Basics of shallow foundation- Bearing Capacity.pptx

bearing capacity;
Shallow foundation;
Special Cases of Shallow Foundation;
Uplift capacity of shallow foundation;
Bearing Capacity of layered soil;
Footing on layered soil;
Eccentrically loaded foundation; bearing capacity of shallow foundation

1. Bearing Capacity of Shallow Foundations G eo t echn ica l Eng inee r i ng Prof. Samirsinh P Parmar Department of Civil Engineering, Faculty of Technology Dharmsinh Desai University, Nadiad-387001 E-mail: [email protected]

2. B ea r i n g C apac i ty o f Foo t i n g o n La y e r e d So i l H omo g e n e ous B c ’ , φ ’ , γ D D f D  B t a n(45   ' ) ~ B 2 2 A pp ro x i ma t e m e th o d ( f o r l a y e r ed s oil ) : Us e a v e r a g e v a l ue of D e p th o f r u p tu r e z o n e , D C a s e 2 L a y er 1 is s t r o n g er th an l a y er 2 B D D f D i s t r i bu t e the s t r esse s t o l a y e r 2 b y 2 : 1 m e th o d and c h ec k the b e a r i ng c apa c i ty a t th i s l ev e l. F i nd a l s o B C u s i ng pa r a m e t e r s o f l a y e r 1 . Ch oos e the m i n i m um v a l ue f o r d es i g n O r a d o p t sp ecial B C th e or y c 2 , φ 2 , γ 2 c 1 , φ 1 , γ 1 C a s e 1 L a y er 1 is w ea k er th an l a y er 2 C o ns e r v a t i v e a pp r o ac h: D es ig n u s i ng pa r a m e t e r s o f l a y e r 1 B D D f c 2 , φ 2 , γ 2 c 1 , φ 1 , γ 1 H  H  H  ..  c 1 H 1  c 2 H 2  c 3 H 3  ... 1 2 3 c av H 1  H 2  H 3  ..  t a n  1 H 1  t a n  2 H 2  t a n  3 H 3  ... t a n  av s h e ar s t r e n g th pa r a m e t e r s

3. B ea r i n g C apac i ty o f Foo t i n g o n La y e r e d So i l L a y er 1 is s t r on g e r than l a y er 2 Q D f B D c 2 , φ 2 , γ 2 c 1 , φ 1 , γ 1 De p t h H is r el a t i v ely la r g e F u ll f ail u r e sur f ace d ev el o p s in t o p sur f ace De p t h H is r el a t i v ely s m all P un c h i n g sh ear f ail u r e in t o p sur f ace ( l a y er 1) Ge n e r al sh ear f ail u r e in b o t t o m l a y er ( l a y er 2)

4. B ea r i n g C apac i ty o f Foo t i n g o n La y e r e d So i l   H H B K t a n  2 D f    L B     H 1  B B 2 c ' H L F o r r ec t a ngu lar f oo t i ng : q u  q b  s a 1 2 2 1 1  1                             <q t De p t h H is r el a t i v ely sm all Pun c h i ng s h e ar f a il u r e i n t o p s u r f a c e ( l a y e r 1 ) q u of l a y e r ed s oil = q u (c o ns i d e r i n g g e n e r al s h ear f ail u r e in b o t t o m l a y e r , l a y er 2) +q u (c o ns i d e r i n g pun c h in g sh ear f ail u r e in t o p sur f ace, l a y er 1) F o r s tr ip f oo t i n g , th e t e rm B / L =  c 2 N c ( 2 ) s c ( 2 )   1 ( D f  H ) N q ( 2 ) s q ( 2 )  0. 5  2 B N  ( 2 ) s  ( 2 ) q b  c 1 N c ( 1 ) s c ( 1 )   1 D f N q ( 1 ) s q ( 1 )  0. 5  1 B N  ( 1 ) s  ( 1 ) q t w he r e, c ’ a i s t h e adh e s io n K s i s t h e pun c h i n g sh ear c o e f f i c i ent q t i s t h e b ea r i n g c ap a c i t y o f t h e t o p s oi l l ay er q b i s t h e b ea r i n g c ap a c i t y o f t h e b o t t o m s oi l l ay er H i s t he he i g ht o f t o p l ay er ϕ 1 i s t h e an g l e o f i n t e r nal f r i c t io n o f t o p s oi l ϕ 2 i s t h e an g l e o f i n t e r nal f r i c t io n o f b o t t o m s oi l a q u ( c o n s i d er i ng g e n e r al s h e ar f a il u r e i n b o t t om l a y e r , l a y e r 2 ) q u ( c o n s i d er i ng g e n e r al s h e ar f a il u r e i n t o p l a y e r , l a y e r 1 ) F o r c o h e s io n le s s s oil, c c an b e a ssum ed as

