a t e l y the same e l e v a t i o n as the base. Water i s measured i n t o the f l a s k f r o m a 100 ml b u r e t t e . A p i c t u r e of a m u l t i p l e u n i t s a tu ra ­t o r i s shown i n Figure 6. This has a c a p a c i t y o f 16 specimens w h i c h may be s a t u r a t e d s i m u l t a n e o u s l y . Vacuum of a p p r o x i m a t e l y 25 i n . o f

minutes to two weeks, depending on the d e n s i t y and the c h a r a c t e r i s t i c s of t he m a t e r i a l . Commonly about one day i s r equ i r ed f o r undis turbed specimens of good subgrade m a t e r i ­a l s . The specimen i s again measur­ed a f t e r s a t u r a t i o n has been ob-t a i n e d .

The v a l v e i n the sample cap i s c l o s e d and the vacuum hose i s r e ­moved. The specimen i s ready t o be placed i n the compression chamber.

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This s t ep i n the procedure s h a l l be o m i t t e d f o r specimens which are t o be r u n a t t h e i r e x i s t i n g o r f i e l d m o i s t u r e c o n t e n t .

3> Conduct o f T r i a x i a l Compression T<est - T h e l u c i t e c y l i n d e r i s p laced on the ^rubber gasket i n the g roove o f t he base p l a t e and the head pJate i s p laced on the c y l i n ­de r , making c e r t a i n t h a t the c y l i n ­der sets i n the groove i n the head p l a t e . The rubber gasket must be i n p lace i n the groove i n the head p l a t e . The head p l a t e i s t u r n e d r e l a t i v e t o the base p l a t e t o p e r ­m i t the d i a l t o be read convenient ­l y d u r i n g the t e s t . The head p l a t e

i s t i g h t e n e d , u s i n g t h e f e e l e r gauge t o make su re t h a t t h e head p l a t e i s p a r a l l e l t o the base p l a t e .

The p i s t o n i s i n s e r t e d i n the head p l a t e and p l a c e d i n c o n t a c t w i t h the sample cap . The assenbled c o m p r e s s i o n chamber i s p l a c e d on the- lower p l a t e n o f the compression machine i n the proper p o s i t i o n f o r t h e hoses t o be a t t a c h e d and t h e d i a l t o be r e a d . I t i s c e n t e r e d a c c o r d i n g t o t h e c o n c e n t r i c r i n g s on t he upper b e a r i n g b l o c k and the p i s t o n . The d i a l a rm i s s e t i n p l a c e on t h e p i s t o n and t h e Ames d i a l put i n p o s i t i o n f o r an i n i t i a l r eed ing . The g l y c e r i n hose i s c o n ­n e c t e d t o the base p l a t e and t h e c o m p r e s s o r s t a r t e d , f o r c i n g t h e g l y c e r i n f r o m t h e r e s e r v o i r i n t o the compression chamber. The va lve i n t he head p l a t e - i's open d u r i n g t h i s process , .

The t i m e r may be s t a r t e d a t t he - t ime the compressor i s s t a r t e d . I t

c o u l d be s t a r t e d l a t e r i f d e s i r e d , as t he t i m e has no b e a r i n g on t h i s p o r t i o n o f t he t e s t . However, i t does se rve t o p r o v i d e a r e c o r d o f the t ime elapsed f rom t h i s s t e p i n the p r o c e d u r e t o t h e end o f t h e t e s t .

Vhen the compress ion chamber i s f u l l o f g l y c e r i n , the v a l v e i n the head p l a t e i s c l o s e d i f the p r e s ­

sure i n t h e g l y c e r i n r e s e r v o i r i s not more t han 20 l b per sq i n . I f t he p r e s su re i s ^oo h i g h when the c o m p r e s s i o n chamber i s f u l l o f g l y c e r i n , t h e v a l v e i n t h e base p l a t e i s c lo sed f i r s t and then the v a l v e i n t h e head p l a t e . The a i r pressure i n the g l y c e r i n r e s e r v o i r i s a d j u s t e d t o not more t h a n 20 l b per sq i n . and t h e v a l v e i n t h e base p l a t e i s a g a i n opened. When the compression chanber i s f u l l o f g l y c e r i n , the exac t l a t e r a l p r e s ­su re o f 20 l b p e r sq i n . i s t h e n a p p l i e d t o the specimen.

The va lves between the specimen and t h e wa te r p i p e t t e s a r e opened and r e a d i n g s t a k e n on the w a t e r l e v e l i n the p i p e t t e s . For s p e c i ­mens h a v i n g l i t t l e volume change one o f t h e p i p e t t e s may be c l o s e d f r o m the sys t e f l i .

A f t e r t he assembled compression chamber i s p l a c e d on t h e t e s t i n g mach ine and the c o r r e c t l a t e r a l pressure i s a p p l i e d an i n i t i a l l o ad r e a d i n g i s o b t a i n e d . Some t e s t i n g machines a r e so equipped t h a t the load readings may be made ze ro when the assenbled apparatus i s ' i n p lace and the l a t e r a l pressure i s a p p l i e d . T h i s e l i m i n a t e s t h e n e c e s s i t y f o r s u b t r a c t i n g t h e i n i t i a l r e a d i n g f r o m st i isequent r e a d i n g s . '

The l o a d i s a p p l i e d a t a c o n ­s t a n t r a t e o f s t r a i n by means o f t h e compression machine. The r a t e o f s t r a i n used depends upon t h e type o f m a t e r i a l b e i n g t e s t e d . I t has been customary t o use a r a t e o f s t r a i n o f 0.005 i n . per min on smal l specimens and 0 . 0 1 i n . per m i n on l a r g e spec imens . These r a t e s o f s t r a i n were se lec ted a f t e r a number o f t e s t s were r u n by i n c r e m e n t a l l o a d i n g . Each i n c r e m e n t was ap­p l i e d and l e f t u n t i l t h e d e f o r m a ­t i o n f o r e a c h m i n u t e o f t i m e e l apsed decreased t o a r e l a t i v e l y s m a l l v a l u e . The t o t a l l e n g t h o f t ime requ i red f o r conduc t ing a t e s t by i n c r e m e n t s was compared w i t h t h a t f o r a cons t an t r a t e o f s t r a i n and the above r a t e s were c h o s e n .

17

Readings a re t a k e n a t r e g u l a r i n t e r v a l s o f d e f o r m a t i o n , the f r e ­quency o f r e a d i n g s depending upon the data t o be obta ined and the use w h i c h i s t o be made o f i t . The example i n T a b l e 8 may serve as a g u i d e . These r e a d i n g s c o n s i s t o f v e r t i c a l d i a l r e a d i n g s , t i m e , v e r ­t i c a l l o a d , and p i p e t t e r e a d i n g s . I f t he p i p e t t e s become e i t h e r f u l l or empty d u r i n g a t e s t , the t h r e e -way v a l v e c o n n e c t i n g the p i p e t t e s , a s p i r a t o r b o t t l e and water hose t o the specimen i s manipulated t o pa r ­t i a l l y d r a i n or f i l l t he p i p e t t e s .

The l a t e r a l p r e s s u r e i s main­t a i n e d c o n s t a n t t h r o u g h o u t a p a r ­t i c u l a r t e s t . The t e s t i s c o n t i n u ­ed u n t i l the d e s i r e d da ta has been o b t a i n e d . For f l e x i b l e pavement subgrades about 0 . 2 - i n . d e f o r m a t i o n a f t e r the l o a d b e g i n s ' t o i n c r e a s e a t i t s most r a p i d r a t e f o r t he t e s t i s ample f o r c o n d i t i o n s o r d i n a r i l y encountered. The exact d e f o r m a t i o n r e q u i r e d may be d e t e r m i n e d f r o m c a l c u l a t i o n s e x p l a i n e d under CAL-CULATKWS and any v a r i a t i o n f r o m t h e above f i g u r e may be o b t a i n e d . I n case o f doub t t h e t e s t may be c o n t i n u e d u n t i l a 0 . 3 - or 0 . 4 - i n . decrease i n h e i g h t i s o b t a i n e d t o insu re s u f f i c i e n t d a t a . Some t e s t ­i n g t ime may be saved on the b e t t e r subgrades , o n base m a t e r i a l s , and on aspha l t m i x t u r e s , s ince the t e s t need be c o n t i n u e d o n l y u n t i l t h e maximum s t r e s s r e q u i r e d f o r the c a l c u l a t i o n s has been o b t a i n e d .

When the t e s t has been comple t ­ed , the v a l v e i n the wa te r l i n e a t t h e base p l a t e i s c l o s e d , the com­p r e s s i o n machine i s s t o p p e d , and t h e l a t e r a l p r e s su re i s r e l e a s e d . The <air hose i s c o n n e c t e d t o t h e v a l v e i n the head p l a t e , the v a l v e i s o p e n e d and t h e g l y c e r i n i s f o r c e d b a c k i n t o t h e g l y c e r i n r e s e r v o i r . The p i s t o n i s prevented f r o m b e i n g f o r c e d e n t i r e l y out o f t he head p l a t e d u r i n g t h i s ope ra ­t i o n . The specimen i s removed f r o m the base p l a t e , w e i g h e d , and oven-d r i e d t o c o n s t a n t we igh t a t 230 F .

Disturbed Subgrade Samples -Subgrade samples which are obta ined i n a d i s t u r b e d s t a t e are handled i n a s l i g h t l y d i f f e r e n t manner f r o m u n d i s t u r b e d samples .

1 . R o u t i n e P h y s i c a l Tes t s - These t e s t s i n c l u d e p l a s t i c i n d e x , me­c h a n i c a l a n a l y s i s , s p e c i f i c g r a v ­i t y , and s t anda rd compac t ion . The procedures f o r these t e s t s are g iven i n "Highway M a t e r i a l s " b y the Ameri ­can A s s o c i a t i o n o f S t a t e Highway O f f i c i a l s and i n s p e c i f i c a t i o n s of t he " A m e r i c a n S o c i e t y f o r T e s t i n g M a t e r i a l s S t a n d a r d s . "

The s tandard coiq>act ion t e s t i s conducted on raw s o i l s as they are sampled and a l s o on those t r e a t e d w i t h o t h e r m a t e r i a l s such as c e ­ment, a s p t i a l t , o r aggregate . Com­p a c t i o n t e s t s a r e r u n on t r e a t e d s o i l s w i t h the same percen tage o f admix tu re as i s t o be used f o r the t r i a x i a l compression t e s t . I n ad­d i t i o n t o the t e s t s as named above, some m a t e r i a l s must be c u r e d or s p e c i a l l y t r e a t e d b e f o r e t r i a x i a l c o m p r e s s i o n t e s t s a re c o n d u c t e d . M a t e r i a l s m i x e d w i t h cement may a l s o be t e s t e d f o r d u r a b i l i t y t o d e t e r m i n e t h e i r a b i l i t y t o w i t h -

' s t a n d w e a t h e r i n g .

2 . T r i a x i a l C o m p r e s s i o n T e s t -P r e p a r a t i o n - M a t e r i a l s wh ich have a maximum s i z e not g rea te r than 3/8 i n . may be p repa red i n a mold 2 . 8 i n . b y 8 i n . M a t e r i a l s w i t h a n a p p r e c i a b l e q u a n t i t y o f l a r g e r s ized p a r t i c l e s must be prepared i n a mold 5 i n . by 14' i n .

( a ) D e n s i t y - Specimens m a y b e molded by s t a t i c l o a d a p p l i e d by means o f a p i s t o n i n a mold o f the proper s i ze or they may be compact­ed w i t h a hanmer i n accordance w i t h the method o f c o n d u c t i n g s t anda rd c o m p a c t i o n t e s t s . Base m a t e r i a l s .and o t h e r s o f a s i m i l a r n a t u r e may r e a d i l y be hammered t o t h e same d e n s i t y as t h a t o b t a i n e d i n t h e

^ s t a n d a r d c o m p a c t i o n t e s t and sub-* sequent ly be s a t u r a t e d . D i f f i c u l t y

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has been encounte red i n hammering spec imens o f some m a t e r i a l s and s a t u r a t i n g them t o o b t a i n r e s u l t s comparable t o t h a t of, u n d i s t u r b e d s a m p l e s . The t y p e o f m a t e r i a l makes a c o n s i d e r a b l e d i f f e r e n c e i n t h e pe ' r cen tage o f s t a n d a r d com­p a c t i o n t o w h i c h a specimen must bC' remolded i n o rde r t o o b t a i n r e ­s u l t s c o m p a r a b l e t o u n d i s t u r b e d s e n i l e s . Any p a r t i c u l a r percentage of s tandard compaction i s ve ry d i f ­f i c u l t t o o b t a i n by any me thod o t h e r t h a n s t a t i c l o a d i n g .

H i g h l y p l a s t i c c l a y s when ham­mered i n f i v e l i f t s i n v a r i a b l y have a non -un i fo rm d e n s i t y . The tendency toward n o n - u n i f o r m d e n s i t y i n ­c reases p r o g r e s s i v e l y f r o m l i g h t f r i a b l e s o i l s t o t h e heavy c l a y s o i l s . T e s t r e s u l t s on hammered remolded specimens e s p e c i a l l y o f more p l a s t i c m a t e r i a l s a t v a r y i n g degrees o f s a t u r a t i o n a r e no t d e ­pendable ' . Such r e s u l t s a r e non­u n i f o r m and not r e p r o d u c i b l e . Ttiey a r e a d v e r s e l y a f f e c t e d by v a r i a ­t i o n s i n d e n s i t y and m o i s t u r e and n o n - u n i f o r m c o m p a c t i o n w i t h i n the specimen.

I n o rder t o o b t a i n u n i f o r m i t y o f r e s u l t s spec imens a re molded by s t a t i c load t o predetermined d e n s i ­t i e s and a t a s a t u r a t e d c o n d i t i o n . An i n v e s t i g a t i o n was made o f a group o f 629 t e s t s o f u n d i s t u r b e d specimens and 219 t e s t s o f s t a t i ­c a l l y remolded specimens t o d e t e r ­mine t h e p e r c e n t a g e o f s t a n d a r d compac t ion a t w h i c h t o mold s p e c i ­mens a t a s a t u r a t e d c o n d i t i o n t o g i v e t h e t h i c k n e s s o f f l e x i b l e pavement r e q u i r e d e q u i v a l e n t t o un ­d i s t u r b e d s a t u r a t e d specimens o f t h e same c l a s s i f i c a t i o n , p l a s t i c i n d e x , and d e n s i t y . I n a d d i t i o n , 73 t e s t s were conducted on t e n u n ­d i s t u r b e d samples and s e v e r a l hun­d r e d pounds o f d i s t u r b e d m a t e r i a l obtained a t the same depth f r o m one l o c a t i o n . A l l specimens, t h e r e f o r e , were as n e a r l y as poss ib l e composed o f i d e n t i c a l m a t e r i a l . T'he d i s ­t u r b e d m a t e r i a l was molded i n t o

specimens a t v a r i o u s c o n d i t i o n s o f m o i s t u r e and d e n s i t y . The r e s u l t s of t h i s i n v e s t i g a t i o n p rov ided da ta f o r remolding specimens as shown i n Table 3 .

TABLE 3

P l a s t i c Inlex

0 11 16 21 26

10 15 20 25 30

31 - 35 36 - up

Mold at PercenUge of Standard Compaction

1G2 100

98 96

92 90

Table 3 shows va lues d e s i r e d f o r t h e t e s t spec imen. Most subgrade s o i l s r e b o u n d s l i g h t l y when the pressure i s re leased a f t e r mo ld ing . To compensate f o r t h i s , va lues one percent h igher are used f o r comput­i n g the amount o f s o i l and mois ture r equ i r ed f o r mold ing .

A procedure has been devised by w h i c h t e s t r e s u l t s o n spec imens which are molded at some other per ­centage o f s tandard eonpac t ion a re ad ju s t ed t o g ive r e s u l t s equ iva l en t t o t h a t w h i c h would be lObtained a t the p e r c e n t a g e g i v e n i n T a b l e 3 . Consequent ly a s l i g h t v a r i a t i o n i s a l l o w a b l e and proper e v a l u a t i o n o f the m a t e r i a l may s t i l l be made.

Tests on remolded specimens a r e approx ima t ions o n l y t o be used f o r e s t i m a t i n g purposes . They are ex­p e c t e d t o be r e a s o n a b l y c l o s e t o t h e r e s u l t s o b t a i n e d f r o m u n d i s ­t u r b e d samples i f t he d e n s i t y ob­t a i n e d i n c o n s t r u c t i o n i s r eason­a b l y c l o s e t o t he maximum d e n s i t y ob ta ined by standard compaction. I n the t r i a x i a l t e s t c a l c u l a t i o n s , t he t h i c k n e s s r e q u i r e d i s a d j u s t e d one i n c h f o r each pound per c u b i c f o o t v a r i a t i o n between t h a t ob ta ined i n the specimen and the value conqjuted f r o m Table 3. A specimen t e s t ed a t a d e n s i t y lower than d e s i r e d shows g r e a t e r t h i c k n e s s r e q u i r e d . T'he t e s t r e s u l t s are a d j u s t e d by sub-

19

t r a c t i n g t h e n u m e r i c a l d i f f e r e n c e i n d e n s i t i e s f r o m t h e t h i c k n e s s c a l c u l a t e d .

( b ) Mois tu re Content - The mois-t u r e c o n t e n t o f m a t e r i a l t o be molded a c c o r d i n g t o t h i s procedure i s i n c r e a s e d t o t h a t w h i c h w i l l c o m p l e t e l y s a t u r a t e the specimen. T h i s v a l u e i s d e t e r m i n e d f r o m a s e t o f z e r o a i r v o i d s c u r v e s as g i v e n i n F i g u r e A-7 i n Appendix A.

( c ) M i x i n g - Water i s added t o the m a t e r i a l t o be molded and'mixed i n t h o r o u g h l y e i t h e r by hand o r w i t h a m e c h a n i c a l m i x e r . Those m a t e r i a l s w h i c h have f a i r l y d r y a g g r e g a t i o n s o f p a r t i c l e s a r e p l a c e d i n an a i r - t i g h t c o n t a i n e r f o r a p e r i o d o f s e v e r a l hours t o o b t a i n u n i f o r m d i s p e r s i o n o f t h e w a t e r t h r o u g h o u t t h e m a t e r i a l .

( d ) M o l d i n g - The m o l d and p i s t o n s are d e s i g n e d t o p r o d u c e a specimen h a v i n g a p r e d e t e r m i n e d vol imie . The amount of d r y m a t e r i a l r e q u i r e d t o f i l l t h i s v'olume i s computed f o r t he d e n s i t y d e s i r e d . The m o i s t u r e c o n t e n t r e q u i r e d f o r c o m p l e t e s a t u r a t i o n i s u s e d t o compute the wet w e i g h t . The proper we igh t o f wet m i x t u r e i s p l aced i n the mold i n t h r ee o r more p o r t i o n s , and rodded o r tamped s u f f i c i e n t l y t o g e t a l l o f t h e m a t e r i a l i n t o t h e m o l d . A t h i n pape r d i s c i s used on each end o f the specimen t o p r even t m a t e r i a l f r o m s t i c k i n g t o t h e p i s t o n s . S u f f i c i e n t l o a d i s a p p l i e d t o press the m a t e r i a l down t o the r e q u i r e d l e n g t h . A 20 ,000-I b compression machine may be used. The load i s mainta ined f o r a p e r i o d o f f i v e m i n u t e s b e f o r e b e i n g r e ­l eased . A plunger 12 i n . i n l e n g t h i s then used t o f o r c e the specimen out o f the mold . The specimen need no t be c o n f i n e d a f t e r removal f r o m the mold .

