EXPERIMENTAL STUDY OF BEARING CAPACITY IN LAYERED CLAYS

XPRIMNTAL STUDY F BARING CAPACITY IN LAYRD CLAYS UN TUD XPRIMNTAL D LA FRC PRTANT DS CUCHS D'ARGIL J.D. BRWN, Ph.D., NAT Postdoctorate Fellow Norwegian Geofechnical Institute, slo, Norway G.G. MYRHF, Ph.D.,D.Sc., Dean of ngineering Nova Scotio Technical College, Halifax, Canada SYNPSIS The u ltim a te b e a rin g c a p a c ity o f fou n d a tion s r e s tin g on c la y s u b s o ils has b een in v e stig a te d fo r the c a s e o f a s t iff la y e r o v e r ly in g a s o ft la y e r, and the c a s e o f a s o ft la y e r o v e r ly in g a s tiff la y e r. The stu d ies have b een b a se d on m o d e l te s ts u sin g c ir c u la r and s tr ip fo o tin g s, and using a ran ge o f la y e r th ick n e s s e s and c la y s tre n g th s. T he a n a ly se s have b een c a r r ie d out in te r m s o f-to ta l s t r e s s e s. F o r s tiff la y e r s o v e r ly in g s o ft la y e r s, fa ilu r e o c c u r s by the fo o tin g punching through the top la y e r, and w ith fu ll d e v e lo p m e n t o f the b e a rin g c a p a c ity o f the lo w e r la y e r. F o r the se co n d c a s e, fa ilu r e o c c u r s m a in ly by sq u e e in g o f the s o ft la y e r b etw e e n the fo o tin g and the s tiffe r lo w e r la y e r, w ith s o m e in te r a c tio n b etw een the la y e r s a s the stren g th r a tio a p p r o a c h e s unity. q u a tion s and ch a rts g iv in g the a p p r o p r ia te m o d ifie d b e a rin g ca p a c ity f a c t o r s a r e p r e s e n te d, d e r iv e d fr o m the e m p ir ic a l re la tio n s h ip s obta in ed in the e x p e r im e n ta l s tu d ie s. IN TR D U C TI N A fa i r ly c o m m o n p r o b le m in fou n d a tion e n g in e e rin g is that o f a s s e s s in g the u ltim a te b e a rin g c a p a c ity o f s u b s o ils c o n s is t in g o f tw o o r m o r e la y e r s o f cla y having s ig n ific a n tly d iffe r e n t stren gth and d e fo r m a tion c h a r a c t e r is t ic s. W h ere th e re a re o n ly tw o such la y e r s, e a ch o f w h ich p o s s e a s e s fa ir ly u n ifo rm p r o p e r t ie s, the p r o b le m m a y be r e s o lv e d in to a c o n s id e r a tio n o f tw o c a s e s, a r e la tiv e ly thin s tiff la y e r o v e r ly in g a th ick s o ft la y e r, and a thin soft la y e r o v e r ly in g a th ick s tiff la y e r. A n e x a m p le o f the f i r s t ty pe ca n be found w h e re a s tiff c r u s t in the u p p er p o r tio n o f a s o ft e r d e p o s it has b een fo r m e d by su ch agen ts a s d e s ic c a t io n and w e a th e r in g. A n e x a m p le o f the s e co n d ty pe m a y be found w h ere s o ft p o s t -g la c ia l c la y s o v e r lie o ld e r, s tiffe r g la c ia l till d e p o s its. The b e a rin g c a p a c ity o f h o m o g e n e o u s s o ils has b een the s u b je c t o f e x te n s iv e s tu d ie s. T h e se have y ie ld e d r e s u lts w h ich e ith e r a r e c o r r e c t f o r the stated a s s u m p tio n s, su ch as the P r a n d tl s o lu tio n fo r a p e r fe c t ly p la s tic fou n d a tion m a te r ia l, o r con ta in a p p r o x im a tio n s w h ich h ave b een found by fie ld e x p e r ie n c e o r m o d e l stu d ie s to be s u ffic ie n tly a c c u r a te to p e r m it th e ir u se w ith c o n fid e n c e. T h is situ ation d o e s not ob ta in to the sa m e d e g r e e in the c a s e o f n o n -h o m o g e n e o u s s u b s o ils. The s o lu tio n s w hich have b een a d v a n ced ( e. g. B utton, 1953 and T ch e n g, 1956) a r e, f o r the m o s t p a rt, e ith e r a d m itte d ly v e r y a p p r o x im a te, o r u n v e rifie d by te s ts o r a n a ly se s o f fu ll- s c a le fo u n d a tio n s, o r e ls e con ta in a ssu m p tio n s w h ich d o not a p p e a r to be e n tir e ly ju s tifia b le. The p u rp o s e o f th is p a p e r is to p r e s e n t the r e s u lts of a s e r ie s o f m o d e l fo o tin g te s ts c a r r ie d out on tw o - la y e r c la y fo u n d a tio n s. T he p r o b le m con ta in s m an y v a r ia b le s, and the lim ita tio n s o f the study m a y be seen fr o m the fo llo w in g p o in ts, w h ich se t fo rth the s c o p e o f the e x p e r im e n ta l w o rk. 1. A ll stu d ies w e re c a r r ie d out in te r m s o f the u ndrained sh e a r stren gth o f the c la y, using tota l s t r e s s o r 0 * " a n a ly s e s.. S tu d ies w e r e co n fin e d to s u r fa c e lo a d in g s, u sin g rig id s tr ip and c ir c u la r fo o tin g s w ith rou gh b a s e s. 3. nly one type of cla y w as u se d. T h e r e fo r e, although the stren gth o f the c la y w a s v a r ie d, the d e fo r m a tio n p r o p e r t ie s re m a in e d e s s e n t ia lly con sta n t. T h is is a c c e p ta b le in so fa r as the b eh a v io u r o f the c la y under loa d, p a r tic u la r ly at fa ilu r e, ca n be c h a r a c te r i e d by the u ndrained sh e a r stren gth a lo n e. H o w e v e r the extent to w hich the fa ilu r e lo a d is g o v e r n e d b y the a ctu a l s t r e s s -d e fo r m a t io n b e h a v io u r of the s o il m a y im p o s e a lim ita tio n on the a p p lic a b ility o f the r e s u lts. P R P R T I S F TH C L A Y T he cla y u sed in the fo o tin g te s ts w as an in o rg a n ic c la y o f m ed iu m p la s t ic ity, con ta in in g about 35 p e r ce n t m in u s m ic r o n s i e, p r e d o m in a n tly illit e. F a ilu r e s tra in s o f th is m a te r ia l in the re m o u ld e d state w e r e too high to p e r m it a s a tis fa c to r y eva lu a tion o f the te s ts. A c c o r d in g ly, sla k ed lim e w as added to the c la y in the p r o p o r t io n o f p e r cen t o f the d r y w eigh t o f the s o il, in o r d e r to m ake it m o r e b r ittle. It is g e n e r a lly a p p r e c ia te d that the u ndrained stren gth a s m e a s u r e d in tr ia x ia l te s ts d o e s not n e c e s s a r ily p r e d ic t the u n d rain ed stren g th w hich m a y be m o b ili e d in fie ld sta b ility p r o b le m s. S o m e o f the r e a s o n s fo r d is a g r e e m e n t a re in situ anis o t r o p y and ro ta tio n o f p r in c ip a l p la n es d u rin g s h e a r, plane stra in e ffe c t s, r e la tio n b etw een peak and p o s t-p e a k stre n g th s (th e p r o g r e s s i v e fa ilu r e 45

problem ), time dependency of undrained strength, and laboratory sample sie and degree of d is turbance. These factors also affect m odel tests, although to a lesser degree, and required 6pecial tests and careful evaluation in the analysis of the footing tests reported herein. In Fig. 1 and Table 1 are sum maried some of the strength behaviour p roperties of the test clay. All com pression test specim ens were trimmed from blocks of clay com pacted in the same way a6 the footing test clays. The effect of the application of confining pressures to the undrained strength may be noted. Also, unconfined ( U) samples failed by vertical splitting or along a single shear plane; undrained triaxial (UU)test samples failed on one, or perhaps two, well defined shear planes. Plane strain tests showed no significant difference in undrained strength or failure strain. Tim e effects w ere negligible within the range of testing times which were used. Sample sie effects and d isturbance due to trimm ing of specim ens were judged to be minimal. BRWN and MYRHF Sample Inclination degrees Table 1. C u C u ( vert) ef % _!