( e ) W e i g h i n g and M e a s u r i n g -A f t e r the specimen has been molded I t i s weighed. The diameter of the specimen i s o b t a i n e d by measur ing w i t h a p a i r o f c a l i p e r s t w o d i ­a m e t e r s a t t h e t o p , m i d d l e , and

b o t t o m o f t h e specimen. These s i x measurements are r e c o r d e d on t h e d a t a sheet ( T a b . 6 ) and ave raged .

The area of the specimen i s com­p u t e d or o b t a i n e d by r e f e r r i n g t o a T a b l e o f Areas such as i s g i v e n i n Appendix A .

A 1 2 - i n . r u l e d i v i d e d i n t o hun­dred ths o f an inch i s used t o meas­u r e the h e i g h t o f the specimen a t t h r e e p laces e q u a l l y spaced around t h e c i r c u m f e r e n c e . These t h r e e measurements are recorded and the average computed . The volume o f t h e specimen i s c a l c u l a t e d by m u l ­t i p l y i n g the area o f the specimen by the h e i g h t .

The c a l c u l a t e d mois tu re con ten t i s used f o r comput ing an e s t i m a t e d d r y w e i g h t o f the specimen. T h i s i s used t o compute an e s t i m a t e d d e n s i t y o f t h e spec imen a t t h i s t ime t o determine whether or not i t i s w i t h i n nn a l l owab le range o'f two percent o f the d e s i r e d d e n s i t y . I f t h e d e n s i t y i s n o t w i t h i n t h e s e l i m i t s a new spec imen i s u s u a l l y p r e p a r e d .

( f ) C u r i n g - Subgrades u s u a l l y have a p e r i o d o f c u r i n g between the t ime o f ea r thwork c o n s t r u c t i o n and t h e a d d i t i o n o f the s u r f a c e . There i s a l s o a c u r i n g p e r i o d b e f o r e any c o n s i d e r a b l e amount o f t r a f f i c w h i c h would cause f a i l u r e uses the r o a d . I t i s a g e n e r a l l y accep ted f a c t t h a t t h i s c u r i n g process i n ­creases the s t a b i l i t y o f b o t h s i b -g rades and base m a t e r i a l s . T r i ­a x i a l compress ion t e s t s have sub­s t a n t i a t e d t h i s o b s e r v a t i o n . A f t e r c u r i n g some m a t e r i a l s show a s l i g h t and o t h e r s a c o n s i d e r a b l e inc rease i n s t a b i l i t y . 'The s t a n d a r d p r o ­cedure i n Kansas t h e r e f o r e r equ i r e s t h a t a l l r e m o l d e d s p e c i m e n s be p l a c e d i n a m o i s t c a b i n e t f o r a p e r i o d o f f o u r days t o undergo a c u r i i i g p rocess . The mo i s tu r e c o n ­t e n t o f these specimens i s p r a c t i ­c a l l y unchanged d u r i n g t h i s t i m e .

( g ) Assenbl ing - A f t e r the s p e c i ­men has b e e n c u r e d i t i s a g a i n weighed and measured as p r e v i o u s l y

20

d e s c r i b e r l . A base p l a t e i s p r e ­p a r e d f o r r e c e i v i n g t h e specimen f o r t e s t . The base p e d e s t a l i s f i l l e d by p o u r i n g w a t e r i n t o i t and i f necessary a l l o w i n g s u f f i c i - ' e n t w a t e r t o r u n o u t t h r o u g h t h e w a t e r v a l v e d u r i n g t h i s o p e r a t i o n t o i n s u r e t h a t no a i r i s ent rapped i n t h e b a s e . A r u b b e r s l e e v e i s p o w d e r e d , s l i p p e d o v e r t h e wood f o r m i n g c o r e , p l a c e d on t h e base p e d e s t a l , and secured w i t h rubber bands. The rubber s leeve i s r o l l e d down o f f the f o r m i n g core on t o the base p e d e s t a l . One porous stone i s p l a c e d on the base.- The specimen i s p l aced on the 'base and the r u b ­b e r s leeve r o l l e d up around i t . A second porous s t one i s p l a c e d on t o p o f t h e specimen and the sample cap pu t on i t . The rubbe r s leeve i s secured a t t h e t o p w i t h rubber bands .

M a t e r i a l s which do not have s u f f i c i e n t cohes ion to permit t h i s procedure may have the rubber sleeve attached by other means. One method is to place the cutting tool used for undisturbed specimens around ' the remolded specimen and ro l l ing the rub­ber s leeve up around the c u t t i n g t o o l . T h i s i s then s l ipped upward leaving the rubber s leeve around the s i^cimen.

The v a l v e i n the sample cap i s t h e n c l o s e d . The specimen i s now ready t o be p l a c e d i n the compres­s i o n chamber.

3 . Conduct o f T r i a x i a l Compression Tes t - The procedure f o r d i s t u r b e d subgrade specimens i s t h e same as f o r und is tu rbed stbgrade specimens. T h i s was se t f o r t h on pages 16 t o l 7 .

- Base Materials - Two types o f base m a t e r i a l s are e v a l u a t e d . These are ( 1 ) p r e l i m i n a r y samples f o r de­s i g n o f a p r o j e c t and ( 2 ) samples o f f i n a l mix as a c t u a l l y used ob­t a i n e d d u r i n g or a f t e r c o n s t r u c ­t i o n . The f i r s t o f t h e s e may be o b t a i n e d as a comple te m i x t u r e o r may be a c o m b i n a t i o n o f s e v e r a l t ypes o f m a t e r i a l . T - r i a x i a l com­p r e s s i o n t e s t s a re r u n o n l y on the combined m i x t u r e o r comple te sam-

p le^

1 . R o u t i n e P h y s i c a l T<ests - Each m a t e r i a l i s ana lyzed by c o n d u c t i n g p l a s t i c i n d e x and g r a d a t i o n t e s t s . Proper p r o p o r t i o n s a re de t e rmined f o r a combined m i x t u r e . P l a s t i c index and g r a d a t i o n a r e a l s o r u n on the f i n a l m i x t u r e . S tandard com­p a c t i o n i s not r u n on i n d i v i d u a l m a t e r i a l s , bu t i s r u n on the f i n a l m i x t u r e . The procedures f o r these t e s t s are g i v e n i n "Highway M a t e r i ­a l s " b y t h e American A s s o c i a t i o n o f S t a t e H i g h w a y O f f i c i a l s and i n s p e c i f i c a t i o n s o f t h e " A m e r i c a n

S o c i e t y f o r T e s t i n g M a t e r i a l s S t a n d a r d s . "

The s tandard compact ion t e s t on m a t e r i a l s w i t h a c o n s i d e r a b l e amount o f p a r t i c l e s g r e a t e r t h a n 3 / 4 i n . i s c o n d u c t e d i n a m o l d l a r g e r t h a n t h e s t a n d a r d P r o c t o r m o l d . A mold h a v i n g a volume o f 1/10 c u f t o f s i m i l a r p r o p o r t i o n s i s o r d i n a r i l y used w i t h 56 b l o w s on each o f 4 l i f t s .

2 . T r i a x i a l C o m p r e s s i o n T e s t s -Prepa-ra t ion - M a t e r i a l s which have a maximun s i z e g r e a t e r than 3/8 i n . a r e prepared i n a mold 5 i n . by 14 i n .

( a ) D e n s i t y - Spec imens a r e molded w i t h a s t a n d a r d AASHO ham­mer or s u i t a b l e a d a p t a t i o n t h e r e o f . D e n s i t y shou ld be ob ta ined equal t o t h e s t a n d a r d c o m p a c t i o n v a l u e . Granu la r m a t e r i a l s a re molded more s u c c e s s f u l l y w i t h a hammer than by s t a t i c l oad w i t h a p l u n g e r .

( b ) Mois ture Content - The mois­t u r e c o n t e n t o f base m a t e r i a l s t o be molded a c c o r d i n g t o t h i s p r o ­cedure i s made equal t o the opti|num m o i s t u r e c o n t e n t as d e t e r m i n e d b y the s t anda rd c o m p a c t i o n t e s t .

( c ) M i x i n g - Water i s added t o the . m a t e r i a l t o be molded and mixed t h o r o u g h l y e i t h e r by hand or w i t h a mechanical m i x e r . Those m a t e r i a l s which have f a i r l y d r y aggrega t ions o f p a r t i c l e s o r w h i c h have t h e

21

mois ture content increased a p p r e c i ­a b l y sho-uld be p l a c e d i n an a i r ­t i g h t c o n t a i n e r f o r a p e r i o d o f s e v e r a l h o u r s to- o b t a i n u n i f o r m d i s p e r s i o n of water throughout t he m a t e r i a l .

( d ) M o l d i n g - Base m a t e r i a l s w h i c h a re t o be hammered i n t h e l a r g e mold are placed i n n ine l i f t s g r a d u a t e d u n i f o r m l y i n t h i c k n e s s f r o m 2 i n . i n t he b o t t o m l i f t t o 1.2 i n t he t o p l i f t . I f p laced i n l i f t s o f equa l t h i c k n e s s , those i n the bo t tom would be compacted t o a h i g h e r d e n s i t y . Each l i f t i s com­p a c t e d w i t h 39 b lows o f t h e com­p a c t i o n hammer co r r e spond ing t o 25 blows i n a 4 - i n . mold . The c o l l a r i s r e m o v e d a n d t h e t o p o f t h e specimen trimmed f l u s h w i t h the t o p o f t h e m o l d . P a r t i c u l a r c a r e should be e x e r c i s e d i n o b t a i n i n g a smooth plane s u r f a c e . The specimen i s removed f rom the mold by f o r c i n g i t upward i n t o t h e s p l i t f o r m i n g j a c k e t ( H . i n F i g . 5 ) , w h i c h i s p a r t o f t h e t r i a x i a l equ ipmen t .

T h r e e wooden b l o c k s 5 i n . i n d i a m e t e r and 5 i n . i n h e i g h t a r e

.used as a p l u n g e r i n removing t h e s p e c i m e n . A c o m p r e s s i o n machine w i t h 3 6 - i n . c l e a r a n c e o r o t h e r s u i t a b l e d e v i c e i s used f o r t h i s p r o c e d u r e .

( e ) W e i g h i n g and M e a s u r i n g -A f t e r the specimen has been molded i t i s weighed. The diameter o f the specimen i s o b t a i n e d by measur ing w i t h a p a i r o f c a l i p e r s t w o d i ­a m e t e r s a t t h e t o p , m i d d l e , and b o t t o m o f t h e specimen. These s i x measurements a r e r e c o r d e d on t h e d a t a sheet ( T a b . 6 ) and averaged .

The area of the specimen i s com­puted or ob ta ined by r e f e r r i n g t o a Tab le o f Areas such as i s g i v e n ' i n T a b l e A-3 i n Appendix A .

A s u i t a b l e r u l e d i v i d e d i n t o h u n d r e d t h s o f an i n c h i s used t o measure the h e i g h t o f the specimen a t t h r e e p l a c e s e q u a l l y spaced a r o u n d t h e c i r c u m f e r e n c e . These th ree measurements are recorded and the average t a k e n .

The volume o f t h e spec imen i s c a l c u l a t e d by m u l t i p l y i n g the area o f t he specimen by the h e i g h t .

The c a l c u l a t e d mo i s tu r e con ten t i s use'd f o r comput ing an e s t ima ted d r y w e i g h t o f t h e specimen. T h i s i s used t o compute an e s t i m a t e d d e n s i t y o f t h e s p e c i m e n a t t h i s t ime t o determine whether or not i t i s w i t h i n an a l l o w a b l e range o f two percent o f the d e s i r e d d e n s i t y . I f t he d e n s i t y i s n o t w i t h i n t h e s e l i m i t s a new spec imen i s u s u a l l y p r e p a r e d .

( f ) C u r i n g - I t i s g e n e r a l l y conceded t h a t base m a t e r i a l s s h r i n k and become more s t a b l e d u r i n g a c u r i n g p roces s i m m e d i a t e l y a f t e r c o n s t r u c t i o n . I n o r d e r t o c o r r e ­l a t e l a b o r a t o r y t e c h n i q u e w i t h f i e l d c o n d i t i o n s , base m a t e r i a l s when molded i n t o specimens f o r t r i ­a x i a l compression t e s t s are p laced i n a mois t c a b i n e t f o r a p e r i o d o f f o u r days .

( g ) S a t u r a t i o n - A f t e r the s p e c i ­men has b e e n c u r e d i t i s a g a i n weighed and measured as p r e v i o u s l y d e s c r i b e d . Some o f t h e i t ems r e ­f e r r e d t o i n t h e n e x t f e w p a r a ­graphs a r e shown i n F i g u r e 5 . The base p l a t e i s p r e p a r e d f o r use on the s a t u r a t o r shown i n F i g u r e 6 .

The wa t e r hose i s connected t o the base p l a t e and t h e base pedes­t a l f i l l e d w i t h w a t e r f r o m t h e w a t e r f l a s k , mak ing s u r e t h a t no a i r i s entrapped i n the water hose.

The rubber s l eeve i s powdered, s l i p p e d over the wood fo rming c o r e , p l a c e d on t h e base p e d e s t a l and s e c u r e d w i t h r u b b e r b a n d s . The r u b b e r s l e e v e i s r o l l e d down o f f t h e , f o r m i n g c o r e o n t o t h e base p e d e s t a l . One p o r o u s s t o n e i s p l a c e d on t h e t o p o f t h e specimen and t h e spec imen i s i n v e r t e d and p l a c e d on t h e base p e d e s t a l . The rubbe r s l eeve i s r o l l e d up a round the specimen.

A second porous s t o n e i s t h e n p l aced on t o p o f t he specimen and the sample cap put on i t . The r u b ­ber s leeve i s r o l l e d up around the

22

sample cap and secured w i t h rubber bands . The rubber hose connec ted t o t he vacuum l i n e i s a t t a c h e d t o the sample cap and vacuum a p p l i e d u n t i l wa te r i s p u l l e d t h r o u g h the specimen and c o l l e c t s i n t'he water t r a p p r o v i d e d i n t h e s u c t i o n l i n e near the specimen. T'he volume o f wa t e r c o l l e c t e d i n t h e water t r a p i s s u b t r a c t e d f r o m t h e volume o f w a t e r g o i n g i n t o the specimen t o d e t e r m i n e the net volume o f wa te r t a k e n d u r i n g s a t u r a t i o n . S a t u r a ­t i o n o f most base m a t e r i a l s i s u s u a l l y o b t a i n e d i n f r o m a f e w minu tes t o a few h o u r s , depending on the c h a r a c t e r i s t i c s o f t h 6 ma­t e r i a l .

The specimen i s a g a i n measured a f t e r s a t u r a t i o n . The d i s t a n c e f r o m the bo t t om o f the base pedes­t a l t o the t o p o f the sample- cap i s measured . T h i s i s t h e h e i g h t o f t h e specimen p l u s a c o n s t a n t c o n ­s i s t i n g o f t he h e i g h t o f t h e base p e d e s t a l , t w o porous s t o n e s , and the sample c a p . T h i s c o n s t a n t i s s u b t r a c t e d t o g i v e t h e net h e i g h t o f the spec imen .

The average diameter i s obtained as b e f o r e and t w i c e t h e t h i c k n e s s o f the rubber s leeve s u b t r a c t e d t o g i v e t h e average net d i a m e t e r o f t h e s p e c i m e n . The a r e a o f t h e specimen i s t h e n de te rmined as be­f o r e . The net volume o f the s p e c i ­men i s c a l c u l a t e d by m u l t i p l y i n g the area o f the spiecimen by the net h e i g h t .

The v a l v e i n t he sample cap i s c l o s e d and t h e vacuum hose i s r e ­moved. The specimen i s t hen ready t o be p l a c e d i n t h e c o m p r e s s i o n chamber .

3 . Conduct o f T r i a x i a l Compression Tes t - The p rocedu re f o r base ma­t e r i a l s i s s i m i l a r t o t h a t p r e v i ­o u s l y d e s c r i b e d on pages 16 t o 17 . w i t h the f o l l o w i n g e x c e p t i o n s . A s t e e l c y l i n d e r i s used i n p lace of a l u c i t e c y l i n d e r . The r a t e o f s t r a i n i s 0 . 0 1 i n . per m i n . Read­i n g s a re t a k e n f o r each 0 . 0 1 - i n .

d e f o r m a t i o n u s u a l l y th roughout the t e s t . V e r y l i t t l e d e f o r m a t i o n i s o r d i n a r i l y r e q u i r e d and t h e t e s t need be c o n t i n u e d o n l y u n t i l t h e maximum s t r e s s r e q u i r e d f o r t he c a l c u l a t i o n s has been o b t a i n e d .

Asphalt Mixtures - T r i a x i a l compress ion t e s t s a re conducted on a spha l t m i x t u r e s t o de termine p r o ­p o r t i o n s t o be u sed , t o de te rmine c o n d i t i o n s o f t h e m i x t u r e s w i t h r e spec t t o a e r a t i o n , c u r i n g , e t c . , and t o e v a l u a t e m i x t u r e s as c o n ­s t r u c t e d .

1 . R o u t i n e P h y s i c a l T e s t s - I f a mix tu re of aggregates must be made, g r a d a t i o n s are r u n on the v a r i o u s m a t e r i a l s t o de termine the p r o p o r ­t i o n s . I f the aggregates have a l ­ready been combined, a g r a d a t i o n t o check aga ins t s p e c i f i c a t i o n s i s a l l t h a t i s r e q u i r e d .

The usua l t e s t s are conducted t o d e t e r m i n e t h e c h a r a c t e r i s t i c s o f the bi tumen used i n a s p h a l t i c pave­ments .

2 . T r i a x i a l C o m p r e s s i o n T e s t -P r e p a r a t i o n - P r e l i m i n a r y i n f o r m a ­t i o n o b t a i n e d f r o m the r o u t i n e p h y s i c a l t e s t s i s used i n p repar ing specimens f o r t r i a x i a l t e s t s .