í_ * ( vert) 0 1.0 1. 60 1.0 45 1. 08 0. 94 0. 59 60 1. 10 0. 50 0. 31 90 1. 0 0. 75 0. 47 Results of Undrained Triaxial Anisotropy Tests - Average Values this way a degree of saturation of about 95 per cent was obtained. The clay was placed in lifts having a com pacted thickness of 0. 5 to 0. 75 inches ( ca. 1 to cm ), with the interface between the lifts being made deliberately uneven, to reduce bedding effects. The interface between the upper and lower layers was levelled, then roughened with a series of grooves so that the clay layers "in terlock ed and slipping at the boundary was prevented. The interface was sealed as well as possible against m oisture migration by a coating of liquid rubber latex. The clay was cured for 7 days prior to testing. APPARATUS AND TST PRCDUR The raw clay was blended with the required amounts of water and hydrated lime in a M uller m ixer, which em ploys a pair of heavy rolling wheels to knead the clay, and was found to be satisfactorily thorough in mixing. The clay was then packed into the footing test boxes, described below, by hand, using a kneading action, and in The test box for strip footing tests was about 7 inches long by 6 inches wide by 1 inches deep, and is illustrated in Fig.. It was constructed with 0. 5 inch thick (1.31 cm) plate glass sides, which correspond to the intermediate principal planes in a strip footing test. The plate glass was chosen for its rigidity and for minimum friction when greased. Test boxes for the circular tests were square with dim ensions approximately 1 x 1 x 10 inches. Footings were made of mild steel, 3 inches wide by - -------- *! o o r> } n C5 0^Í) o d 3o UU TSTS 3 U (0r 0 3)f C u A X IA L S T R A IN e*a> Fig. 1. Undrained shear strength behaviour of the lim e stabilied test clay. 46

BARING CAPACITY p r e s s u r e, p r o g r e s s iv e fa ilu r e, e tc. F ig.. T y p ic a l a rra n g e m e n t fo r s tr ip fo o tin g te s t s. 6 in ch e s lon g ( 7. 6 x 15. c m ) fo r the s trip, and 3 in ch e s d ia m e te r ( 7. 6 c m ) fo r the c ir c u la r fo o t in g s. The b a s e s w e r e m ade rou gh by glu ein g a la y e r o f m e d iu m q u a rt sand on th em. F o r the te s ts, the fo o tin g s w e r e th rea d ed onto a loa d in g ra m w hich o p e r a te d th rou gh a lu b r ica te d b a ll b e a rin g g u id e, to e n su re that they did not ro ta te, and the d ir e c tio n o f lo a d re m a in e d v e r t ic a l. L oa d s w e r e g e n e r a lly m e a s u r e d through a p rov in g rin g ; the am ou nt o f guide fr ic t io n w as ch e ck e d, h o w e v e r, u sin g a lo a d c e ll ju st a b ove the footin g in so m e o f the te s ts, and it w as found to be n e g li - g ib le. T e s ts w e re run at a ra te o f 0. 15 in ch e s ( 0. 