( a ) L a b o r a t o r y M i x t u r e s - A f t e r t h e g r a d a t i o n has been de t e rmined f o r combined aggrega tes (combined e i t h e r i n t h e f i e l d o r i n t h e l a b o r a t o r y ) , t h e p e r c e n t a g e o f b i t u m i n o u s m a t e r i a l r e q u i r e d i s c a l c u l a t e d by one o f a number o f e m p i r i c a l f o r m u l a e a v a i l a b l e f o r use . For a c t u a l m i x i n g ope ra t ions the agg rega t e i s hea ted t o 100 F' i n a f o r c e d d r a f t oven and t h e b i t u m i n o u s m a t e r i a l i s hea t ed t o midway i n t h e r a n g e o f w o r k i n g temperatures s p e c i f i e d f o r the type b e i n g u s e d . The a s p h a l t i s i n ­c o r p o r a t e d w i t h t he aggregate i n a mechanica l m i x e r , i f a v a i l a b l e , or by hand m i x i n g m e t h o d s . U n l e s s a e r a t i o n i s d e s i r e d , t h e mixes are p laced i n an oven a t 100 F f o r one t o two hours b e f o r e m o l d i n g .

23

( b ) F i e l d Mix tu res - F i e l d mixed samples a re t h o r o u g h l y mixed and heated i n the same manner as l abo r ­a t o r y m i x t u r e s b e f o r e m o l d i n g .

( c ) Mold ing - I n fo rming s p e c i ­mens a mold 5 i n . i n diameter by 16 i n . i n l e n g t h which has been heated t o 100 F i s u s e d . A s u f f i c i e n t q u a n t i t y of heated m a t e r i a l t o f o r m a specimen a p p r o x i m a t e l y 12 i n . i n l e n g t h i s weighed. T h i s i s p l aced-i n the mold i n t h r ee l i f t s and each l i f t rodded 25 b lows . The specimen i s t h e n compacted under a s t a t i c l o a d o f 2 , 0 0 0 l b p e r sq i n . and he ld f o r 5 minu tes . I t i s t hen r e ­moved f r o m the mold and a l l o w e d t o remain a t room t empera tu re f o r a t l e a s t 5 hou r s b e f o r e t e s t i n g . A cons t an t - t empe ra tu r e room f o r con­d u c t i n g t r i a x i a l t e s t s on t h i s type of m a t e r i a l i s d e s i r a b l e .

( d ) Weighing and Measuring - The specimen i s weighed and the d e n s i t y i s de termined. The diameter o f the specimen i s o b t a i n e d by measur ing w i t h a p a i r o f c a l i p e r s t w o d i ­amete rs a t t he t o p , m i d d l e , and bo t tom o f the specimen. These s i x , measurements a r e r e c o r d e d on t h e da ta sheet (Tab . 6 ) and averaged . The a rea o f the specimen i s com­pu ted or o b t a i n e d by r e f e r r i n g t o a T a b l e o f Areas ^uch as i s g i v e n i n T a b l e A-3 i n Appendix A .

A s u i t a b l e r u l e d i v i d e d i n t o h u n d r e d t h s o f an i n c h i s used t o measure the h e i g h t of the specimen a t t h r e e p l a c e s e q u a l l y spaced a round t h e c i r c u m f e r e n c e . These three measurements are recorded and the average t a k e n . The volume o f the specimen i s c a l c u l a t e d by m u l ­t i p l y i n g the a rea of t he specimen by the h e i g h t . '

( e ) A s s e m b l i n g - The r u b b e r s l e e v e i s powdered , s l i p p e d over t he wood f o r m i n g c o r e , p l a c e d on the base pedes t a l , and secured w i t h rubber bands. The rubber sleeve i s r o l l e d down o f f the forming core on t o the base p e d e s t a l . One porous stone or m e t a l b l o c k i s p l a c e d on the base. The specimen i s p l aced

on the base p e d e s t a l , and the r u b ­ber s leeve i s r o l l e d up around the specimen.

A second porous s tone or m e t a l b l o c k is placed on top o f the s p e c i ­men and the sample cap pu t .on i t . The rubber s l e e v e i s ' r o l l e d up around) the sample cap and' secured w i t h rubber b a n d s . The s p e c i m e n i s then ready t o be p l a c e d i n t h e compression chamber.

The procedure f o r t h i s t e s t i s s l i g h t l y d i f f e r e n t f r o m those p r e ­v i o u s l y desc r ibed f o r other m a t e r i ­a l s . No water i s a d m i t t e d t o t h e specimen d u r i n g the t e s t ; t h e r e f o r e the water hose i s not connected t o the base p l a t e . The water va lve i s l e f t open t o p r e v e n t b u i l d i n g up pressure i n the specimens.

3 . Conduct o f the T r i a x i a l Compres­s i o n Test - The p r o c e d u r e f o r asphal t mix tures i s s i m i l a r t o t h a t p r e v i o u s l y d e s c r i b e d on pages 16 t o 17 w i t h the f o l l o w i n g e x c e p ­t i o n s . Since water i s not admit ted t o the specimen, a l l r e fe rences t o water a r e d i s r e g a r d e d .

A s t e e l c y l i n d e r i s used i n p l a c e o f a l u c i t e c y l i n d e r . The ra te o f s t r a i n i s 0 . 0 1 i n . per m i n . Readings a re t a k e n f o r each 0 . 0 1 -i n . d e f o r m a t i o n u s u a l l y th roughout the t e s t . Very l i t t l e d e f o r m a t i o n i s o r d i n a r i l y r e q u i r e d and the t e s t need be c o n t i n u e d o n l y u n t i l t h e the maximum s t ress r e q u i r e d f o r the c a l c u l a t i o n s has been ob ta ined .

METHOD OF APPLYING TEST DATA

R e s u l t s f r o m t r i a x i a l compres­s i o n t e s t s may be a p p l i e d t o t h e d e s i g n o f f l e x i b l e s u r f a c e s i n v a r i o u s ways. The method used i n Kansas f o l l o w s a m o d i f i c a t i o n o f the fo rmula presented by Palmer and Barber i n Proceedings, Highway Re­search Board V o l . 20 , (1940) . D i s ­cuss ion of the t h e o r y on which t h i s f o r m u l a i s based i s p r e s e n t e d i n the December 1940 i s s u e o f Public

24

ffoads. The m o d i f i e d f o r m u l a i s a p p l i ­

cab l e t o single uheel loads and i s as f o l l o w s :

Where:

T - Thickness r e q u i r e d

Cp = Modulus o f d e f o r m a t i o n o f pavement o r s u r f a c e cour se

C = Modulus o f d e f o r m a t i o n o f subg rade o r subbase

- P = Base w h e e l l o a d

m =• T r a f f i c c o e f f i c i e n t based on vo lume o f t r a f f i c '

n = S a t u r a t i o n c o e f f i c i e n t based on r a i n f a l l

a = Radius o f area o f t i r e c o n ­t a c t c o r r e s p o n d i n g t o Pm

TRAFFIC COEFFICIEKTS - A s t a t e law i n Kansas l i m i t s ^ v e h i c l e s t o an 1 8 , 0 0 0 - l b a x l e l o a d . T h i s r e s u l t s i n a maximum whee l l o a d o f 9 ,000 l b w h i c h i s o r d i n a r i l y c a r r i e d on d u a l w h e e l s . T h i s load i s recom­mended f o r d e s i g n by the P r e s i ­d e n t ' s Committee f o r the Design o f an I n t e r - R e g i o n a l System o f H i g h ­ways. U s u a l l y r i g i d pavements are designed f o r highways w i t h a g rea t volume of such heavy t r a f f i c . F l e x ­i b l e pavements a r e d e s i g n e d f o r highways which c a r r y a l e s se r num­ber of l o a d s .

The p e r c e n t a g e o f v e h i c l e s c a r r y i n g maximum loads as r e l a t e d t o t h e o t h e r v e h i c l e s i s f a i - r l y c o n s t a n t over most o f the S t a t e ' s h ighways. The v a r i a t i o n a f f e c t i n g d e s i g n occurs m o s t l y i n the t p t a l volume o f t r a f f i c .

C o e f f i c i e n t s have been de te rmin­ed accord ing t o the volune o f t r a f ­f i c . These- c o e f f i c i e n t s , t h e i r e f f e c t i v e w h e e l l o a d s and t h e i r c o r r e s p o n d i n g r a n g e s o f t r a f f i c a re shown i n Tab le 4 .

,S " P e r m i t t e d d e f l e c t i o n o f s u r ­face

When the load i s a p p l i e d by dual wheels, t h e e f f e c t i v e r a d i u s o f t i r e con tac t area f o r the combina­t i o n i s not e a s i l y d e t e r m i n e d . To solve t h i s d i f f i c u l t y the s t resses imposed by each t i r e a r e computed s e p a r a t e l y . The modulus o f d e ­f o r m a t i o n of the subgrade which i s r e q u i r e d t o l i m i t t h e t o t a l d e ­f l e c t i o n o f t h e s u r f a c e t o t h a t p e r m i t t e d may t h e n be d e t e r m i n e d . Thus the t h e o r y of the f o r m u l a i s used by c o m p u t i n g t h e e f f e c t o f earch t i r e s e p a r a t e l y w i t h o u t t h e n e c e s s i t y o f b i n d i n g the i n d e t e r ­mina te v a l u e of the e f f e c t i v e con­t a c t a rea .

The d e r i v a t i o n o f t h i c k n e s s c h a r t s w h i c h s i m p l i f y the d e t e r m i ­n a t i o n o f t h i c k n e s s r e q u i r e d i s g i v e n i n A p p e n d i x B .

T r a f f i c Coeff ic ient

1 5 /6 2/3 1/2

TABLE 4

Wheel Load

l b . 9/000 7,500 6.000 4,500

Total T r a f f i c

ve^ per day

1,500 - up 900 -1,500 300 - 900

SO - 300

AREA OF CONTACT - Dua l wheel loads may be c o n s i d e r e d as o n e - h a l f t he whee l l o a d on each o f two t i r e s . The a r ea o f c o n t a c t f o r each o f t h e s e t i r e s i s d e t e r m i n e d f r o m a c t u a l t i r e c o n t a c t d a t a . Seve ra l s izes and types of t i r e s were l oad ­ed and areas of c o n t a c t de te rmined f o r each l o a d . An average v a l u e was computed f o r the s i ze and type o f t i r e w h i c h o r d i n a r i l y c a r r i e s the load f o r each s i ze cons ide red . For use i n c a l c u l a t i o n s t h i s area

i s c o n s i d e r e d e q u i v a l e n t t o a c i r c l e of the same area . These areas of contact are used as the e f f e c t i v e area of contact at the sur face .

SATURATION COEFFICIENTS - Service records of highways «fiich have been under t r a f f i c fo r a number of years were studied' to a r r ive at values of the s a t u r a t i o n c o e f f i c i e n t to be used i n the ana lys i s . The method of using th i s c o e f f i c i e n t w i th the t r a f f i c c o e f f i c i e n t i s explained i n d e t a i l i n Appendix B.

A map of Kansas showing the average annual r a i n f a l l f o r each county from 1898 t o 1945 inc lus ive i s shown i n Appendix A. The values of the saturat ion c o e f f i c i e n t based on average r a i n f a l l are g iven i n Table 5.

TABLE 5

S a t u r a t i o n C o e f f i c i e n t

n 1 . 0 0 . 9 0 . 8 0 .7 0 .6

Average Annua l R a i n f a l l

3 5 . 0 3 0 . 0 2 5 . 0 2 0 . 0 1 5 . 0

i n . 4 5 . 0

- - 3 4 . 9 - - 2 9 . 9

2 4 . 9 1 9 . 9

PERMITTED DEFLECTION - The value of S, the permitted d e f l e c t i o n of the s u r f a c e , i s 0 .1 i n . f o r f l e x i b l e pavemeots used i n Kansas. This va lue was de te rmined f rom many measurements o f numerous f l e x i b l e pavements i n various conditions and c o r r e l a t e d w i t h o ther values as g iven p r e v i o u s l y . This value of 0 .1 i n . , a r r i v e d at from a study of service records i n Kansas, also agrees w i t h the f i n d i n g s o f some other i n v e s t i g a t o r s .

MODULUS OF DEFORMATION-the s tress-s t r a i n curve i s used f o r determin­ing the modulus of deformation of the m a t e r i a l be ing t e s t e d . For s t e e l and other s i m i l a r mater ials

25

the modulus of- e l a s t i c i t y i s de­f ined as the r a t i o of the increment of u n i t stress t o the increment of un i t deformation w i t h i n the e l a s t i c l i m i t . The slope of the s t r a igh t l i n e gives the modulus of e l a s t i c i ­t y . I f the s t r e s s - s t r a in graph is curved as i s usual i n the case o f s o i l s and s o i l mixtures, the modu­lus of deformat ion i s not a con­stant but a variable depending upon the range of stress f o r which the modulus i s ca l cu l a t ed .

The modulus o f de fo rmat ion i s the secant modulus between the two poin ts on the s t r e s s - s t r a i n curve l i m i t i n g the range of stress de­termined, or the stress d i f fe rence divided by the s t r a i n .

STRESS DIFFERENCES - A load applied at the surface of the road creates stresses i n the mater ia l below the surface. These stresses may be re­solved i n t o v e r t i c a l , h o r i z o n t a l , and shear stresses. The greatest stress at any point under the sur­face may not be i n a v e r t i c a l o r h o r i z o n t a l d i r e c t i o n , but at some ang le f r o m t h e s e . The l o w e s t s t ress i s at r i g h t angles t o the maximum s t r e s s . The p r i n c i p a l stress d i f f e r e n c e occurs i n such a d i r e c t i o n that no shear stresses need be considered. The maximum p r i n c i p a l stress d i f f e r e n c e under dual t i r e s my be computed from the v e r t i c a l , h o r i z o n t a l , and shear stresses imposed by each t i r e . The maximum p r i n c i p a l stress d i f ference decreases -with increase i n depth below the su r face , the re fo re the maximum pr inc ipa l stress di f ference occurring i n the sid}grade i s at the top o f the subgrade.

THICKNESS REQUIRED - The method of computing the thickness of any type of f l e x i b l e surface, base course, or sub-base upon a subgrade is more ea s i l y described w i t h an example. This i s done under CALCULATIONS. Charts have been prepared which make t h e d e t e r m i n a t i o n o f the

26

th ickness r e q u i r e d much s impler thnn by the use of a formula alone. The d e r i v a t i o n o f these charts i s given i n Appendix B.

The th ickness of any type o f su r face course , base course , or sub-base may be computed. A combi­nation of these component parts may also be computed by a formula given wi th the example.

CALCULATIONS

Some calcula t ions are made dur­ing the conduct o f the t r i a x i a l t e s t . A few of these have been mentioned. However, many of the calculations which may be performed dur ing the conduct of the tes t are set f o r t h i n t h i s sect ion i n order that a l l work of - th is type may be found i n one place .

MOISTURES AND DENSITIES - Although actual moisture contents and densi­t i e s are not computed u n t i l a f t e r the tes t i s conducted and the test

ecimen has been oven d r i e d , the, explanation i s given here t o avoid breaking i n t o the remainder of the c a l c u l a t i o n s . These may conveni­e n t l y be pe r fo rmed on the da ta sheet as shown i n Table' 7. Suf­f i c i e n t i n f o r m a t i o n i s g iven on that sheet to show how most of the ca lcula t ions are performed.

Using the s p e c i f i c g r a v i t y of the material and the zero a i r voids curves (Figure A-7 i n Appendix A ) , ca lcu la t ions are made fo r the per­centages of water required t o com­p l e t e l y f i l l the voids at each of the dens i t i e s as computed.

The v a r i a t i o n f rom complete s a t u r a t i o n i s a l s o c a l c u l a t e d . These values are summarized on a sheet designed especia l ly for th i s purpose ( F i g . A-8, Appendix A ) .

EXAMPLE HO. 1 - In order t o make the explanations more understand­able and of p r a c t i c a l v a l u e , a spec i f i c example is given i n which

a base course and pavement are to be p laced upon a subgrade. The example chosen for this is Test No. 2955, tested under Laboratory No. AA-3735. Sample No. 92, taken from Project 160-4-F-451 ( I S ) i n Baiber County, Kansas. The test data are shown i n Tables 6, 7, and 8. The s t r e s s - s t r a i n curve i s shown on F i g u r e 9.

The t r a f f i c count on t h i s high­way shows 255 vehicles per day. I t is estimated (planning survey) that the t r a f f i c cn th i s highway w i l l be 320 vehicles per day by 1960; there­fore the t r a f f i c c o e f f i c i e n t m i s 2 /3 . The average annual r a i n f a l l f o r the per iod f rom 1898 to 1945 i n c l u s i v e f o r Barber County was 25.5 i n . The sa tura t ion c o e f f i c i ­ent n i s 0.8; therefore the t h i c k ­ness chart on Figure 8* (m s 2/3 , n = 0 . 8 ) i s used.

Test Data - The pipet te read­ings are used to d e t e r m i n e ' t h e volume change of the specimen. I t i s determined by sub t rac t ing each p i p e t t e reading from the i n i t i a l r ead ing . The p i p e t t e s are c a l i ­brated i n m i l l i l i t e r s and the v o l ­ume of the specimen is computed in cubic inches; therefore the change i n volume as read by the change i n p i p e t t e s i s conve r t ed t o cub i c inches. A conversion tab le , such as Table A-6 i n Appendix A, is con­venient fo r t h i s purpose, or the volume i n m i l l i l i t e r s may be d i ­v i d e d by 1 6 . 3 9 , t h e number o f m i l l i l i t e r s per cubic i n c h .

I n t h i s d i s c u s s i o n , the term "corrected va lues" refers to those calculated for each set of readings as the t e s t progresses dur ing ap­p l i c a t i o n o f the v e r t i c a l l o a d .

^The t h i c k n e s s s c a l e s c h a r t i s based on modulus o f d e f o r m a t i o n of f l e x i b l e p a v e -

<ment (Op) p f 1 5 , 0 0 0 l b per sq i n . For o t h e r v a l u e s w h i c h might be found f o r o ther types of f l e x i b l e pevenent mixture a new s c a l e can be q u i c k l y cons truc ted by use of the "combinat ion f o r m u l a " on page 33 or c a n be f igured for i n d i v i d u a l c a s e s by t h i s formula.

27

TABLE 6

Project.

Lab. Mo.

STATE HIGBWAY COMMISSIOK OF iAlfSAS

TRIAXIAL COMPRESSIOK TEST DATA

General Information Test Ito. Base No.

l60->»-F (15) Barter

2955

AA-3755 Sample No. .Dat

Description of Specimen. Xfiodlstuzted B l l t y olay loan

Vacuum to Saturate Specimen

Glycerin P r « . « » i i r g 20 Lbs/sa. in. 105A

.cm Bg. Total. Allowance for Difference m Bead KOtB: Bead of 10.0 cm. Olycerin is equal to that of one cu. Bg.

DIMENSIONS OF SPECIMEN

.cm. Bg.

.cm. Bg.

.cm. Bg.

Diameter Before

Saturation After

Saturation Beieht Before

Sat. After

Sat.

lot >.8l 2.83 2.8? three ueasurenents i n c l u d -iftf the Constant for Pedes­t a l , Gap, i f i l t e r Stones

11.1*0 UUA la 2.dl 2.82

three ueasurenents i n c l u d -iftf the Constant for Pedes­t a l , Gap, i f i l t e r Stones i l . * 3

Bottom 2.8>f ll . l l2 11.1*3 Average Diameter 2 .9? 2.83 Average ll.lt2 U.l*3 Rubber thickness

"

.Ok Constant 3.50 .̂50

tet Diameter 2.79 2.79 Ket Beieht 7.92 7.95

Area 6.11 6.11 rnl«M« W.39 1(8.1*5

SATURATION DATA

DATS tIMB Burette Reading

fotal to Date

Voter through

Bet tolume of ffater taken

3-l*-l*6 10:25 a.m. 0 II 7:35 p.m. Z It 8:00 P.1IU 65

3-5-W 9:30 a.m. 5 70 5 65

-

28

TABLE 7

STATE HIGBVAY COMMISSIOH OF KAKSAS TRIAXIAL COMPRESSIOM TEST DATA

Moisture and Density Computation

MOISTURE DATA

Test Mo. 2955

As Cut

ils Molded

As Cured

A f t e r Satura­

tion

End of

Test

¥et l/elght (Sample * Fan) 2512 . . . . Dry Weight (Sample * Pan) ____ mmmm mmmam . . . . Tare Weight of Pan 971 . . . . Wet Weight of Sample 2^1 . . . . 1589

Dry Weight of Sample 1321 1321

Weight of Moistvre 220 220 268

Water Taken During Saturation . . . . 65 . . .u

Total lioiatvre After Saturation 285

Ifoistwre (% of Dry Weight) 16.6 21.6 20.3

DEMSITY DATA

5 / > - / . . / t / r fi-atJity 2,65

n^y » ' / : . . «« . c 1321

Multiplied by n.Sof =

Before Saturation After Satura­

tion 1

5 / > - / . . / t / r fi-atJity 2,65

n^y » ' / : . . «« . c 1321

Multiplied by n.Sof =

As Cut f

its Molded

Pushed Out

After Satura­

tion 1

Divided by Tolvme in Cu. In. W.39

Bqvals Density in Lhs/Cu. Pt. lOi^.2 l O i ^ . l

Koiatwre at Zero A ir Foids 22 22

Tar tat i on fro* Zero A%r 7oids -5 0

29

TABLE 8

COMPUTATIOH SSEET FOR TRIAXIAL COMPRESSIOM TEST

Initial Readings Test Mo. 2955

Sheet Mo. 1 of 1

UeiPht 7.93 Area 6.11 Volume USM Hnri^nntnl. Pressure ^LSMBMIM^

rOLOMS CKAKS DATA TKPT. DBPO BH. DATA Area Sq.In.

Load Lbs.

Unit Time

«r:H:S Pipettes

ml. Ou.Ch,

ml. Ou.Ch.

Cit Jfb roi.

Oujn. Dial Bead

Cum. Ch.

Str. %

Bt. In.

Area Sq.In.

Load Lbs.

Stress p . s . i .

0: 2:15 20.0 48.45 1.00 7 . » 6.11 0

3:00 15.3 1.00 7.93 0

:̂55 13.2 .99 .01 .13 7.92 0

6<50 12.0 .98 .02 .25 7.91 0

8:50 11.0 .97 .03 .38 7.90 0

10:1»0 10.4 .96 .04 .50 7.89 0

12'M 9.8 10.2 .62 47.83 .95 .05 . 0 7.88 9 1.5

Ikik^ 9.2 10.8 .66 .79 .94 .06 .76 7.87 22 3.6

16:50 8.6 U.l^ .70 .75 .95 .07 .88 7.86 35 5.8

19:00 8.1 11.9 .73 .72 .92 .08 1.01 7.85 46 7.6

21:10 7.6 22.k .76 .69 .91 .09 1.14 7.84 58 9.5

22:52 7.2 12.8 .78 .67 .90 .10 1.26 7.83 69 11.3

2l̂ t40 6.9 13.1 .80 .65 .89 .11 1.39 7.82 75 11.9

26:35 6.5 13.5 .82 .88 .12 1.51 7.81 80 13.1

28:30 6.2 13.8 .84 .61 .87 .13 1.64 7*80 86 14.1

30:35 6.0 14.0 .85 .60 .86 .14 1.77 7.79 91 14.8

32:35 5.7 lU.3 .87 .58 .85 .15 1.89 7.78 97 15.8

k2'M k.6 15.4 .94 .51 .80 .20 2.52 7.73 116 18.8

52:30 3.8 16.2 .99 .46 .75 .25 3.15 7.68 121 19.6

1:02:30 2.8 17.2 1.05 .40 .70 .30 3.78 7.63 ]28 20.6

30

The corrected volume f o r each set of readings is the i n i t i a l volume minus each volume change. I f a p ipe t te reading i s larger than fhe i n i t i a l , the volume change is nega­t i v e and the co r rec ted volume i s obtained by s u b t r a c t i n g a lgebra­i c a l l y f rom the i n i t i a l volume.

The deformat ion i s determined by s t i} t rac t ing each Ames d i a l read­ing from the i n i t i a l reading. The s t r a i n may be expressed as a per­centage of the i n i t i a l height or a decimal r a t i o to the i n i t i a l height . I t i s the deformat ion d i v i d e d by the i n i t i a l he igh t . I f expressed i n percentages, the q u o t i e n t ob­ta ined is m u l t i p l i e d by 100. The co r rec t ed height o f the specimen is obtained by subtracting the de­formation from the i n i t i a l he ight . The corrected area i s the corrected volume d i v i d e d by the c o r r e ' ' t e d h e i g h t .

The u n i t stress i s obtained by d i v i d i n g the net load by the cor­rec ted area . A s p e c i a l form has been found t o be very h e l p f u l i n making these c a l c u l a t i o n s . I t i s included wi th the example. Table 8. Calculations are s u f f i c i e n t l y accu­ra t e w i t h a good t e n - i n c h s l i d e r u l e and set t ings may be made such t h a t the area need not be r ead . This i s q u i t e t ime-saving and i t provides a l l o f the values which are necessary.

Stress-Strain Curves - The tes t r e su l t s are p lo t t ed on r ec t ­angular c o o r d i n a t e paper us ing s t r a i n as the abscissa and u n i t s t r e s s as the o r d i n a t e f o r each

• p o i n t . The example g i v e n f o r a subgrade i s p l o t t e d on Figure 9. A curve drawn through these points should provide a s t ra ight l i ne near the beginning of the curve. At no time should the curve become steep­er than th i s s t ra ight l ine por t ion . The s t ra ight l i ne should be extend­ed back t o the zero o rd ina te . I f i t f a i l s t o intersect t h i s ordinate a t zero a c o r r e c t i o n must be ap­

p l i e d i n computing the moduJus. The examples show how th is is done. Fa i lure t o intersect at zero may be due t o one or more o f s e v e r a l causes such as rebound o f the specimen, poor sea t ing , improper al ignment of the specimen i n the t e s t i n g apparatus, e t c . I t does not m a t e r i a l l y a f f e c t the t e s t i f the c o r r e c t i o n i s made. >

Modulus of Deformation of Pavement The modulus of deforma­t i o n was p r e v i o u s l y expla ined t o some extent but a d e t a i l e d method of c a l c u l a t i o n i s given here. I t i s more s imply c a l c u l a t e d f o r a f l e x i b l e pavement than f o r a sub-grade and for . that reason a f l e x ­i b l e pavement su r f ace course i s used as an example. The s t ress -s t r a i n curve i s shown on Figure 7.

The s t r e s s - s t r a i n curve f o r a pavement i s e s sen t i a l l y a s t r a igh t l i n e fo r a stress considerably i n excess o f that f i gu red fo r normal highway t r a f f i c loads. Therefore, i t i s usual ly a constant for a l l of the c o e f f i c i e n t s used here.

For t h i s example the char t on F igu re 8 (m = 2 / 3 , n - 0 . 8 ) i s

' used. The der ivat ion of t h i s chart i s shown i n Appendix B. For these c o e f f i c i e n t s the maximum s t r e s s d i f f e r e n c e i s approximately 42 l b per sq i n . , the maximtjm poin t X on the 2/3 curve.

R e f e r r i n g to the s t r e s s - s t r a i n curve f o r Test No. 46S8 i n Figure 7, fo r a bituminous mat or dense graded surface course, the modulus of deformation is computed as f o l ­lows:

The u n i t s t r a i n a t a stress of 42 i s 0 .0051. However, a correc­t i o n is required fo r the s t r a i g h t l i n e por t ion of the curve where i t in tersects the zero ordinate . The co r r ec t i on i n t h i s case is 0.0023. thus the net s t r a i n is 0.0028.

The modulus of de fo rmat ion is the s t ress d i f f e r e n c e d i v i d e d by the s t r a i n which i n t h i s case i s

31

STATE mCHWAY COMMISSION OF KANSAS

STRES&STRAIN CURVES far

TRIAXIAL TESTS

• J t e . N « . WS8

L - No. _AA-Ja32 . . .

MAIBUL J!???? PrSplf̂ Surface Course

U H H R U B D BaimuiB -

amuRD Yn " ^

F U J I C T

CODIfTT

DA».?-9-'«6 Tuft.

CAW BT-. C H K X D B T iICJE

No

1 6 0 - 1 , - F j , a ( 1 5 )

B a r b e r

a B C N o . m JB

UNITBTBAIN

Figure 7. St ress-Stra in Curve - The en t i r e sheet i s reproduced (70% of f u l l s i z e ) t o show the Kansas form f o r recording t h i s data.

32

A large number of tests on t h i s type of specif ied mixture i n Kansas has r e s u l t e d i n the value o f at least 15.000 l b per sq i n . and th i s f i g u r e i s o r d i n a r i l y used f o r de­s i g n . Mixtures having d i f f e r e n t s p e c i f i e d c h a r a c t e r i s t i c s a re evaluated i n t h i s manner and the par t icu lar values obtained are used

' i n design. Frequent tests are con­ducted on mater ia ls a c t u a l l y use'd i n cons t ruc t ion fo r s p e c i f i c p ro ­j e c t s t o determine whether or not t h i s value is being obtained.

are s t r a i g h t l i n e s . This i s not the case for a subgrade. The pur­pose o f the pavement and base course i s t o w i t h s t a n d s t resses greater than those which th^ sub-grade w i l l withstand. I f the sub-grade were capable of withstanding the maximum stress imposed by the wheel load, then the only purposes f o r a pavement would be t o r e s i s t abrbsion of t r a f f i c and shed water..

The subgrade example (No. 1) w i l l now be ca r r i ed through design operations. The chart on Figure 8

T-Thickness of mat (Cp>l5,000 p.8.i.) Required (Inches) 20 IS 10 8 7 6

I n i l I I I 4

- L . 2 I 0

SO

•

A

40

I S O

20

CO 10

I 2 3 4 C-Modulus of Deformation of Suborode in Thousonds (p s i.)

Figure 8. Thickness Chart f o r m-Z/Si n-0.8 , S=0.1 i n .

Subgrade Evaluation - As long as the s p e c i f i c a t i o n s remain un­changed a constant va lue of the modulus of deformat ion of a b i t u ­minous mat or a s p e c i f i e d base course i s used fo r any p a r t i c u l a r set of c o e f f i c i e n t s , and f o r a l l sets of coe f f i c i en t s having maximum stress differences not greater than that where the s t ress -s t ra in curves

i s used f o r ( h i s design as p r e v i ­ously determined from the t r a f f i c and s a t u r a t i o n c o e f f i c i e n t s .

The modulus of deformat ion fo r subgrade s o i l s ( s t r e s s - s t r a i n curves which are not e s s e n t i a l l y s t r a i g h t l i n e s ) i s determined by the f o l l o w i n g methods:

Two values of stress differences are chosen w i t h i n the range of the

33

s t r e s s - s t r a i n curve values which have not more than 2 l b per sq i n . d i f f e r e n c e between them and which are such tha t when p l o t t e d they w i l l f a l l on opposite sides of the t r a f f i c c o e f f i c i e n t l ine being used (This assumes using the chart cor­responding t o the proper r a i n f a l l c o e f f i c i e n t ) .

Unless one i s f a m i l i a r w i th the curve being considered, a p r e l i m i ­nary t r i a l c a l c u l a t i o n may e a s i l y be made as an a id i n choosing the proper s t ress d i f f e r e n c e s . When the s t r a i n i s 0 .01 , the modulus o f deformation i s 100 times the stress d i f f e r e n c e . An approximat ion i s s u f f i c i e n t l y accura te f o r t h i s t r i a l . For the subgrade sample ( F i g . 9 ) when the net s t r a i n i s 0 . 0 1 , the s t r e s s d i f f e r e n c e i s a p p r o x i m a t e l y 14 . Locate t h i s point on the thickness chart shown as " A " where the stress d i f f e rence i s 14 and the modulus of deforma­t i o n i s 1400. I t f a l l s somewhat above the curve fo r ffl»2/3. There­fo re the s t ress d i f f e r ences of 10 and 12 are chosen f o r ca lcula t ions .

UNIT BnUIN

Figure 9. S t r e s s - S t r a i n Curve, Test No. 2955, Lab. No. AA 3735, Sample No. 92. Subgrade M a t e r i a l , Und i s tu rbed , Sa tu ra t ed . P r o j e c t 160-4-F-451 ( 1 5 ) . Barber County, Mar. 7. 1946.

Now going t o the s t r e s s - s t r a i n curve ( F i g . 9 ) w i t h values of 10 and 12 the deformation (corrected f o r a zero abscissa) fo r a s t ress of 10 i s 0.0066 and fo r 12 the de­

formation is 0.0082. The moduli of de fo rma t ion fo r these two values are :

10 0.0066

s 1520 and 12 0.0082

1460

When these points are p lo t ted on the thickness chart for n 0.8 and 5 = 0.1 inch (F ig . 8 ) , they f a l l on opposite sides of the curve for m " 2/3, thus the values f o r s t ress d i f f e r e n c e are s a t i s f a c t o r y . Had these points not f a l l e n one on each side of the curve then other values would need to be chosen.

Thickness of Mat Required -These two points are connected and from where t h i s l ine intersects the curve (B on the cha r t ) a v e r t i c a l l i n e i s drawn to the scale at the top of the chart f o r m = 2 /3 . The th ickness of sur face requ i red i s found on the scale at the l e t t e r " C " .

In the example shown 6 inches of a surface course having a modulus of deformation of 15,000 p s i i s re­quired over the subgrade whose mod­ulus of deformation i s approximate­l y 1500 p s i for the stress d i f f e r ­ence applicable t o t h i s c o n d i t i o n .

I t has been the Kansas pract ice t o obtain t o t a l thickness of f l e x ­i b l e pavement required and subse­q u e n t l y by the f o l l o w i n g method a r r ive at the combination of e i ther sub-^se and surface thicknesses or of base course and surface t h i c k ­nesses which should be used.

Comdtnatton Thicknesses ~ When a combination of two types of f l e x ­i b l e course i s desi rable the f o l ­lowing formula may be used:

tt = f t , - tpj

Where: s thickness o f base, course or

sub-base tg - thickness of f l e x i b l e pave­

ment requi red d i r e c t l y on the subgrade

a thickness of f l e x i b l e pave­ment desired i n the eonrbina-t i o n

34

t t = (6 - 2)

Cp = modulus of de fo rmat ion of f l e x i b l e pavement

C( = modulus of de fo rma t ion of base course or sub-base

In the above example where 6 i n . of b i tuminous mat (C^ = 15 ,000) was required when placed d i r e c t l y on the subgrade, i t becomes desir- . able t o use a 2 - i n . t h i c k b i t u m i ­nous wearing course over a gravel-binder s o i l s t ab i l i zed layer (who&e-modulus Ct = 6 ,000) on the sub-g r a d e . The t h i c k n e s s o f t h e

g rave l -b inde r s o i l may be de t e r ­mined by s i b s t i t u t i n g i n the formu­l a :

15000

• Therefore the design for a f l e x ­i b l e pavement over t h i s subgrade w i l l c a l l f o r a ' 2 - i n . bi tuminous mat over a 6 - i n . base' course.

For convenience a table has been p repa red f o r d e t e r m i n i n g these th i cknes ses . I t i s i nc luded i n Appendix A as Table A6.

The above example shows the steps necessary t o determine th i ck ­nesses of any coiribination of f l e x ­i b l e courses. While i t may appear a t f i r s t glance t o be somewhat i n ­v o l v e d , a f u r t h e r study and more' comple t e u n d e r s t a n d i n g of the system w i l l demonstrate the r e l a ­t i v e ease w i t h which the des ign thickness problem can be so lved .

Kansas has been u s ing t h i s method f o r several years and Kansas engineers are s a t i s f i e d that i t i s t h e b e s t method t h a t has been e v o l v e d f o r such a c o m p l i c a t e d problem. The system encompasses a wide va r i e ty of s o i l conditions and has the f l e x i b i l i t y necessary t o permit i t to be adapted to changing t r a f f i c or d i f f e r e n t c l i m a t i c con­d i t i o n s .

EXAMPLE NO. 2 - In t h i s example, the basic data w i l l be given and the s t r e s s - s t r a in curves shown f o r the base course m a t e r i a l and f o r one undisturbed sample of the sub-

grade. The c a l c u l a t i o n s w i l l be carr ied through for the information r e s u l t i n g from tes ts at t h i s one loca t ion on the p ro jec t . This w i l l be followed wi th a summation of re­s u l t s o f a l l of the tes ts made on samples throughout the p ro jec t . The resultant overa l l design fo r t h i ck ­ness of bituminous mat and crushed rock base course for the project as a whole w i l l be s ta ted . The p ro­j e c t (No. 50-N-23-F 410 (21 ) i s now under cons t ruc t i on i n Douglas County. I t i s 12.452 mi long. The a c t u a l t r a f f i c count i n 1942 was 540 vehicles per day; 675 vehicles per day are predicted for I960. The t r a f f i c c o e f f i c i e n t m is 2/3 (Table A - 1 ) . The average annual r a i n f a l l f r o m 1898 t o 1945 was 36.2 i n . per year. The saturat ion c o e f f i c i ­ent n i s 1.0 (Table A - 2 ) . There­f o r e use the thickness char t f o r m - 2 /3 , n - 1.0 ( F i g . 10) .

Bituminous Surface Course (Bituminous Mat) - The bituminous mat i s t o be the same as described fo r Example 1, the curve fo r which i s shown i n Figure 7.

The steps necessary t o a r r ive at the modulus of deformation of f l e x ­i b l e pavement Cp of 15,000 l b per sq i n . were described p rev ious ly . Th i s value w i l l be used i n these c a l c u l a t i o n s .

Subgrade - The subgrade con­s i s t s of a clay wi th a l i q u i d l i m i t o f 54 and a p l a s t i c index of 28 con ta in ing 10 per cent sand f r a c ­t i o n and 46' per cent c l a y ' f r a c t i o n . The undisturbed sample taken t o an 8 - i n . depth below the surface re­vealed a dry dens i ty of 91 l b per cu f t and a' moisture content of 28 per cent, a r e l a t i v e l y low densi ty and h i g h mois ture c o n t e n t . The sample i s AA-4385 No. 84-TTiax ia l Test No. 5525.