4 cm ) p en e tratio n p e r m in u te; th is r e la tiv e ly fa s t sp eed w as c h o s e n to m in im i e m o is t u r e m ig r a tio n du rin g loadin g. The m o d e o f fa ilu r e and s lip pla n es w e re o b s e r v e d both d u rin g the te s t and a fte r w a r d s, w hen the c la y w as b ein g r e m o v e d fr o m the box. F TIN G S N H M GNUS C L A Y A n um ber o f s tr ip and c ir c u la r fo o tin g te s ts w e re c a r r ie d out on h o m o g e n e o u s b e d s o f cla y. T h e ir ch ie f p u rp o se w as to d e te rm in e the a v e r a g e und rain ed s h e a r stren g th, C, m o b ili e d in the cla y, so that the in t e r -r e la tio n s h ip o f the fa c to r s m en tion ed e a r lie r cou ld be a s s e s s e d. It w as a ssu m e d that the c la s s ic a l P ran d tl s o lu tio n fo r the u ltim ate b e a rin g ca p a c ity, q^, o f s tr ip fo o tin g s on a r ig id -p la s t ic m a te r ia l, w hich g iv e s a b ea rin g ca p a city fa c t o r, N c, o f 5. 14 in the w e ll known e x p r e s s io n qf = C N c (1 ) should be ob ta in ed in th ese te s t s. The c o r r e s p o n d in g value o f N c fo r rough c ir c u la r fo o tin g s w as taken as 6. 05, a fte r the a n a ly sis o f a s o n and Shield ( 1 9 6 0 ). The ca lcu la te d c o r r e c t io n fa c t o r s to be a p p lied to the u n con fin ed sh e a r stren gth w e r e then found to be 1. 10 and 1. 1 fo r the s tr ip and c ir c u la r fo o tin g s, r e s p e c t iv e ly. T h e se v a lu e s w e r e c o n sisten t w ith e s tim a te s m ade o f the sum o f the in d iv id u a l c o r r e c t io n s fo r a n is o tro p y, con fin in g In a d d ition, the g e n e ra l lo a d -s e ttle m e n t b eh a v iou r and fa ilu r e o n e s o f the h o m o g e n e o u s foun dation s w e re o b s e r v e d. T y p ic a l lo a d -s e ttle m e n t c u r v e s a re show n in F ig. 3 ( a ). F o r s tr ip fo o tin g s the in d i ca ted fa ilu r e o n e s c o n s is te d o f a b a se w edge with s id e s in clin e d at an a v e ra g e angle o f 48 d e g r e e s to the h o r i o n ta l, o n e s o f ra d ia l sh e a r exten d in g to a depth o f 0.8 5 B, w h ere B w as the fo o tin g w idth, at a d is ta n ce o f 0.8 B fr o m the v e r t ic a l plane o f s y m m e tr y, and fin a lly, o n e s o f h o r i o n ta l sp littin g in the p a s s iv e R ankine o n e s w hich exten d ed to the fr e e s u r fa c e s. T h is ru p tu re fig u r e d o e s not a g r e e w ith that found fo r a p e r fe c t ly p la s tic m a te r ia l 0.. T h is d is a g r e e m e n t is to be e x p e c te d, sin c e the cla y, although c o n s id e r e d in th e o ry to be a p e r fe c t ly p la s tic m a te r ia l w ith 0s, in fa c t p o s s e s s e s in tern a l fr ic tio n, w hich g o v e r n s the shape o f the rupture fig u re ( Skem pton 1948). A t the sa m e tim e, h o w e v e r, n eith e r d o e s the o b s e r v e d ru ptu re s u r fa c e a g r e e w ith that p ostu la ted f o r a w e ig h tle s s c o h e s iv e -fr ic t io n a l s o il, w hich is g o v e r n e d by the H v o r s le v e ffe c t iv e angle o f in tern a l f r ic t io n, f o r this cla y betw een 0 and 5 d e g r e e s. The shape o f the o b s e r v e d s u r fa c e s u g g e sts a m o b ili e d fr ic t io n angle o f about 10 d e g r e e s, w hich is in g e n e ra l a g re e m e n t w ith the a rg u m en ts put fo rth by B je r r u m and K en n ey ( 1967) that in b rittle s o ils fa ilu r e is due to a s tru ctu ra l b rea k d ow n w hich o c c u r s b e fo r e the fr ic tio n is fu lly m o b ili e d. The one o f h o ri o n ta l sp littin g, a d ja ce n t to the fr e e s u r fa c e s on e ith e r sid e o f the fo o tin g, is in turn in a g re e m e n t w ith the o b s e r v e d sp littin g type o f fa ilu r e o f the h o r i o n ta lly tr im m e d u n con fin ed test s p e c im e n s. 5 10 $ 16 Û 0 ll. 5 F ig. 3 B A R IN G P R S S U R - p si 0 30 40 S 60 70 80 90 B A R IN G P R S S U R - p s i 0 30 40 50 60 70 I I HMGNUS 1 (CIRCL). T y p ic a l lo a d -s e ttle m e n t c u r v e s of s tr ip ( B) and c ir c u la r ( R) fo o tin g s, fo r d iffe r e n t top la y e r th ic k n e s s e s, H. 47

BRWN and MYRHF F r o m th ese o b s e r v a tio n s it m a y be seen that the p a ttern o f fa ilu r e beneath a fo o tin g is a fu n ction o f fr o m the h o m o g e n e o u s te s t r e s u lts, w as a p p lied to the u n con fin ed sh e a r stren gth o f e a ch la y e r. the p h y s ic a l m od e o f ru ptu re o f the c la y. T h is A depth fa c to r w as a ls o u sed, to a llo w fo r the m od e o f ru p tu re, in b rittle c la y s at le a s t, is s tro n g e ffe c t o f p e n e tra tio n, s, on the b e a rin g c a p a c ity. ly dep endent on the s tru ctu re o f the c la y, the fa ilu r e m e c h a n ism o f w hich is not a d eq u ately T h is fa c to r v a r ie d fr o m 1. 0 f o r p u re punching, as d is c u s s e d b e lo w, to ( 1 + 0. 4 s) fo r fu lly d e v e lo p e d d efin ed by con v en tion a l M o h r -C o u lo m b co n c e p ts fa ilu r e o n e s in the u p p er la y e r. The b e a rin g o f co h e sio n and fr ic tio n. c a p a c ity fa c to r, N, d efin ed w ith r e s p e c t to the u n con fin ed sh e a r stren gth o f the top la y e r, C t, is thus g iv e n by F TIN G S N S T IF F C L A Y V R L Y IN G S F T C L A Y qf ' j C t Nm i 1 + kb> ( V T h is co n fig u ra tio n c o n s is te d o f tw o c la y la y e r s, each o f con sta n t stren g th. The r a tio o f top la y e r th ick n e ss to width o r d ia m e te r o f fo o tin g, H /B o r H / R. v a rie d fr o m 0. 5 to 3. 0. and the stren gth o f the top la y e r w as up to 4 tim e s the stren gth o f the bottom la y e r. T h e se lim its w e re taken to e n c o m p a s s the p r o b a b le ran ge o f v a lu e s e n co u n te re d in p r a c t ic e. T y p ica l lo a d -s e ttle m e n t c u r v e s fo r s tr ip and c ir c u la r fo o tin g s a re show n in F ig. 3 ( a ). The point o f fa ilu r e s is c le a r ly in d ica te d ; fo r the w hole te st s e r ie s, fa ilu r e o c c u r r e d at an a v e ra g e p en e tratio n o f 16 p e r cent o f the fo o tin g w idth in the s tr ip fo o tin g te s ts and 7 p e r ce n t in the c ir c u la r footin g te s ts. The b e h a v io u r o f both ty p es o f fo o tin g s w as q u a lita tiv e ly s im ila r, and h e n ce both w e r e a n a ly ed in the sa m e w ay. A v a r ia b le c o r r e c t io n fa c t o r, j, d e r iv e d w h ere is the b e a rin g p r e s s u r e at fa ilu r e, and both j and k a r e v a r ia b le. If the c la y w e re an id e a l r ig id p la s tic m a t e r ia l, j Cf w ould be con sta n t and s w ould be e r o, g iv in g the fo llo w in g equ ation s, an a logou s to equation ( 1) s tr ip q, = C. N (3 ) r ^f t m s v ' c ir c u la r q,. C N (4 ) ^f t m e ' ' V a lu e s o f Nm fo r both s tr ip and c ir c u la r footin g te s ts a re show n in F ig. 4. The n u m b e rs a c co m p a n y ing ea ch data p oin t a r e the th ic k n e s s-w id th r a tio s at fa ilu r e. It m a y be noted that d iffe r e n t v a lu e s of j w e r e u sed in p r e lim in a r y a n a ly s e s, and although th ese ch anged the ca lc u la te d v a lu e s o f Nm and C b /C t, they did n ot ch ange the g e n e r a l p a ttern o f the r e s u lts to any a p p r e c ia b le d e g r e e ; thus the a:»- u 1.91 1.89 u S o a LiJ C (o ) S T R IP F TIN G S (b )C IR C U LA R F T IN G S 0. 