The ' s t r e s s - s t r a in curve of the subgrade mater ia l i s shown i n F i g ­ure 11 and w i l l be used i n the thickness calculat ions. A p r e l i m i ­nary t r i a l ca lcu la t ion for a s t r a i n of 0.01 gives a s tress d i f f e r e n c e

35

T-Thickness of mot (Cp> 15,000 p s i ) Required (Inches) 7 9 9 4

50

40

S30

•20

CO 10

c

-A — y

C-Modulus of Deformation of Subgrade in Thousands (p s i ) Fig. 10.-Thickness chart for m - 2 / 3 . n" 1.0, S"O.I inch.

Figure 10. Thickness Chart f o r nrT/i, n=1.0, S=0.1 i n .

of approximately 10 and a modulus of deformation of 1000. This point p l o t t e d on the thickness chart at " A " i s considerably above the curve fo r IB " 2 /3 . This indicates that much smaller values must be u s e d and s t r e s s d i f f e r e n c e va lues o f f o u r and s i x a re chosen fo r a t r i a l . From the above s t r e s s -s t r a i n curve we f i n d a s t r a i n of 0 .0051 at 4 l b per s q . i n . and 0.0066 at 6 l b per sq. i n . A cor­r e c t i o n of 0.0023 i s t o be sub­t r a c t e d f r o m each of the above s t r a i n values (zero abscissa cor­r e c t i o n ) . The cor rec ted s t r a i n s thus become 0.0028 a t 4 p s i and 0.0043 at 6 p s i . Then:

. 3 1 4 3 0 . modulus o f d e f o r n a t i o n 0 . 0 0 2 8 a t 4 p s i

And:

» - 1 4 0 0 . Biodulus o f d e f o r o M t i o n 0 . 0 0 4 3 . a t 6 p s i

Note : The modulus o f d e f o r s a t i o n f o r a p a r t i c u l a r t e s t n e v e r i n c r e a s e s w i t h a n i n c r e a s e i n s t r e s s d i f f e r e n c e , s i n c e the s t r e s s - s t r a i n c u r v e a t no p l a c e faeceoBS s t e e p e r t h a n the s t r a i g h t l i n e p o r t i o n n e a r the b e g i n n i n g of the t e s t .

These two points when p lo t t ed on t h e t h i c k n e s s c h a r t ( F i g . 10 ) straddle the curve f o r m = 2/3 , so the t r i a l stress d i f f e rence values are s a t i s f a c t o r y f o r use.

The v e r t i c a l l i n e BC f rom the III s 2/3 curve and the l i n e drawn between the two points shows tha t the required thickness fo r m - 2/3 i s 9 i n . i f composed e n t i r e l y o f bi tuminous mat m i x t u r e .

This i s not economical nor de­s i rab le so i t i s necessary to f i n d the thickness of crushed store base

36

t h a t p o r t

• 40

I S »

can be placed i n l i e u o f a i o n o f the b i tuminous mat.

S

jOI M U N I T S T R A I N

A3

Figure 1 1 . S t r e s s - S t r a i n Curve, Test No. 5525, Lab. No. AA-4385, Sample No. 84. Subgrade M a t e r i a l , Undisturbed, Saturated, Project 50-N-23-410 ( 2 1 ) . Douglas County , Feb. 7, 1947

Base Course - The base course i s required t o meet Kansas Standard Specif icat ions, Ed i t ion of 1945, t o consis t of a dense graded crushed l imestone w i t h approximate ly t en

.percent' passing the No. 200 s ieve , w i t h a p l a s t i c index l i m i t e d be­

tween 1 and 6. Numer̂ ous t r i a x i a l tests on t h i s type of mixture have produced a curve as shown i n Figure 12.

Th is curve i s a s t r a i g h t l i n e from the o r i g i n t o a stress d i f f e r ­ence of more than the required 42 p s i . No c o r r e c t i o n need be made f o r s t r a i n . Therefore any p o i n t taken on t h i s l i n e and d iv ided by i t s corresponding s t r a i n w i l l give the modulus of deformation of t h i s compacted mix ture . At 50 p s i the c a l c u l a t i o n becomes:

— - 10,000 p s i modulus o f de-0«005 formation for crush­

ed stone base course Cofflbtnatton of Base Course and

Bttumtnous Mat Thicknesses - T<he next step i s t o compute a conbina-

t i o n o f t h i c k n e s s e s o f crushed stone base course and bituminous mat t o r e p l a c e t h e 9 inches o f s t ra ight bituminous mat shown to be required.

I t i s de s i r ab l e t o p lan f o r a bi tuminous mat having a f i n i s h e d thickness of three inches on the basis of t r a f f i c , s o i l , and c l i ­matic condit ions at t h i s l o c a t i o n .

On t h i s subgrade a t o t a l o f 9 inches'of bituminous mat or equiva­l e n t (modulus o f d e f o r m a t i o n -15,000) i s r e q u i r e d . The lower

JOl UNIT STRAIN

Figure 12. S t r e s s - S t r a i n Curve, Test No. 6260-R, Lab. No. AA-4517, Sample No. 4 . Base M a t e r i a l , Re­molded, S a t u r a t e d , P r o j e c t 166-18F-356 ( 1 3 ) . Cowley County, May 29, 1947.

po r t i on of t h i s t r a f f i c supporting course i s t o consist of a crushed

37

stone base course, which has been found to have a modults of deforma­t i o n of 10,000. Using the conversion formula

H = gives

f*s - V CP

h = /9 3) 3 /15 .000 ^ 10.000

The f i n a l design then c a l l s f o r a 3 - i n . b i tuminous mat on 7 i n . o f crushed stone base course over the subgrade s o i l used in th i s example.

Due t o the reasonable ease w i t h which t h i s work can be done and i n order t o avoid the necess i ty of p l a c i n g too much re l i ance on any one sample from any given loca t ion , i t i s general pract ice t o take two or more und i s tu rbed samples f o r each mi le . This pract ice produces a good o v e r a l l p i c tu r e of the re ­quirements f o r each p r o j e c t and permits an economical e v a l u a t i o n o f the d e s i g n . Of course l o c a l areas of weak sidigrades are sampled more f requent ly t o determine t h e i r extent and values.

This p r o j e c t , 50N-23-F 410 (21) Douglas Co., as was ea r l i e r stated, i s 12.452 mi les i n l e n g t h . The survey p a r t y took 40 undis turbed samples from th i s p ro jec t , an aver­age of approximately three samples per m i l e . This ra te of sampling was deemed necessary because of the non-uniform character o f the t e r ­r a i n i n t h i s area. Numerois shale s t ra ta were encountered as w e l l as some stream bottom land, causing a number of questionable areas whose extent i t was necessary t o deter­mine. On the f i r s t 9K mi. the tes t r esu l t s show required thicknesses o f crushed stone base ranging from 4 to 9 i n . w i t h the great m a j o r i t y of r e s u l t s i n d i c a t i n g 8 i n . The range was due t o varying density i n the subgrade. and to small areas of good s o i l cond i t i ons . The, extent of these areas was not of s u f f i c i ­

ent magnitude t o a l t e r the p l a n thickness so t h i s part of the pro­ject i s b u i l t w i t h a 3 - i n . b i t u m i ­nous mat and an 8 - i n . crushed stone base. The remaining approximately three miles requi red thicknesses of base course ranging from 10 t o 14 i n . wi'th most resul ts at 12 i n . according t o test resul t s . The two tests i n d i c a t i n g a need f o r 14 i n . were i n seepy areas and contained s h a l e - l i k e matQ.r ia l . These are being drained and b a c k f i l l e d w i t h the proper s o i l so there i s being constructed on t h i s three miles a 3 - i n . bituminous mat and a 1 2 - i n . crushed stone base course.

CONCLUSION

In t h i s p u b l i c a t i o n the essen­t i a l workings of the ,Kansas system fo r designing f l e x i b l e surface and base courses for highway construc­t i o n have been de sc r i bed . This system has been i n use i n t h i s State fo r several years w i t h good success. There i s no doubt tha t improvements w i l l be made t o the system f rom time t o time as more agencies make use of the system and as t h i s o rganiza t ion continues t o conduct work of th is nature.

The system has been s i m p l i f i e d as much as possible at t h i s t ime, however the reader must bear i n mind that th i s i s a complex problem wi th many factors which have an im­p o r t a n t b e a r i n g on the o v e r a l l s o l u t i o n . This may w e l l be the r e a s o n why o t h e r more s i m p l e methods have not been e n t i r e l y suc­c e s s f u l ; no r e a l l y simple so lu t ion w i l l be s a t i s f a c t o r y f o r any prob­lem i n v o l v i n g , so many v a r i a b l e f a c t o r s .

A l l of the fac tors enter ing the problem are accounted for as simply as possible i n the Kansas system. The treatment of the var iab les i s r ead i ly adaptable t o e x i s t i n g con­d i t i o n s as w e l l as possible fu tu re condi t ions .

38

Many organiza t ions seeking t o solve the problem of f l e x i b l e pave­ment de s ign are t u r n i n g t o t h i s system. I t has the basic elements of p r a c t i c a l l y a l l other forms of s t ruc tu ra l design proven t o be ade­quate through many years of use.

I n b r i e f fo rm the i m p o r t a n t steps required t o use t h i s method successful ly are:

1. The s o i l s laboratory must be equipped w i t h a t r i a x i a l apparatus s imilar i n nature t o that described. Other types producing the same re­sul ts would be s a t i s f a c t o r y .

2 . Undisturbed sainples should be used fo r determining accurate road conditions whenever possible. Even though laboratory compacted speci­mens are used, as on a p r o j e c t which is f i r s t t o be graded, a f o l ­l o w - u p check w i t h u n d i s t u r b e d samples taken from the subgrade of the f inished roadbed is advised fo r f i n a l design purposes.

3. Sampling should be performed as f r e q u e n t l y as i s necessary t o represent the p ro jec t cond i t i ons , p r e f e r a b l y a t a minimum of two samples per m i l e , w i t h c loser i n ­tervals for unusual condit ions.

4'. Once samples are taken i t is necessary t o care for them so that they w i l l a r r i v e i n the t e s t i n g machine w i t h p r e c i s e l y the same s t r u c t u r e and d e n s i t y charac ter ­i s t i c s tha t they hiad i n the road­bed.

5. Saturat ion of the samples i s opt ional . Kansas engineers believe i t t o be the best way t o a r r i v e at comparat ive e v a l u a t i o n s f o r a l l types of m a t e r i a l . Moisture con­ten t s i n subgrades do f l u c t u a t e , but greater d i f f i c u l t y is caused by basing design on s o i l i n a conpara-t i v e l y d r y c o n d i t i o n which l a t e r becomes saturated i n place under a base course or bituminous surface than i s caused when the reverse i s t r u e . D i f f e r e n t amounts of r a i n ­f a l l are accounted fo r i n the design method by the use o f s a t u r a t i o n

c o e f f i c i e n t s . Conditions of mois­t u r e f o r t e s t i n g purposes other than those d e s c r i b e d w i l l make necessary the use of d i f f e r e n t co­e f f i c i e n t s .

6. S t r e s s - s t r a i n curves are drawn f o r a l l subgrade samples. When f i r s t us ing t h i s method i t w i l l be necessary t o obtain stress-s t r a i n curves f o r base course and surface mixtures , but i f standard mixtures are generally used, only a few such determinations w i l l be re­q u i r e d . These w i l l e s t a b l i s h values which may conf i d e n t l y - b e used as moduli and need not be re­eva lua ted unless s p e c i f i c a t i o n s change.

7. The moduli of deformation fo r subgrade samples are calculated aivl from the proper thickness chart the t o t a l thickness of f l e x i b l e pave­ment required i s determined.

8. The t h i c k n e s s o f wea r ing course des i red i s es tabl ished and by use o f the convers ion formula wi th the modulus of the base course or sub-base to be used, the t h i c k ­nesses of the various courses are determined.

Referring to the paper "Appl ica­t i o n o f T r i a x i a l Compression T«s t Results To The Calculation of Flex­i b l e Pavement Thickness" by E.S. Barber , Highway Engineer of the Publ ic Roads Admin i s t r a t ion , pre­sented at the DecenlMr 1946 meeting o f the Highway Research Board we quote the f o l l o w i n g - - " In co r r e l a t ­i n g observations o f pavement per­formance i n v o l v i n g var ious loads and m a t e r i a l s , i t i s h e l p f u l t o have a theore t ica l re la t ionship be­tween the pavement th ickness and the m a t e r i a l t e s t r e s u l t s .

*Thus, w h i l e the r e s u l t s o f f i e l d observations are r e q u i r e d , t h e i r a p p l i c a t i o n may be broadened and t h e i r e v a l u a t i o n made more quant i ta t ive i f they are correlated by means o f t e s t r e s u l t s on th'e .component ma te r i a l s w i t h the a i d o f t h e o r e t i c a l r e l a t i o n s h i p s . "

E s s e n t i a l l y , t h i s i s what has'

39

been done i n th is work. The p rac t i* c a l working aspects of the design method have been studied and corre­l a t e d w i t h l a r g e q u a n t i t i e s o f f i e l d data «nd s e r v i c e da ta t o create a workable system of f l e x ­i b l e pavement design.

Much of the t h e o r e t i c a l t r e a t ­ment of th i s problem was omitted i n t h i s r e p o r t i n o rde r t h a t t h i s system of design could be presented i n as simple a manner as possible .

Mr. Barber aided us i n Che process of b l e n d i n g the t h e o r e t i c a l and p r a c t i c a l aspects o f t h i s work . Therefore , f o r a more f u l l under­standing o f the theory upon irf i ich t h i s system i s based we urge a study of Mr. Barber 's 1946 Highway Research Board Paper.

The methods by which theory i s incorporated i n the preparat ion of t h i s system are g iven i n Appendix B.

REFERENCES

1. L . A. Palmer and E. S. Barber. "Soi l Displacement Under a Circular Loaded Area". Proceedings Highway Research Board V o l . 2 0 . (1940) pages 279-286. (Also Public Roads, V o l . 21 . No. 10. DfC. 1940.) Dis­cussed by W. S. Housel, L . A. Palmer, ,and C. A. Hogentogler, J r . pages 314 t o 332. 2. E. S. Barber, " A p p l i c a t i o n o f T r i a x i a l Compression Test Results t o the C a l c u l a t i o n s o f F l e x i b l e Pavement Thickness"', Proceedings Highway Research Board, V o l . 26, (1946) . 3. L . A. Palmer and E. S. Barber, "The Set t lement o f Ear th Embank­ments", Public Roads, V o l . 2 1 . No. 9, NoveiAber 1940. 4 . C. A. Hogen tog le r and E . S. Barber, ^Essential Features of T r i ­a x i a l Shear Tests" , Public Roads, V o l . 20. No. 7, September, 1939. 5 . T . A. Middlebrooks and G. E. Ber t ram. "The Design o f A i r p o r t Pav ing f r o m the S o i l Mechanics V i e w p o i n t " , Civil Engineering, Ju ly , 1942. 6. Norman W. McLeod, Department of Asphal t Technology, I m p e r i a l O i l L i m i t e d , (1941), " S o i l Technology Applied t o Modern Highway and A i r ­port Construct ion". 7. Norman McLeod. Department o f Asphalt Technology, I m p e r i a l O i l

L imi t ed , (1939), "A Utanual of S o i l Science A p p l i e d t o Subgrade and Base Course Design". 8. B. K. Hough, J r . , "Technique of Determining Shearing S t reng th -o f S o i l s " , P r o g r e s s R e p d r t o f a S p e c i a l Committee o f the S o i l s Mechanics and Foundation D i v i s i o n on the Technique o f S o i l Tes t s . Proceedings, ASCE, February. 1942, D i s c u s s i o n by Glennon G i l b o y i n February, 1942. Discussion by C. D. Beerup i n A p r i l , 1942. Discussion by P. C. Rut ledge i n September, 1942. 9. A. C. Benkleman, "Present Knowl­edge i n the Des ign o f F l e x i b l e Pavements", Public Roads. V o l . 19, January, 1938. 10. D. M. Taylor . " L i m i t Design of Foundations Ik Embankments", Pro­ceedings, Highway Research Board, (1939). page 454 to 459. 11. Fred Burggraf , " F i e l d Tests on B e a r i n g C a p a c i t y , Shear ing and Penetra t ion Resistance ttt Se t i« '* , Proceedings Highway Research Board, 1940. Pages 287 t o 298. 1'2. V. A. Endersby, "The Mechanics of Granular and Granu l a r -P l a s t i c Mater ia l s w i t h Specia l References t c Bituminous Road Mate r i a l s and Subsoi ls" , Proceedings, ASTM V o l . 40 . ( 1 9 4 0 ) . Pages 1154 t o 1174. 13. A. T. Goldbeck, "A Method o f

40

design of Non-Rigid Pavements f o r Highways and A i r p o r t Runways ", Pro~ ceedtngs. Highway Research Board, V o l . 20 (1940) . Pages 258 t o 270. 14. W. S. House1, " S o i l s Mechanics i n Engineering", Proceedings, Engr. Conf. i n Soi l s f o r Engrs., Michigan State College, March. 1941. Pages 74 t o 98. 15. W. S. House1, Dept. 'Engr. Re^ search , U n i v e r s i t y o f Mich igan ,

Des ign o f F l e x i b l e S u r f a c e s " . 16 . P r e v o s t Hubbard and F . C. F i e l d , ' " R e q u i r e d Thickne-ss o f Asphal t Pavement i n R e l a t i o n t o Subgrade S u p p o r t " , Proceedings Highway Research Board , V o l . 20 ( 1 9 4 0 ) . Pages 271 t o 278. 17. Leo Jurgenaon, "The Sheering Resistance o f S o i l s " . C o n t r i b u ­t ions t o S o i l Mechanics, Bos. Soe. C. E. Pages 184 t o 226. 18. W. W. Pagon, "Resis tance o f S o f t F i l l t o S t a t i c Wheel Loads", Proceedings ASCE ( F e b . 1 9 4 2 ) . Pages 237 t o 254. 19. H. Q. Spangler and H. 0. Ustrud, "Wheel Load S t r e s s D i s t r i b u t i o n Through F l e x i b l e Type Pavements Proceedings Hi^way Research Board* V o l . 20 (1940). Pages 235 t o 257. 20. K a r l Terzaghi . "General Ifedge Theory of Ear th Pressure", Trans­actions ASCE (Oct . 1941). Pages 68 t o 80. 2 1 . W. S. Housel, Dept. Engr. Re­search , U n i v e r s i t y of Mich igan , "The Design of F l e x i b l e Surfaces". 22. Dr. Miles S. Kersten, "Progress Report of Subcommittee on Methods of Measuring S t rength of Sii>grade Soi l -Review of Methods of Design of F l e x i b l e Pavements". Proceed­ings, Highway Research Board V o l . 25. Pages 8 t o 18. 23. W. H . Campen, "Report o f Sub­committee on Methods of Subgrade, Subbase, and Base Preparat ion fo r Strength", Proceedings, Highway Re­search Board , V o l . 25 , ( 1 9 4 5 ) ,

Pages 18 t o 23.