0.4 0.6 0,8 1.0 LW R LA Y R SH A R S T R N G T H _ C b / U P P R LA Y R SH A R S T R N G T H / c t 0. 0.4 0.6 0.8 1.0 LW R LA YR SH A R STRN G TH _ C b / U P P R LA YR SH A R S TR N G TH / c t F ig. 4. x p e rim e n ta l v a lu e s o f m o d ifie d b e a rin g c a p a c ity fa c t o r s fo r s tiff c la y o v e r ly in g s o ft c la y. 48

BARING CAPACITY cr h- u o Z cc co Q U. o U P P R LA Y R S H A R ST R N G T H _ Ct U P P R LA Y R S H A R S T R N G T H _ C t L W R LAYR S H A R ST R N G T H Vc. F ig. 5. x p e rim e n ta l valu es o f m o d ifie d b e a rin g ca p a c ity fa c t o r s fo r s o ft c la y o v e r ly in g s t iff cla y. equations g iv en b e lo w a re not s e n s itiv e to m o d e r a te ch anges in the c o r r e c t io n fa c to r, w h ich w as a d m ittedly not r ig o u r o u s ly evalu a ted. F o r both sets of te s ts, the s im p le s t c u r v e s w hich m ay be fitted to the data a re a s e r ie s o f stra ig h t lin es, w hich y ield the follo w in g equations : Strip fo o tin g s, Nm g = 1.5 ^ + 5. 14^ i 5.14 ( 5) C ir c u la r fo o tin g s, N = 3. 0 ^ +6.05 * 6.05 (6) m c K Uj The use of th ese equations w ill lead to an o v e r estim a te o f about 10 p e r cen t in v a lu e s o f Nm in the ra n ge C l/ C j * 0.7 ; the m o r e c o r r e c t va lu es a re in d ica te d by the n o n -lin e a r it y o f the c u r v e s in th ese r e g io n s in F ig. 6. If th ese eq u a tion s a re in te rp re te d in te r m s o f p h y s ic a l b e h a v io u r, it is seen that the f ir s t te r m is r e p r e s e n ta tiv e o f so m e type o f punching sh ea r th rou gh the s tiff top la y e r, with the s e co n d te r m su g g e stin g fu ll m o b ili a tio n of the b e a rin g c a p a c ity o f the lo w e r la y e r. T h is in tre p re ta tio n is su p p o rte d by o b s e r v a tio n s m ade of the fa ilu r e o n e s d e v e lo p e d in the te s te. F o r sim p le sh e a r punching, the f ir s t te r m s in equation s ( 5) and ( 6) shou ld be H /B and 4 H / R, r e s p e c t iv e ly ; th e r e fo r e the fu ll valu e o f punching sh e a r d o e s not s e e m to be d e v e lo p e d. F TIN G S N S F T C L A Y V R L Y IN G S T IF F C L A Y T he te s t c o n fig u ra tio n s w e re s im ila r to th ose u sed in the p r e c e d in g s e c tio n. The r a tio o f the stren g th s o f the la y e r s v a r ie d a ll the w ay fr o m unity, the h o m o g e n e o u s c a s e, to in fin ity, w h e re the lo w e r la y e r is an unyielding, rough and rig id b a se. T y p ic a l lo a d -s e ttle m e n t c u r v e s fo r the s tr ip and c ir c u la r fo o tin g s a re show n in F ig. 3 (b ). A g a in, the poin t o f fa ilu r e is c le a r ly in d ica te d ; a v e ra g e fa ilu r e p en e tra tio n s fo r the co m p le te s e r ie s o f s tr ip and c ir c u la r fo o tin g te sts w e re 6 and 3 p e r cen t o f the fo o tin g w idth, r e s p e c t iv e ly. In a lm o s t a ll c a s e s, fa ilu r e a p p e a re d to be co n fin e d to the s o ft u p p er la y e r on ly, and the o b s e r v e d ru pture o n e s in d ica ted sq u e e in g o f the s o ft c la y la te r a lly, u nder the fo o t in g, and a sp littin g type o f fa ilu r e o f the c la y b e lo w the fr e e s u r fa c e s on e ith e r sid e o f the fo o tin g. A n u m ber o f te s ts on thin c y lin d e r s and b lo c k s w e r e 49

BRWN and MYRHF oc b- u 0 Q. U 1 tr a Q U. Q LWR LA Y R SHAR STRN G TH U P P R LA Y R SHAR STRN G TH a h u LW R LA Y R SHAR S TRN G TH U P P R LA YR SHAR STRN G TH Fig. 6, Relation between modified bearing capacity factors and shear strength ratio, C, /C, for strip and circular footings. 1 also carried out to assist in the evaluation of the footing tests. The analysis of the results depended again on an assessm ent of the shear strength of the clay. The effects of anisotropy, confining pressure and progressive failure were variable, depending on the configuration of the problem, and a p recise evaluation of individual cases was not possible. Considéra^ tion of all factors led to an average correction factor of the same magnitude as that found in the hom o geneous footing tests. The e rror in the estimated 50

BARING strength a s s o c ia te d w ith this p r o c e d u r e w as e s t i m ated to be le s s than - 5 p er cen t. The m o d ifie d b e a rin g c a p a c ity fa c to r N w as found fro m equation ( ) fo r both ty p es o f fo o tin g, and the re su lts a re show n in F ig. 5. The dash ed lin es re p re se n t the g ra p h ica l b e st fit. The s o lid lin es have been d e r iv e d by u sing an in te r a c tio n fo rm u la of the Rankine type, w hich is of the fo rm N = N 1 N N l + N (?) CAPACITY under c ir c u la r fo o tin g s. T hen it can be show n that the b e a rin g c a p a city fa c to r f o r re cta n g u la r fo o tin g s, N, is g iv en by Nm r = Nm c B /L + N m s ( 1 - B /L ) N_ and N_ a re obtain ed fro m F ie. 6 fo r the m e m s a p p ro p ria te v a lu e s o f C b /C t, and H /B. F o r h o m o g en eou s fou n d a tion s, equation ( 1) r e d u c e s to that given by Skem pton ( 1951), I = 5 ( 1 + 0. B /L ) In this equation and a re the equation s o f two separa te ph en om en a, w hich in te ra ct in such a w ay that the equation w hich r e la te s both p h enom ena is given by N. T h is type o f e m p ir ic a l equation has found s u c c e s s fu l a p p lica tio n in the in te ra ctio n betw een a x ia l c o m p r e s s io n and b u ck lin g in s tr u c tu r al c o lu m n s. In the p r e s e n t a p p lica tio n, N j, r e p r e se n ts the equation fo r Nm ob ta in ed fr o m tests w here the lo w e r la y e r is a rou gh, rig id b a se, (e q u a tio n s ( 8 ) and ( 9), b e lo w ), and N^ r e p r e s e n ts the equation fo r Nm w h e re a P ran d tl ru p tu re fa ilu re in v o lv e s both the upper and the lo w e r la y e r. The m a x im u m v a r ia tio n b etw een Nm v a lu e s g iv en by the best fit and the Rankine fo rm u la cu rv e s is about 10 p e r cen t. The r e s u lts o f the te s ts h avin g a rou gh, rig id b ase fo r the lo w e r la y e r gave the fo llo w in g v a lu e s f o r N : Strip F o o tin g s, C ir c u la r F o o t in g s, R /H ^ 1.5 N = 4.1 4 + 1.1 B /H m s ' (8 ) Nm c = 5.05 + 0.6 6 ( R /H ) (9 ) T h ese eq u a tion s y ie ld v a lu e s o f N c o n s id e r a b ly h igher than the c o r r e s p o n d in g th e o r e tic a l r e la t io n ships fo r a p e r fe c t ly p la s tic m a te r ia l (M e y e r h o f and C haplin, 1 9 5 3 ), w hich a re N = 4.1 4 + 0.5 B /H ( 10) m s ' ' ' Nm (, = 5.0 5 + 0.33 ( R /H ) ( 11) The su b stitu tion o f e p ic y c lo id a l s lip s u r fa c e s fo r the cy c lo id a l s u r fa c e s u sed