24 . ' Ralph A. Freeman and 0 . J . P o r t e r , " F l e x i b l e Pavement Test Section f o r 300,000-Lb. Airplanes , Stockton, C a l i f o r n i a . " Proceedings Highway Research Board , V o l . 25 (1945). Pages 23 t o 44 . 25. W. H. Campen and J . R. Smith, "An Analysis o f F i e l d Load Bearing Tests Using P l a t e s " , Proceedings Highway Research Board, V o l . 24 ( 1 9 4 4 ) . Pages 87 t o 104. 2 6 . Dona ld M. B u r m i s t e r , "The Theory o f Stresses and Disp lace ­ments i n Layered Systems and A p p l i ­c a t i ons t o the Design of A i r p o r t Runways", Proceedings Highway Re­search Board. V o l . 23 (1943). Pages 126- 148. 27. H. G. N e v i t t . "A Mathematical A n a l y s i s o f Some Phases o f the F lex ib le Surface Design Prob lem" , Proceedings, H i^way Research Board V o l . 23 (1943). Pages 149-154. 2 8 . Roland Vokac, "Thickness o f Surface and Base Courses f o r Flex­i b l e Pavements". Proceedings, High­way Research Board. V o l . 23 (1943) Pages 155-165. 29. 0 . J . Por ter . "Foundations f o r F l e x i b l e Pavements". Proceedings, Highway Research Board . V o l . 22 ( 1 9 4 2 ) . Pages 100-143. 30. T . A. Middlebrooks and Capt. G. E. Bertram, Engr . . A i r Forces. U. S. Arny. " S o i l Tests f o r Design of Runway Pavements". Proceedings, Highway Research Board . V o l . 22 (1942). Pages 144-184. 3 1 . K e i t h Boyd, " A n A n a l y s i s o f Wheel Load Limits as Related to De­sign ".Proceedtnfs. Highway Research Board. V o l . 22 (1942) . Pages 185-198. 32. M. Q. Spangler. "The S t ruc tura l Design of F lex ib le Pavements". Pro­ceedings, Highway Research Board, V o l . 22 ( 1 9 4 2 ) . Pages 199-224. 3 3 . A. C. Benkelman, "Report o f Committee on F l e x i b l e Type Pave-

41

ments", M. G Spangler, "Wheel Load Stress D i s t r i b u t i o n Through F lex­i b l e Type Pavements", Proceedings, Highway Research Board , V o l . 21 ( 1 9 4 1 ) . Pages 110 t o 117. 34. W. S. Housel , "Load Tests on F l e x i b l e Surfaces" , Proceedings , Highway Research Board , V o l . 21 (1941) . Pages 118-136. 35 . A. T. Goldbeck, "S tud ie s o f Subgrade Pressures Under F l e x i b l e Road Surfaces", Proceedings, High­way Research Board, V o l . 19 (1939). Pages 164-174. 36. B. E. Gray, "Present Design Practice and Construction Develop­ments i n F l ex ib l e Pavements", Pro­ceedings, Highway Research Board, V o l . 19 ( 1 9 3 9 ) . Pages 175-192. 37. L . A. Palmer, "Stresses Under Circular Loaded Areas", Proceedings

Highway Research Board, V o l . 19 ( 1 9 3 9 ) . Pages 397-408. 38. D. L . H o l l , "Shearing Stresses and Sur face D e f l e c t i o n s Due t o Trapezo ida l Loads", Proceedings, Highway Research Board, V o l . 19 (1939). Pages 409-423. 39. Prevost Hubbard, " S o i l Bearing Tests and F l e x i b l e Pavement De­s ign" , Research Series No. 10, The Asphalt I n s t i t u t e , August 1, 1944. 40. "Design of Asphalt Pavements fo r Highway and Ai rpo r t Engineers", by the Engineering and Development Committee, D i v i s i o n 3, The Asphalt I n s t i t u t e , 1945. 4 1 . J . B. Kineer, "A t l a s of Ameri­can A g r i c u l t u r e " , Part 2 Cl imate , Section A, P rec ip i t a t i on and Humid­i t y (1922), 48 pages.

42

APPENDIX A

TABLES AND CHARTS CONVENIENT FOR CALCULATION

TABLE A l TRAFFIC COEFFICIENTS TABLE A2 SATURATION C(SFFICIENTS

T r a f f i c Coefficient

•

1

5/6

2/3

1/2

Wheel Load I t

9,000

7,500

6.000

4,500

T r a f f i c veh per day

1500 - up

900 - 1500

300 • 900

50 - 300

Saturation Coefficient

n

1 0

0 9

0 8

0 7

0 6

Average Annual Rainfa l l

in

35 0 - 45 0

30 0 - 34 9

25 0 • 29 9

20 0 - 24 9

15 0 - 19 9

389

35 9 36 3 38 0

37« 316 39 k wnotson

375 38 0 ko 3 '•*%-

37 9 39 8

38 3 U 2

TOft

3kl 33

Saturation Coefficient n

Figure Al , Average Annual Precipation fo r Kansas from 1898 to 194S i n ­clusive wi th corresponding Saturation Coeff ic ien ts

43

TABLE A3. TABLE OF AREAS

Diameter Area. Diameter Area Diameter Area

2.50 4.91 2.90 6.61 4.90 18.86 2.51 4.95 2.91 6.65 4.91 18.93 2.52 4.99 2.92 6.70 4.92 19.01 2.53 5.03 2.93 6.74 4.93 19.09 2.54 5.07- 2.9« 6.79 4.94 19.17

2.55 5.11 2.95 6.84 4.95 19.24

2.56 5.15 2.96 6.88 • 4.96 19.32 2.57 5.19 2.97 6.93 4.97 19.40 2.58 5.23 2.98 6.98 4.98 19.48 2.59 5.27 2.99 7.02 4.99 19.56

2.60 5.31 3.00 7.07 5.00 19.63

2.61 5.35 3.01 7.12 5.01 19.71 2.62 5.39 3.02 7.16 5.02 19.79 2.63 5.43 3.03 7.21 5.03 19.87 2.64 5.47 3.04 7.26 5.04 19.95

2.65 5.52 3.05 7.31 5.05 20.03 2.66 5.56 3.06 7.35 5.06 20.11 2.67 5.60 3.07 7.40 5.07 20.19 2.68 5.64 3.08 7.45 5.08 20.27 2.69 ~ 5.68 3.09 7.50 5.09 20.35

2.70 5.73 3.10 7.55 5.10 20.43

2.71 5.77 3.11 7.60 5.11 20.51 2.72 5.81 3.12 7.65 5.12 20.59 2.73 5.85 3.13 7.69 5.13 20.67 2.74 5.90 3.14 7.74 5.14 20.75

2.75 5.94 4.75 17.72 5.15 20.83 2.76 5.98 4.76 17.80 5.16 20.91 2.77 6.03 4.77 17.87 5.17 20.99 2.78 6.07 4.78. 17.95 5.18 21.07 2.79 6.11 4.79 18.02 5.19 21.16

2.80 6.16 4.80 18.10 5.20 21.24 2.81 6.20 4.81 18.17 5.21 21.32 2.82 6.25 4.82 18.25 5.22 21.40 2.83 6.29 4 . 8 3 . . 18.32 5.23 21.48 2.84 6.34 4.84 18.40 5.24 , 21.57

2.85 6.38 4.85 18.47 5.25 21.65 2.86 6.42 4.86 18.55 5.26 21.73 2.87 6.47 4.87 18.63 5.27 21.81 2.88 6.51 4.88 18.70 5.28 21.90 2.89 6.56 4.89 18.78 5.29 21.98

•TABLE A4 . MOLDING PERCENTAGES

Plaatie Mold at Ptorcentaie of Index Standard Coapaetlon

0-10 102 11-lS 100 16-20 9» 21-25 96 26-30 M

I 31-35 98 36-up 90

When sand is added to s o i l to provide modified stibKrade, use the fol loving percent­ages when they are higher than the aboire values, use the above table I f higher

Sand Rsreentage of % Standard Conipactian

20 97 30 98 40 99 SO 100 60 101 70 102

TABLE AS t

THICKNESS OF BASE t^ UNDER MAT Cp = 15,000 p s i

list Thickness of I k t i p ' 2 S i n Thickness of I h t = 2 0 in Only of Base (psi) of Base (psi)

*s 6,000 7,000 10.000 6,000 7,000 10,000

3 0 7 0 6 0 6 1 4 1 3 1 2 4 2 0 1 9 1 7 2 7 2 6 2 3 5 3 4 3 2 2 9 4 1 3 9 3 5

6 4 8 4 5 4 0 5 4 5 2 4 6 7 6 1 5 8 5 2 6 8 6 4 5 8 8 7 5 7 1 6 3 8 2 7 7 6 9

9 8 8 8 4 7 5 9 5 9 0 8 1 10 10 2 9 7 8 6 10 9 10 3 9 2 11 11 6 11 0 9 8 12 2 11 6 10 4

12 12 9 12 2 10 9 13 6 12 9 11 5 13 14 3 13 i 12 0 15 0 14 2 12 7 14 15 6 14 8 13 2 16 3 15 5 13 8

15 17 0 16 1 14 4 17 7 16 8 15 0 16 18 4 17 4 15 5 19 0 18 0 16 1 17 19 7 18 7 16 7 20 4 19 3 17 3

18 21 1 20 0 17 8 21 7 20 6 18 4 19 22 4 21 3 19 0 23 1 21 9 19 6 20 23 8 22 5 20 1 24 5 23 2 20 7

45

TABLE A6. CONVERSION TABLE

M i l l i l i t e r s t o Cubic Inches

•I eu i n . ' ml eu I n . • t , cu i n . • I cu i n . nl cu i n

0.2 .01 8.2 .50 16.2 .99 24.2 1.47 32.2 1.96 0.4 .02 8.4 .51 16.4 1.00 24.4 1.49 32.4 1.98 0.6 .0* 8.6 .52 16.6 1.01 24.6 1.50 32.6 1.99 0.8 .05 8.8 .54 16.8 1.03 24.8 1.51 32.8 2.00 1.0 .06 9.0 .55 17.0 1.04 25.0 1.53 33.0 2.01

1.2 .07 9.2 .56 17.2 1.05 25.2 1.54 33.2 2.03 1.4 .09 9.4 .57 17.4 1.06 25.4 1.55 33.4 2.04 1.6 .10 9.6 .59 17.6 1.07 25.6 1.56 33.6 2.05 1.8 ' .11 9.8 .60 17.8 1.09 25.8 ' 1.57 33.8 2.06 2.0 .12 10.0 .61 18.0 1.10 26.0 1.59 34.0 2.07

2.2 .13 10.2 .62 18.2 1.11 26.2 1.60 34.2 2.09 2.4 .15 10.4 .63 18.4 1.12 26.4 1.61 34.4 2.10 2.6 .16 10.6 .65 18.6 1.13 26.6 1.62 34.6 2.11 2.8 .17 10.8 • 66 18.8 1.15 26.8 1.64 34.8 2.12 3.0 .18 11.0 .67 19.0 1.16 27.0 1.65 35.0 2.14

3.2 .20 11.2\ .68 19.2 1.17 27.2 1.66 35.2 2.15 3.4 .21 11.4 .70 19.4 1.18 27.4 1.67 35.4 2.16 3.6 .22 11.6 .71 19.6 1.20 27.6 1.68 35.6 2.17 3.8 .23 11.8 .72 19.8 1.21 27.8 1.70 35.8 2.18 4.0 .24 12.0 .73 20.0 1.22 28.0 1.71 36.0 2.20

4.2 .26 12.2 .74 20.2 1.23 28.2 1.72 36.2 2.21 4.4 .27 12.4 .76 20.4 1.24 28.4 1.73 36.4 2.22 4.6 .28 12.6 .77 20.6 1.26 28.6 1.74 36.6 2.23 4.8 .29 12.8 .78 20.8 1.27 28.8 1.76 36.8 2.25 5.0 .31 13.0 .79 21.0 1.28 29.0 1.77 37.0 2.26

5.2 .32 13.2 .81 21.2 1.29 29.2 1.78 37.2 2.27 5.4 .33 13.4 .82 21.4 1.31 ^ 29.4 1.79 37.4 2.28 5.6 .34 13.6 .83 21.6 1.32 29.6 1.81 37.6 2.29 5.8 .35 13.8 .84 21.8 1.33 29.8 1.82 37.8 2.31 6.0 .37 14.0 .85 22.0 1.34 30.0 1.83 38.0 2.32

6.2 .38 ' 14.2 .•87 22.2 1.35 30.2 1.84 38.2 2.33 6.4 .39 14.4 .88 22.4 1.37 30.4 1.85 38..4 2.34 6.6 .40 14.6 .89 22.6 1.38 30.6 1.87 38.6 2.36 6.8 .41 14.8 .90 22.8 1.39 30.8 1.88 38.8 2.37 7.0 .43 15.0 .92 23.0 1.40 31.0 1.89 39.0 2.38

7.2 .44 15.2 .S3 23.2 1.42 31.2 1.90 39.2 2.39 7.4 .45 15.4 .9* 23.4 1.43 31.4 1.92 39.4 2.40 7.6 .46 15.6 .95 23.6 1.44 31.6 1.93 39.6 2.42 7.8 .48 15.8 .96 23.8 1.45 31.8 1.94 39.8 2.43 8.0 .49 16.0 .98 24.0 1.46 32.0 1.95 40.0 2.44

46

T-ThiekneM of Mot IC,* IS.OOO p * i ) Required { I n c h e s ) 40 eo 15 . . . . 10 . 8 ^ 6 9 * 3 ? i

X i n 6 ^ ^0 '.0. ? T ? ? J 2_

C-Modulus of Deformation of Subgrode in Thouiands ( p s i ) Fig A-2.-THICKNESS CHART for n- I .O, S - O l i n c h . •

T - T h i c k n e s s of Mot (Cp • 15,000 p s i ) Required ( I n c h e s ) 40 eo IS 10 8 7 6 9 4 3 2

•

30. 2 0 19 • • 'P • ? 7 ^ ? ± EO 19

C-Modulus of Deformation of Subgrode in Thousondi ( p s i ) Fig. A-3.-THICKNESS CHART for n - 0 9 . S » 0 I inch.

47

T- Thickness ol Mat (Cp* IS,000 p s i ) Required (Inches) 4P . 2P ly, , , , 1.0 , 8 7 6 9 4 3 t 1 0 - L .

s — 9 'P. P

; 1 1 ? ? 9 ><•

9

n .

/ r y

m • <

f

n V

/ n

0 C-Modulus of Deformation of Subgrade in Thousands ( p s i ) Fig A-4-THICKNESS CHART for n - 0 8 , S - O l i n c h .

T- Thickness of Mot (Cp* 15,000 p . s i ) Required (InehAv)

xzo 10 1 7 6 f < ? f ! 9

0 —

IC —i -4 r y

0

0 -

J—' 1 F19. A-5.-THICKNESS CHART for ft-0 7. S"O.I inch

48

T - T h i c k n e s s of Mat ( C ^ ' 1 5 , 0 0 0 p a.i ) Requ i red ( I n c h e s )

I X J . IP . e T 6 1.

C-Modulus of Deformation of SubgroJe in Thousands (p s i.) Fig A-&-THICKNESS CHART for n « 0 . 6 , S -O. l inch.

Spseifie Gravity

rioo

O 9a

1 5 20 a SO Moisture Content (% of Dry W e i g h t )

Fig. A-7.—Zero Air Voids Curves.

49

Figure A8. Forms used i n Kansas for Computations

Project Dm

OOHFUTATION OF E»SE OR SOB-BtSB THICBIESS

County-

Laboratory and Sam^ Numbora S

inchaa ta

Inches inehaa lb par aq in lb par sq in Inohaa *t

inches Ranarka

Subgrada Bua Mat

S

inchaa ta

Inches inehaa lb par aq in lb par sq in Inohaa St *t

inches Ranarka

^ „ V 'V\

Project.

(X3HPUTATI0N OF HAT THIfXNESS

County

.psi -in. Calculated by_

Cheelced by_

. DatcL.

.DateL

Labor­atory Number

Sample Number

Test

Number

1 Lateral Pressure

m Traffic Coef­

ficient

n Sat­

uration Coef.

v ^ l

psi

Net Unit

Strain C

Modulus of Def.

psi

T Thick­ness In.

y ^ - — . ^

SU8CR«DC SOIL CHARACTtRI5TIC5 FLEXIBLt PAVEHtNTS S K I I T pr__

RalNraLi (*v. SINCC I898) 0«H_

( T . « .

<e,( ) <c,( ) T M i f . m . . Rc^vi.tp ( I v c t f ) CUT

STATION

50

4^PENDIX B

DERIVATION OF THICKNESS CHARTS

The desigit of f l ex ib le pavenents is more easily accomplished by the use of thickness c h a r t s than w i t h a f o r m u l a a l o n e . The formula upon which these calculations are based has been given wi th an explana­t ion of each item. Tvo examples were given showing the use of thickness charts fo r determining thickness of f l ex ib l e surface required. The purpose of this appendix is t o exp la in in d e t a i l the d e r i v a t i o n of these charts for those who desire to make a complete study of th i s method.

Although the procedure fo r d e r i v i n g these charts is net p a r t i c u l a r l y compli­cated, a number of calculat ions are i n ­volved. These are followed through step by step so that anyone desi r ing to use th i s method for other conditions w i l l have no d i f f i c u l t y i n substituting other values and deriving other charts.

Stresses in the subgrade are calculated fo r various depths below the surface where the lead is applied. The amounts and loca­tions of OBximuffl p r inc ipa l stress d i f f e r ­ences are determined for load conditions being considered. Def lec t ion curves are used for the determination of the modulus of defornation l imi t ing the deflection to a certain value for each depth considered. A sa tura t ion c o e f f i c i e n t i s introduced t o compensate f o r the e f f e c t of d i f f e r e n t amounts of r a i n f a l l . The de f l ec t i on re­ducing e f f e c t of a surface course is de­termined by using the formula

Tables, curves, and scales are used fo r preparing a chart convenient for determin­ing the thickness of f l ex ib l e pavement re­quired.

The method given in the paper "Applica­t i o n of T r i a x i a l Compression Test Results to the Calcula t ion of F lex ib le Pavement Thickness" presented by E.S^ Barber i n December, 1946, at the Highway Research Board meeting i s used f o r c a l c u l a t i n g stresses at various depths and horisontal distances from the center of one t i r e in a dual t i r e asseobiy. The portions of Tkble 1 i n Mr. Barber's paper used in these ca l ­culations are included as Tables Bl ,B2 and-

B3. For convenience in fo l lowing the de­

velopment of the der ivat ion of the th ick­ness charts the procedure is set f o r t h i n twelve steps. 1. Plotting stress curves

Vert ica l , horizontal, and shear stresses transmitted to a point divided by the pres­sure applied at the surface are shown in Tables B l , B2, and B3. These tables are arranged for several values of the depth r a t i o 2/a and hor i zon ta l distance r a t i o r/a. Hie let ter a is used to designate the radius of t i r e contact area, the le t ter ^ the depth below the surface and the let ter

' r the horizontal distance from the center of load application t o the point consider­ed. Curves similar to those shown in Fig­ure B-1 are obtained from these tables. Hie curves in this figure are for the depth r a t i o only of e/a equals 1 . Other curves must be p lo t t ed fo r other depth r a t i o s . These are i r r e g u l a r curves and must be plotted in order to determine intermediate values between those shown i n the tables for the values of r / a . I t is not possible to interpolate d i r e c t l y from the tables . Working curves f o r determining values i n making computations must be p lo t t ed to a much larger scale than shown in Figure B-1

• OS

I 2 S HariiMlol Rollol Olataau DMdX B> Rodlu

Fit B-I-Slr«tsei Iranamittad to a point ot o dopth ratio ol on*

in order to determine values with s u f f i c i ­ent accuracy. These curves , as w e l l as mny others shorn he rea f t e r , are fo r the purpose of i l l u s t r a t i o n and cannot be read closely enough for naking computations.

2. Tabulation of stress iata In addition to tables B l t o B4 from Mr.

Barber's paper, the data shewn in Table B5 are used in Kansas f o r determining t h i c k ­ness of f l ex ib l e pavement requi red . .

51

To i l lu s t r a t e the procedure an example is given using a t r a f f i c c o e f f i c i e n t * of 2/3. Figure B-2 is a sketch depicting c i r ­cular areas equivalent to the t i r e contact areas with the radius , d i s tance between t i res for a dual t i r e asseiAbly, and h o r i -sontal distances f rom the center of the l e f t t i r e . The center of the l e f t t i r e is used as the origin.merely for conveni­ence in making f u r t h e r c a l c u l a t i o n s . A single point must be used rather than re-

TABLE B l . VERTICAL NORMAL STRESSES TRANSMITTED TO A POINT IN A SEMI-INFINITE MASS FROM A SURFACE LOAD UNIFORMLY DIS­

TRIBUTED OVER A CIRCULAR AREA Depth of point *

Heriiontal radial distance « radius, r

radius 0 0 35 0 5 1.0 1.5 3.0 3.5 3.0 4.0

JL a Vertical norsa 1 stress transmitted to point 4 pressure PI T

applied at sur

0.25 0 986 0 983 0 964 0 460 0 015 0 002 0 000 0.000 0 000 0 S «1 .895 .840 •418 .060 .010 .003 .000 000 0.75 .78* .762 .691 374 105 •035 .no .003 .000 1.0 .646 625 560 .335 .135 043 .016 007 000 1.35 .524 .508 .455 395 .135 057 .033 .010 .001 1.5 434 .413 .374 356 .137 .064 .029 013 .003 1.75 .346 336 .309 .333 .135 .071 037 .018 004 3.0. 284 .377 .358 .194 .I2i 073 .041 .033 006 3 5 .300 .196 .186 .150 .109 073 .044 028 .011 3 .146 .143 137 .117 .091 066 .045 .031 .015 4 .087 086 .083 .076 .061 .053 .041 .031 .018 5 .057 .057 .056 .063 .0(5 .039 .033 .027 .018 7 .030 .030 .029 .038 .037 035 .023 .020 .015 10 .015 .015 .015 .015 014 .014 .013 013 .010 15 007 007 007 .007 .006 006 006 .006 .006

TABLE B2. HORIZONTAL RADIAL NORMAL STRESSES TRANSMITTED TO A POINT IN A SEMI-INFINITE MASS FROM A SURFACE LOAD

UNIFORMLY DISTRIBUTED OVER A CIRCULAR AREA Depth of point * radius 0

Horlsontal radial distance * radiusX. a

0 35 0̂ 5 1.0 1.5 a.O 3.5 3 0 4 0 Rorisontat radial nersBl stress * applied pressure (Poissen's ra t io i • 0 5)

0.35 0.643 0.626 0.565 0.385 0.144 0 058 0.028 0.014 0.004 0.5 .374 .360 .335 .286 .196 .098 .050 .037 •008 0.75 .308 .201 196 .309 .175 .113 .064 .044 .013 1.0 .116 .118 .133 .149 146 104 .069 045 033 1.35 .067 .073 080 107 .116 096 069 .047 .036 1.5 .040 .046 .055 .078 .091 .082 .064 .047 .016 1.75 .035 .028 .035 056 070 068 058 .046 .037 3 0 .016 019 .024 .041 OSS .057 .052 .043 .027 3.5 .008 009 .013 .033 .033 .038 .038 .035 .035 3 .00* .006 .008 .014 .021 .036 .038 .026 .013 4 .001 .003 .003 006 .009 012 015 .016 .016 5 .001 om 003 .009 .005 .007 .008 .009 .010 7 .000 000 .000 .001 .003 003 .003 .004 .005 10 .000 .000 .000 .000 .000 .001 001 .on .001 I S .000 .000 .000 .000 .000 .000 .000 .000 000

52

TABLE 83 . HORIZONTAL RADIAL SHEAR STRESSES TRANSMITTED TO A POINT I N A SEMI-INFINITE MASS FROM A SURFACE LOAD

UNIFORMLY DISTRIBUTED OVER A CIRCULAR AREA

Depth of Horizontal radial distance -f radiusj; . point 4 a radius 0 0.25 0.5 1.0 1.5 2.0 2.5 3.0 4.0

z Hericontal radial shear stress at point « pressure applied at surface

0.25 0.000 0.024 0.065 0.299 0.042 0.014 0.003 0.002 0.001 0.50 .000 .057 .129 .262 .102 .032 ' .013 .006 .002 0.75 .000 .069 .141 .221 .128 .053 .024 .013 .003 1.00 .000 .065 .124 .178 .128 .069 .033 .018 .007 1.25 .000 .053 .i<n .146 .118 .072- .039 .023 .010 1.50 .000 .041 .080 .119 .104 071 .045 !o28 .012 1.75 .000 .033 .062 .094 .091 .068 .0*6 .030 .014 2.00 .000 .0S6 .048 .070 .078 .062 .045 .032 .015 2.5 .000 .016 .030 .050 .056 .050 .041 .032 .018 3 .000 .009 .019 .034 .040 .040 .035 .029 .018 4 .000 .005 .009 .018 .022 .024 .024 .022 .016 5 .000 .002 .005 .010 .013 .015 .016 .016 .013 7 .000 .001 .002 .004 .006 .007 .008 .008 .008 10 .000 .000 .001 .001 .002 .002 .003 .004 .004 15 .000 .000 .000 .000 .001 .001 .(XU .001 .001

TABLE B4. DISPLACEMENTS DUE TO UNIFORM PRESSURE OVER CIRCULAR AREA

pressure x radius • Displacement. S = noduiu, of " *~

e las t i c i ty Depth of Horizontal radial distance * radius, r point « a

2.5 3

0.30 0.26 0.18 0.31 0.27 0.19 0.32 0.27 0.19 0.32 0.28 0.20 0.32 0.28 0.20 0.30 0.27 0.21 0.28 0.25 0.20 0.24 0.23 0.19 0.19 0.18 0.16 0.14 0.14 0.13 0.10 0.10 0.09

Note: Displacement as used in the above table from Mr. Barber's paper is the same as the deflection referred to in other parts of this appendix.

radius 0 - .25 .50 .75 1.00 1.25 1.5 2 SO

a Displacement factor for Foisaon's rat ion : 0 . 5 i ^ 0 1.50 1.48 1.40 1.25 0.95 0.66 0.54 0.39 0.5 1.34 1.31 1.23 1.09 0.89 0.68 0.55 0.40 1 1.06 1.05 0.98 0.89 0.78 0.66 0.56 0.41 1.5 0.83 0.83 0.79 0.73 0.67 0.60 0.52 0.40 2 0.67 0.67 0.65 0.62 0.57 0.53 0.48 0.39 3 0.47 0.47 0.46 0.45 0.43 0.41 0.38 0.34 4 0.36 0.36 0.35 0.35 0.34 0.33 0.32 0.30 5 0.29 0.29 0.29 0.29 0.29 0.28 0.28' 0.2« 7 0.21 0.21 0.21 0.21 0.20 0.20 10 0.15 0.15 0.15 0.15 0.15 0.14 15 0.10 0.10 0.10 0.10 0.10 0.10

53

TABLE B5

Tire 8k Rim Assoc. Radius Dual Single 1940 HRB p. 269 of Average

T r a f f i c Wheel Tire Size Space Contact Con­ U i i t Coefficient Load Load Tire c to c Area ' tact Pressure

• />• M P* b A a P lb lb i n . sq. i n . i n . psi

1 9.000 4,500 9.75x20 10.50x22 13 54 4.15 83.33

5/6 7,500 3,750 9.75x20 12 50 3.99 75.00 2/3 6,000 3,000 9.00x20 11 45 3.78 66.67

8.25x22 1/2 4,500 2,250 7.50x20 10 39 3.52 57.69

* Averages from Kansas State Highwajr OBomissian Planning Board data.

fe r r ing to the center of each t i r e . A load applied at the surface of the

road creates stresses in the nmterial beloir the surface. These stresses nny be re ­solved into ve r t i ca l , hortsontal, and shear

o . in r

4 -S -2 - I 0 1 2 3 4 9 S T a 9 10 11 a 13 14 IS

Fig. B-Z- Radius of eentaet ana and diitanc* bslastn tiras lor m • e/3

stresses. Tables B l , B2, B3 and curves such as those sham in Figure B-1 provide data for determining these valuea. They must be ceoputed at a nunfcer of points for each depth r a t i o considered t o f i n d the mximum principal stress difference factors needed la te r . The selection of a greater number of points t o begin w i t h produces curves of greater extent and shews the trend more c lear ly . When several of these curves have been cosiputed and the ent i re procedure has been fol losnd. the selection of the points at which calculations are re­quired is more easily made. As one becomes more f a m i l i a r w i t h the procedure; fewer points need be selected.

The form "Calculations fo r Stresses", f i l l e d out on page 54 was devised for con­venience i n asking these calculations. The f i r s t l ine gives the distance f r e n 0, the center of the l e f t t i r e as shoam in Figure B-2.

The value of r is the same for the l e f t t i r e as the distance from 0. The value of r from the right t i r e is easily conputed by r e f e r r i n g to Figure B2. L e f t of 0, the value for b is added to the distance from 0. on the r ight of 0, the distance from 0 is subtracted from the value of 6. The values of r/a are computed by dividing each value of r by the value of a. Values of pg/p are determined from the curves such as the one shosm i n Figure B-1 f o r each value of r / a calculated above, keeping the values fo r l e f t and r igh t on the proper lines designated £ and iT. Pg is the v e r t i ­cal neroBl stress transmitted to the point being considered by the pressure applied at the surface by each t i r e . Pg/P i s a r a t i o of the v e r t i c a l normal stress divided by the pressure applied at the surface used f o r convenience i n c a l c u l a t i o n s . Both t i r e s transmit v e r t i c a l stresses i n the same d i rec t ion ; therefore, the values ob­tained from each t i r e are added together.

pr/P i s the h o r i i o n t a l r a d i a l normal s t r e s s at the p o i n t be ing considered eauaed by the pressure p applied at the surface. The values are determined in the same manner and are also added together.

The values of Sr/p f o r each t-ire are also determined in the same manner, however. 9f- 1" the hor isonta l r ad i a l shear stress at the point being considered. Between the centers of the two t i r e s , these shear stresses act i n opposite directions and the smaller one is subtracted from the larger. No s ign i f i cance i s attached to negative

54

CALCULATIONS FOR STRESSES

«•= 2/3 4-= I'OO » ° 3.78 inches

a - 3.78 inches i » 11 inches Distance

fromO -3 .2 -1.6 -1.4 -1.2 -1.0 -0.8 0 1 r I 3 2 1.6 1.4 1.2 1 .8 0 1

a l l ^ 33 12.6 12.4 12.2 12 11.8 U 10

r a

I .79"* .529 .423 .371 .318 .265 .212 .0 .265 r a

s 3.705 3.44 3.332 3.28 3.23 3.175 3.321 2.911 2.646

P

L .^3^ .548 .587 .602 .634 .623 .631 .646 •623 P t .002 .003 .004 .005 .005 .006 .006 .008 •012 P

+ .436 .551 .591 .607 .639 .629 .637 .654 .635

Pr P

L .338 .025 .323 .122 .320 .119 .118 .116 .119 Pr P

g .025 .030 . « 3 .034 .036 .038 .059 .049 .061 Pr P

+ .163 .355 .356 .356 .356 .157 .357 .165 •380

Jr_ P

L .169 .130 .108 .093 .0)32 .068 .055 0 •068 Jr_ P R .007 .010 .012 .033 .033 .015 •016 .021 .028

Jr_ P

+ .176 .140 .320 .106 .095 .083 .071 .021 •OiiO

P P .599 .706 .747 .763 .775 .786 .794 .819 •815

Pe Pr .300 .353 .374 .382 .388 .395 .397 .410 .408

Pi . .521 5.97 .624 .633 .640 .644 .647 .656 .641 P, • P^

2 .221 .244 .250 .251 .252 .251 .250 .246 .233

Px - Pi .i(42 .488 .500 .502 .504 .502 .500 .492 .466

.or9 .111 .125 .333 .338 .143 .147 .164 .177

P, -P^ .486 .499 .500 .502 .501 .500 .492 .464

55

values or to which value' is greater. Out­side of the center of each t i r e in' the dual wheel assembly, these stresses act i n the same direct ion and the values obtained for each t i r e are added together. 3 . Haxtuuti Principal Stress Difference factor

Hie greatest stress at any point under the surface may not be in a v e r t i c a l or ho r i zon ta l d i r e c t i o n , but at some angle from one of these. The stresses which occur in the i r a te r i a l below the surface and also the difference between the maximum and the minimum p r i n c i p a l stresses are important. The v e r t i c a l , horizontal , and shear stresses resulting from a conliination of the two loads applied at the surface have been determined at various po in t s . Stresses may also be determined i n direc­tions other than v e r t i c a l and hor izonta l . Planes nay be determined in which no shear stresses occur. The maximum stress occurs in one of these planes and the minimum at r i g h t angles t o i t . The d i f f e r ence be­tween these two stresses may be calculated without necessitating determination of the directions of these planes. The principal stress differences may thus be determined at various depths below the surface.

The principal stress difference under a single load is determined by mul t ip ly ing the average unit pressure which exists at the surface of the pavement by a factor de­pending upon the r e l a t ive distance below the surface and the characteristics of the o B t e r i a l . A factor amy be determined for stress differences under dual wheels de­pending also upon the spacing center to center of the t i r e s and the area of cen-tact . This factor i s determined frcm other

t OS 04 01 o t > HOfiM S t rn i Rollo

Fit B-3i- Slrtttes ol o point

calculations as shown on the form on page 54 and Mohr's c i r c l e of stress such as the one shown in Figure B-3. The next line on the form is obtained as indicated by adding the t o t a l values of pz/p and pr/p. The f o l l o w i n g l ine i s obtained by d i v i d i n g these values by two. This value is used as the center of the c i r c l e as p lo t t ed i n Figure B-3.

One point on the c i r c l e is plotted from the values obta ined above,' u s ing Pr/P as the horizontal distance from the o r ig in and sr/p as the v e r t i c a l distance, desig-

Z 0 4 0

- 2 - 1 0 I Distance - I n c h e s

Fig. B-4 - Stress difference factors at a depth ratio of one, m <• 2 / 3

nated as i in Figure B-3. A semi-circle i s drawn using the distance from this point on the c i r c l e to the center of the c i r c l e , as obtained, f o r a radius . The two points where the c i r c l e crosses the hor izonta l axis are used in determining the principal stress, d i f f e rence . The point nearer the o r ig in is the minor value p2 ond the other point is the nsjor value Pi. The principal stress difference occurs at such a position that no shear stress w i l l be involved. I t s value is equal t o the diameter of the c i r c l e .

This value may also be determirled nathe-matically by solving for the hypotenuse of a r ight t r i ang le which may be constructed on^Figure B-3 . The hypotenuse is the radius of the c i r c l e as shown from the point A to the center of the semi-circle. Some may prefer t o use the mathematical method.

The value of Pi minus p2, obtained for each distance from 0 shown in the f i r s t

56

line of the form, is the pr incipal stress difference divided by the equivalent un i ­form pressure applied at the surface at that particular point. Several values for the distance from zero are used to deter­mine the maximum value of pi minus ^ 2 each depth r a t i o 2 / a . These values of ^1 minus P2 are plotted for each value of the distance from 0 as shown in Figure B - 4 . A curve is then drawn for determining the maximum pr incipal stress difference factor 'at that depth r a t i o . Factors are deter­mined for a number of depth rat ios and a curve plotted as sham in Figure B-5. For convenience these valuer, are tabulated in Table B6. « . l o c a t i o n of Max'i*v* Prtncipil Stress Difference

A curve is drawn similar to that shmm in Figure B-6. This curve gives the posi­t i o n of the maximum pr inc ipa l stress d i f ­ference at any depth below the surface where the pressure is applied. This shows how i t s pos i t ion varies from the edge of the load at the surface to a point'midway between the t i r e s at considerable depth. I t s value is p r inc ipa l ly t o cheek upon the accuracy of the cooiputations to determine i f any values are out of l i n e , and as a matter of interest and information as to how the posi t ion of maximum values of the p r i n c i p a l stress d i f f e r ence varies w i t h increase i n depth.

depths are obtained by mul t i p ly ing each depth r a t i o by the radius of t i r e contact a. This i s conveniently acconiplished in tabular form i n Table B6.

10 Dipth RaHo Va

Flo.B-a-MsiiiMim prnnpQl alrm Mfsranet vndsr dual t i r t t far I I I - 2 / S

5. Kaximum Principal Stress Difference The naximun principal stress difference

at any depth is obtained by mu l t i p ly ing the average uni t pressure applied at the surface by the factor corresponding to that depth as determined f r m Figure B-5. Table B-6 gives these calculations, f r cn i h i ch a curve , such as shown i n Figure B-7, i s p l o t t e d . For p l o t t i n g t h i s curve the

Distonee Rotio _Q_

r/o

Fig. B-Gi - Locotion of moximum principol stress difference for m<>2/3i

e. Flottit^ Deflection Curves The values i n Table B - 4 from Barber's

paper are plotted similar to the curve for s/a equals 1 in Figure B-8. As explained previously working curves trust be prepared t o a much larger scale wi th intermediate cross-sect ion l ines to provide greater accuracy i n reading.