in the t h e o r e t ic a l d e r iv a tio n in c r e a s e s the s e co n d te r m in eq u a tion s (1 0 ) and (1 1 ) by about 30 p e r cen t, w hich d o e s not p rod u ce a g r e e m ent w ith the e x p e r im e n ta l e q u a tion s. It m a y th e r e fo re be co n clu d e d that in the in te n se ly s tr e s s e d upper la y e r beneath the fo o tin g s, the undrained shear stren gth is not an a c c u r a te m e a s u re o f the sh earin g r e s is ta n c e. H en ce, it is c o n s id e r e d that, for p u r p o s e s o f d e s ig n, the th e o r e tic a l equation s ( 10) and (1 1 ) w hich a re in fa c t lo w e r lim its, should be used in the in te r a c tio n fo r m u la, equation ( 7 ). The solution of th ese equations g iv es the va lu es fo r N and N in F ig. 6. mc m s 6 R C T A N G U L A R F TIN G S The s im ila r itie s o f the m o d e s o f fa ilu r e o b s e r v e d in strip and c ir c u la r fo o tin g te sts a llo w s the use o f the re su lts to d e v e lo p equation s fo r re cta n g u la r fo o tin g s. F o llo w in g M e y e r h o f, ( 1951), it is a ssu m e d that below the c e n tr a l p a rt o f the re cta n g le the b ea rin g s t r e s s e s a r e the sa m e a s b e lo w a s tr ip, and that at the ends the b e a rin g s t r e s s e s a r e e s s e n tia lly th ose CNCLUSINS The re s u lts o f the in v e stig a tio n a re s u m m a r i e d in the ch a rts g iv en in F ig. 6, w hich m a y be u sed in evalu a tin g the b ea rin g c a p a city o f la y e r e d cla y fou n d a tion s. The r e s u lts a re e s s e n tia lly e x p e r im e n ta l, and th e r e fo r e a re ra th er s tr o n g ly a ffe c te d by the c h a r a c t e r is t ic s o f the test cla y. H o w e v e r, it is b e lie v e d that a co n s e r v a tiv e in te r p r e ta tio n has been put upon the fin d in g s, w hich shou ld p e r m it th e ir use in the range o i m o a e r a te iy b r ic u e, s lig h tly s e n s itiv e c la y s. A C K N W L D G M N T S The r e s e a r c h d e s c r ib e d h e r e in w as c a r r ie d out w ith the aid o f a N ational R e s e a r c h C ou n cil o f Canada Studentship and r e s e a r c h gran t. R F R N C S B je r r u m, L. and T. C. K enney, 1967 " f f e c t of stru ctu re on the sh e a r b e h a v io u r o f n o r m a lly co n so lid a te d quick c la y s '. P r o c. G e o te c h n ica l C on f. s lo, : 19. B utton, S. J., 1953 The b e a rin g ca p a city o f fo o tin g s on a tw o l a y e r c o h e s iv e s u b s o il. P r o c. 3rd Int. C o n f. S o il M ech. 1 : 356 a son, G. and R. T. S h ield, I960 " The p la s tic in den tation o f a s e m i-in fin ite s o lid hy a p e r fe c t ly rough c ir c u la r punch. Z A M P ( B a s e l) 11 : 1 : 33 M e y e r h o f, G. G., 1951 The u ltim ate b e a rin g c a p a c ity o f fou n d a tion s. G eotech n iq u e, : 301 M e y e rh o f, G. G. and T. K. C hap lin, 1953 " The c o m p r e s s io n and b ea rin g c a p a c ity of co h e s iv e la y e r s. B r it. J. A p p lied P h y s ic s, 4 : 0 Skem pton, A. W., 1948 The 0» 0 a n a ly sis o f s ta b ility and its th e o r e tic a l b a s is. P r o c. nd Int. C on f. S o il M e ch,, 1 : 7 Skem pton, A. W., 1951 The b e a rin g ca p a city o f c la y s. " P r o c. B u ildin g R e s e a r c h C o n g r e s s, L on don T ch en g, Y., 1956 P o u v o ir p orta n t d* un s o lid e c o m p o s é d e deux c o u ch e s p la stiq u e s d iffé r e n t e s. " T h e s is. U n iv e rsity o f P a r is. 51