9. Determination of Moiulva of Deformation for a Certain Deflection

The curve is used for determining the modulus of deforiEBticn of the subgrade at various depths for the corresponding stress differences which w i l l allow the amount of def lect ion permitted. For this example, a d e f l f c t i o n of 0.1 i n . is used for a dual

57

D « p t h Rg B - 7 - Relation of stress difference to depth for m • 2 /3

wheel assenfcly. Values are assuned for the modulus of d e f o r n a t i o n of the subgrade C and c a l c u l a t i o n s made f o r the t o t a l de­f l e c t i o n i n each case. The curve i n Figure B-8 g ives the values of SO/pa f o r va lues of r/a. S u b s t i t u t i n g the f a c t o r f for so/pa and t r anspos ing , Pa

The most c r i t i c a l c o n d i t i o n e x i s t s a t each dep th r a t i o a t the p o i n t where the grea tes t d e f l e c t i o n occurs , p rov ided t h a t i t i s a l s o the p o i n t of maximum p r i n c i p a l s t ress d i f f e r e n c e . For t r i a x i a i compres­s i o n t e s t s o f subgrades w h i c h p reducr

— ^

HMlionlol RsMi Olttmc* O i < I M e> Redto- ' f r Fig. B-a- Dliploctineiil (odor eurvo ol o dopth ratio ol (

s t r e s s - S t r a i n curves t h a t are s t r a i g h t l ines f o r s t r e s s d i f f e r e n c e s as h i g h as those required f o r p a r t i c u l a r computations, the modulus of deforiretion f o r each sub-grade i s a c o n s t a n t r e g a r d l e s s o f t he stress d i f f e r e n c e . Since i t i s not p r a c t i ­c a l t o d e r i v e c h a r t s f o r each t r i a x i a i t e s t , a degree of s a f e t y i s i nco rpora t ed f o r s t r e s s - s t r a i n curves w h i c h are not s t r a i g h t l i n e s . Subgrades w i t h such curves are a lso the ones which are o r d i n a r i l y not as sa fe , so t h i s v a r i a t i o n from the s t r i c t t heo re t i c a l procedure is des i rab le . There­f o r e the po in t where the greates t defJec-t ion i s effected by a dua l wheel assembly is chosen f o r determination ot the modulus of deformat ion f o r that d e f l e c t i o n .

For t h i s example of a 2 / 3 . the po in t midway between the t i r e s gives a d is tance r a t i o r/a = 1.455 as shown on the last l i n e

,of Table B-6 and a t the bot tom of F igure B-4 . The d e f l e c t i o n f ac to r curve on Figure B-8 becomes s teeper t o the l e f t of t h i s value and f l a t t e r t o the r i g h t . Therefore , a poin t nearer one of the t i r e s w i l l give a greater d e f l e c t i o n fac to r and a correspond­ing greater d e f l e c t i o n , so a poin t i s se­lected nearer the l e f t t i r e , i n accordance w i t h p rev ious c a l c u l a t i o n s . A f t e r some t r i a l and e r r o r or an i n s p e c t i o n of the curve , i t is found tha t the greatest value f o r the c o m b i n a t i o n i s when r/a f o r the l e f t t i r e equals 0 .2 . The reason f o r t h i s

w i l l be more apparent l a t e r . The radius of contact area a i s 3.78 i n . , making r - 0.76 i n . From the r i g h t t i r e t o t h i s same point r = 11.00-0.76"10.24 i n . , g iv in g a value o f r/a " 2 . 7 1 . Hie slope of the curve on F i g ­u re B - 8 i s t h e same a t b o t h o f these po in t s . This f a c t nakes for an easy method of loca t ing the point of maximum de f l ec t ion a t each depth r a t i o . This p o r t i o n of the example has been f o r a depth r a t i o of one and • ' 2 / 3 . Changes of any values n a t u r a l l y a f f e c t these r e s u l t s .

From work ing curves s i m i l a r t o F igure B-8 values of SC/pa or / are 1.055 f o r the l e f t t i r e and 0.295 f o r the r i g h t t i r e . .

The u n i t pressure appl ied at the surface i s 66.67 l b per sq i n . T h i s , n u l t i p l i e d by the radius of t i r e con tac t a o f 3.78 i n . , g ives pa equals 2 5 2 . 0 . Assuming a va lue f o r the modulus of deformat ion of the sidj-grade C equal t o 3400 p s i , then pa d i v i d e d by C equals 0 .0741. This term m u l t i p l i e d by the f a c t o r f o f 1.055 f o r the l e f t t i r e gives a d e f l e c t i o n of 0.0783 i n . , and by f of 0.295 f o r the r i g h t t i r e gives a d e f l e c ­t i o n o f 0.0219 i n . Adding these va lues g i v e s a t o t a l d e f l e c t i o n of 0.1002 i n . Other values may be assumed f o r C and the corresponding values determined f o r t o t a l d e f l e c t i o n . When C equals 3410, S equals

58

TABLE B6. RELATION OF DEPTH. HORIZONTAL DISTANCE. AND STRESS DIFFERENCE FOR TRAFFIC COEFFICIENT m= 2/3

Stress Depth Hor i son ta l Distance Di f f e rence Stress ^ Ra t io Depth Distance Ra t io f a c t o r Di f fe rence

« / o z r r / o ^1 - H P (Pi - P2> i n . I n . ps i

0.00 .000 -3.78 •1.000 .6366 42.44 0.25 .945 -3.4 - .899 .626 41.74 0.50 1.890 • -2.6 - .688 .597 39.80 0.75 2.835 -1.9 - .503 .555 37.00 1.00 3.780 -1.2 - .318 .502 33.47 1.25 4.725 -1.0 - . .265 .427 28.47 1.50 5.760 -0.8 - .212 .362 24.13 1 75 6.615 -0.6 - .159 .306 20.40 -2.00 7.560 -0.4 - .106 .261 17.40 2.50 9.45 -0.4 - .106 .200 13.33 3.00 11.34 -0.2 .053 .164 10.93 4.00 15.12 *1.0 * .265 .114 7.60 5.00 18.90 *2.0 * .529 .084 5.60 7.00 26.46 O.O « .794 .053 3.53

10.00 37.80 »4 .0 «1.058 .030 2.00 15.00 56.70 •5.5 41.455 .013 0^87

0 0999; and when C equals 3420, S equals 0.0995. These values are p lo t t ed in Figure B - 9 . A curve may be drawn through these points and where i t in tersects the v e r t i c a l l i n e f o f the d e s i r e d d e f l e c t i o n , i n t h i s c a s e ' O . l i n . , the modulus of defornnat ion (3407 p s i ) may be read w h i c h w i l l a l l o w t h i s amount of d e f l e c t i o n . Th i s i s done f o r s e v e r a l v a l u e s of the d e p t h r a t i o .

Tab le B-7 i s made f r o m these curves showing the values of the. depth r a t i o z / a , the depth z and the modulus of deformat ion C wh ich a l lows the d e s i r e d amount of de­f l e c t i o n . A curve as shown i n Figure B-10 IS p l o t t e d from t h i s t a b l e .

8 . Influence of Saturation Coefficient A s a t u r a t i o n c o e f f i c i e n t i s here i n t r o ­

duced which gives a decreased thickness of surface or base course required i n l o c a l i ­t i e s of less r a i n f a l l . The e f f e c t here i s t o show a> decreased modulus of deforma­t i o n required fo r lesser th ickness . Table B8 IS prepared f rom Figures B-7 and B-10 f o r convenience i n making these c a l c u l a ­t ions and showing the stress d i f f e rences at v a r i o u s depths f o r p l o t t i n g the curve as shown i n F i g u r e B - 1 1 f o r n = 0 . 7 . T h i s curve i s p l o t t e d w i t h the modulus .of de­format ion C as the abscissa and the stress d i f f e r e n c e as the o r d i n a t e . Th i s makes points , p l o t t e d at c e r t a i n values of depth 2 which are designated on the curve.

9. S f f e c t of Surface Course For s a t i s f a c t o r y road service, a mater i ­

a l of greater s t a b i l i t y than the subgrade i s placed upon the subgrade. For the con­d i t i o n s as set f o r t h , such as t r a f f i c co­e f f i c i e n t , s a tu ra t ion c o e f f i c i e n t , and per -

3430

O3420

;34I0

'3400

3390 Q0994 Q0996 Q0998 01000 01002

Total Deflection S (Inches) Rg B-9 -Determinat ion of modulus of deformation for certain deflection when m = 2 / 3 .

59

TABLE B7. RELATION OF DEPTH TO MODULUS OF DEFORMATION

f o r « " 2/3 and S" 0.1 inch

Modulus o f Deforraa t h Ra t io Depth t i o n of Subgrade

z a

C i n . p s i

0 0 4484 0.5 1.89 4089 1.0 3.78 3407 1.5 5.67 2869 2 .0 7.56 2467 3 11.34 1944 4 15.12 1618 5 18.90 1401 7 26.46 1023

10 37.80 741 15 56.70 504

mi t ted d e f l e c t i o n , the depth i s determined a t which d e f l e c t i o n i s l i m i t e d t o 0.1 i n . A be t t e r i m t e r i a l may be of less thickness than the depth of subgrade 2 which would be required to l i m i t the d e f l e c t i o n of a poin t at that depth to the spec i f i ed amount. The depth z does not need t o be found except i n the d e r i v a t i o n of the th ickness charts . 70. Thickness Reduction factor

The thickness of the be t t e r ma te r i a l i s found by the formula

f = 2.

S3

o 2

I o i ,

? 0 2 0 4 0 6 0 * D « p t ( i t . I n c h a i F i j B - I O - R e l o t i o n of depth to modulus of deformotioa for m • 2 / 3

Where: I- th ickness o f surface course or pave­

ment r equ i red 2° d e p t h t o a p o i n t i n the subgrade

where d e f l e c t i o n wou ld be a s p e c i ­f i e d amount due t o a toad on the subgrade i t s e l f

(7= modulus o f d e f o r m a t i o n of subgrade Cp= modulus o f d e f o r m a t i o n of pavement

-V%i^.^. . .y . . . .Y. . . .v . . . . 'p .

• 90

O

/ /

/ • •ptht 2 on c u r v t

/

4 o 0 10 20

C - Hodaitt* 01 Dafermotiea (n H u i i d r « d t ( p t . i ) Fig B - l l - Relotion of modului of doformotion, s i ros i ddlii^ anco, depttv ond-WTC^ for m-S, n*0 7, S - 0 1 ineli

Table B9 i s p r o v i d e d showing c a l c u l a ­t i o n s of t h i s f a c t o r f o r a bituminous mat or pavement w i t h a modulus o f de fo rma t ion

° 15,000 p s i . F i g u r e B-12 i s p l o t t e d w i t h these values. For convenience i n pro­v i d i n g a u s a b l e s c a l e f o r d e t e r m i n i n g thickness of pavement r equ i red . Table B-10 i s made f r o m t h i s curve f o r c e r t a i n se­lected values of t h i s f a c t o r and the c o r r e ­sponding modulus of deformation of the sub-grade. These values are then p lo t t ed along a h o r i z o n t a l s c a l e shown on the t o p of F i g u r e B - l l .

11. C o l c t t l a t i o f w for thickness Required The thickness of bituminous surface re ­

q u i r e d on the subgrade is c a l c u l a t e d f o r several values of the depth 2 by the above formula us ing F igure B - l l . For any value of the dep th 2 e r e c t a v e r t i c a l l i n e t o the s ca l e a t the t o p t o f i n d the c o r r e ­sponding f a c t o r . A simple m u l t i p l i c a t i o n of t h i s f a c t o r by z gives the thickness o f pavement requ i red .

12. final Thickness Chart, Figure B - l l would be usable f o r c a l c u ­

l a t i n g t h i c k n e s s e s ; however, c o n t i n u i n g

60

TABLE B8. RELATION OF STRESS tflFFERENCE AND MODULUS OF DEFORMATION WITH VARIATION IN SATURATION COEFFICIENT FOR m= 2/3 AND S= 0 . 1 INCH

Stress Mod. of Def. a t Cer ta in Values of n 0.6 2 D i f f . 1.0 0.9 0.8 0.7 0.6

0 42.44 4484 4036 3587 3139 2690

1 41.60 4260 3834 3408 2982 2556

2 39.70 4000 3600 3200 2800 2400

3 36.60 3670 3303 2936 2569 2202

4 32.30 3340 3006 2672 2338 / 2004

5 27.15 3040 2736 2432 2128 1824

6 23.00 2790 2511 2232 1953 1674

7 19.30 2570 2313 2056 1799 1542

8 16.30 2380 2142 1904 1666 1428

9 14.15 2220 1998 1776 1554 1332

10 12.55 2090 1881 1672 1463 1254

12 10.20 1875 1688 1500 1313 1125

14 8.40 1700 1530 1360 1190 1020

16 7.00 1560 1404 1248 1092 936 18 6.00 1430 1287 1144 1001 858 20 5.20 1320 1188 1056 924 792

25 3.90 1085 977 868 760 651

30 3.10 910 ^ 819 728 637 546

35 2.30 795 716 636 557 477

40 1.80 715 644 572 501 429 45 1.60 650 585 520 455 390

50 1.30 590 531 472 413 354

55 1.00 525 473 420 368 315 56.7 .80 504 454 403 353 302

61

TABLE B9. CUBE ROOT OF C DIVIDED BY

c c 3

c 0 3

0 0 3

15,000 15,000 15.000 15,000 15,000 15.000

100 0.00667 0.1882 1800 .12000 .4932 3500 .23333 .6156 200 0.01333 .2371 1900 .12667 .5023 - 3600 .24000 .6214 300 .02000 .2714 2000 .13333 .5109 3700 .24667 .6272 400 .02667 .2988 2100 .14000 .5192 3800 .25333 - .6328

'500 .03333 -.3218 2200 .14667 .5274 4000 .26667 .643

600 .04000 .3420 2300 .15333 .5352 4200 .28000 .654 700 .04667 .3601 2400 .16000 .5429 4400 .29333 .664 800 .05333 .3764 2500 .16667 .5504 4600 .30667 .674 900 .06000 .3915 2600 .17333 .5576 4800 .32000 .684

1000 .06667 .4054 2700 .18000 .5646 5000 .33333 .693

1100 .07333 .4186 2800 .18667 .5715 5200 .34667 .703 1200 .08000 - .4309 2900 .19333 .5782 5400 .36000 .712 1300 .08667 .4425 3000 .20000 .5848 5600 .37333 .720 1400 .09333 .4536 3100 .20667 .5912 5800 .38667 .729 1500 .10000 .4642 3200 .21333 .5975 6000 .40000 .737

1600 .10^7 .4743 3300 .22000 .6037 6200 .41333 .745 1700 .11333 .4840 3400 .22667 .6097

TABLE B I O . MODULUS OF DEFORMATION OF SUBGRADE FOR CB TAIN VALUES OF 3i - WITH IB = 2/3 / LND S- 0. 1 INCH 2/3 /

C 3,

C P C

pel psi

0.24 . 205 .41 1035 .58 2935 .25 235 .42 U15 .59 3090 .26 265 .43 1195 .60 3250 .27 295 .44 1275 .61 3410 .28 330 .45 1365 .62 3570

.29 365 .46 1460 .63 3755

.30 405 .47 1560 .64 3940

.31 445 .48 1660 .65 4125

.32 490 .49 1765 .66 4320

.33 535 .50 1875 .67 4515

.34 590 .51 1990 .68 4720

.35 645 .52 2110 .69 4920

.36 700 .53 2235 .70 5135

.37 760 .54 2365 .71 5355

.38 825 ' .55 2500 .72 5580

.39 890 >56 2640 .73 5820

.40 960 .57 2785 .74 6070

62

fur ther with two tables and two f igures produces a chart which i s more convenient. Table B l l i s made showing ca lculat ions of c e r t a i n s e l e c t e d va lues of the depth z-multipl ied by the factor

to give the th ickness I , and the corre -

0 20 40 C-Modulut ot dtformation in hundradt (p • i )

Fig B - I 2 - Cube root of C divided by C ,

spending values of the moduli of deforma­t i o n of the subgrade C. These las t two values ( f and C ) are plotted on Figure B-13. from which Table B12 i s made for se­lected values of the thickness of bitumi­nous surface required with the correspond­ing values of the moduli of deformation of the subgrade. From th is table a scale i s provided at the top of F i g u r e B-14 , on which i s reproduced the curve from Figure B-11. The depths z are not designated on F igure B-14 , as they are needed only in the derivation of the charts . This i s one

T-TMcMMn 01 not(C,-lSjOOOp.ulRa«dcid (mcIimI n i i . P i f.r t t . 1 i I i__£_

n 19 (0 15 so C-Hadi ta of oaloninfiN of SOkrooo lo HoodroOo ( « . o l |

Fig B- I4 -Th iekmu chart tor m* 2/3, n*OT, S*OI inch.

of the f i n a l t h i c k n e s s c h a r t s used for determining th i cknes s of mat r e q u i r e d . The bame procedure i s necessary for any other values of P, ; n, or S desired. The. manner of using these charts i s explained i n the text .

C - Modotoo ot Dotonaolloii m Hoodrodo Ip o.i) Fig B-13 - Thicknen ot mot on tubgrodat tor m-Z/S, n - 0 7, S*0 I inch

63

TABLE B l l . COMPUTATION OF THICKNESS OF MAT FOR CERTAIN DEPTHS z AND

CORRESPWDING MODULUS OF D E ­FORMATION OF SUBGRADE FOR

• s 2 / 3 , nv 0 . 7 . 5- 0.1 INCH

TABLE B 1 2 . MODULUS OF DEFORMATION OF SUBGRADE FOR CERTAIN VALUES OF

THICKNESS OF MAT WITH « ' 2 /3 AND S' 0.1 INCH AND SEVERAL VALUES OF ft

Depth 2

3 r— I C

Thick­ness

of Hat

Modulus of Deferimtian ( p s i ) for Saturation Coeff ic ients n of

1.0 0.9 O.a 0.7 0.6 i n . in. psi in .

0 0.593 00 3139 0 4484 4036 •3587 3139 2690 1 .583 0.58 2982 0.5 4310 3885 3440 2990 2560 2 .571 1.14 2800 1.0 4120 3710 3270 2830 2405 3 .555 1.671 2569 1.5 3900 3485 3050 2F40 2210 4 .585 2.340 3006 2 3625 3200 2805 2410 2015

5 .522 2.61 2128 2.5 3310 2910 2540 2180 1820 6 .507 3.04 ' 1953 3 3005 2650 2300 1970 1650 7 .493 3.45 1799 3.5 2770 2430 2090 1790 1495 8 .481 3.85 1666 4 2550 2205 1905 1635 1360 9 .469 4.22 1554 4.5 2340 2015 1755 1500 1240

10 .461 4.61 1463 5 2150 1870 1620 1380 1140 12 .444 5.33 1313 5.5 2000 1750 1510 1275 1050 14 .430 6.02 1190 6 1875 1645 1405 1190 970 16 .418 6.69 10S2 6.5 ' 1760 1540 1320 1115 90S 18 .407 7.33 1001 7 1655 1450 1245 1045 845

20 .396 5.98 924 7.5 1560 1365 1175 980 790' 25 .370 9.25 760 8 1475 1285 1105 915 740. 30 .349 io.47 637 9 1305 1135 975 800 650' 35 .'334 11.69 557 10 1155 1010 860 700 570 40 .324 12.96 501 11' 1025 895 760 615 505

45 .311 14000 455 12 915 800 675 545 445 50 .302 15.10 413 13 820 715 605 485 395 55 .291 16.01 368 14 740 645 545 435 35S. 56.7 .288 16.33 353 15 670 585 490 395 3)0

20 440 385 320 270 220