5. B ea r i n g C apac i ty o f Foo t i n g o n La y e r e d So i l q 1 and q 2 a r e the u l t i mat e b e a r i ng c apa c i t i e s o f a s t r i p f oo t i ng o f w i dth B und e r v er t i c al l o ad o n h omo g e n eo us b e ds o f upp e r and l ow e r so il s , r es p ec t i v e l y , q 1  c 1 N c ( 1 )  0. 5  1 B N  ( 1 ) q 2  c 2 N c ( 2 )  0. 5  2 B N  ( 2 ) P un c h i n g sh e a r c o e f f i c i en t , K s = f ( q 2 /q 1 , ϕ 1 ) Adh es io n , c ’ a = f ( q 2 / q 1 , c 1 ) De p t h H is r el a t i v ely sm all c ’ 1 = 0, ϕ ’ 2 = c ’ 1 = 0, c ’ 2 = ϕ ’ 1 = 0, ϕ ’ 2 = Sp e c i a l c a s es T o p l a y e r i s s t r o ng s and and b o t t o m l a y e r i s s a tu r at e d so ft c l a y T o p l a y e r i s s t r o ng s and and b o t t o m l a y e r i s w e a k e r s and T o p l a y e r i s s t r o ng s a tu r at e d c l a y and b o t t o m l a y e r i s w e a k e r s a tu r at e d c l a y

6. B ea r i n g C apac i ty o f Foo t i n g o n La y e r e d So i l IS 6403 r e co mm e nd a t ion s B e a rin g c a p a c ity o f s t r a tif i e d co he si v e soil (two l a y e r e d s y st e m ) In t he c a se o f t w o l ay e r e d c o hes i v e s oi l s y s t em w h i c h d o n ot e x hib it m a r k e d a n iso t r o p h y , t h e u l t i m a t e n e t b ea r i n g c ap a c i t y o f a s tr i p f oo t i n g c an b e c a l c u l a t e d as q d = c 1 N c , w he r e N c m a y b e o b t a i n e d f r o m c h a r t sh o w n b e l ow N c = 5.14 F o r d e sicc at e d co h e si v e soil

7. E ccen t r ica l l y Loade d Founda t i ons e B Q M Q B = E cce n tr i c ally lo a d ed f o und a t io n F ail u r e sur f ace BL Z q  Q  M BL B 2 L Q 6 M q   ( 1 ) BL B  Q  6 e max q q  Q  6 Qe BL B 2 L q  Q ( 1  6 e ) min BL B Ge n e r al c a s e C o n t act p r e ssu r e e=0 e<B/6 e=B/6 e>B/6 W h e n a f o und at io n i s sub je c t e d t o an e cc en tr i c v e rt i c al lo a d , it tilt s t o w a r ds t h e s id e o f t h e e c c e n t r icit y an d t h e c o n t a ct p r e ssu re in c re as es o n t h e s id e o f tilt an d d e c re as es o n t h e oppo s i t e s id e . W h e n t h e v e rt i c al lo ad Q u lt r ea c h e s t h e u l t i m a t e lo ad , t h e r e w il l b e a f a il u r e o f t h e supp o rt i n g s oi l o n t h e s i d e o f e cc en tr i c i t y . A s a c ons e qu e n c e , s e t tl e m e n t o f t h e f oo ti n g w ill b e asso ci a t e d w it h tilti n g o f t h e bas e t o w a r d s t h e s id e o f e c c e n t r icit y . W hen e>B / 6, q min w il l b e n e g at i v e, w h i c h me ans t e ns io n w il l d ev e lo p. S i n c e s oi l c ann o t t a k e t e ns io n , t h e r e w il l b e a s e p a r at io n b e t w ee n f o und at io n and s oi l und e r l y i n g i t . He n c e, m a x i m u m e c c e n t r icit y no r m a ll y a ll o we d i s B/ 6 w h ere B i s t h e w i d t h o f t h e f oun da ti on . Ulti m a t e lo a d t h a t t h e f o und a tion c a n s u s t ai n c a n b e o b t a i ne d f r o m ultim a t e be a ring c a p a c ity di v id e d b y ef f e c ti v e a r e a . The ef f e c ti v e a r ea A′ i s a m i n i mum c o n t a c t a r ea of t he f o und at io n su c h t h a t i t s c en t r oi d c oi n c i d e s w i t h t h a t o f t h e lo ad.

8. E ccen t r ica l l y Loade d Founda t i ons Hig h t e r a n d A nd r e r s ( 1985) [ f or find i ng e f f e ct i v e a r e a ] F o r f i nd i n g e f f e c t i v e a r e a i n t h e c as e o f t w o w a y e cc en tr i c i t y [ r e c t an g u l ar f oo t i n g], f o u r p o ss i b l e c as e s m a y a r i s e C as e 1 [e L /L ≥ 1/6 and e B /B ≥ 1/6] • C as e 2 [ e L /L < 0. 5 and < e B / B < 1/ 6] • C as e3 [ e L /L < 1/ 6 and < e B / B < 0. 5] C as e 4 [e L /L <1/ 6 and e B / B < 1/ 6] M e y e rh o f a n d IS 6403 [ E f f e c ti v e a r e a m et h o d ] Ge n e r a ll y app li c ab l e f o r o n e w a y and t w o w a y e cc en tr i c i t y w h e n e < B / 6 and e < L / 6 D e t e r m i n e e f f e c t i v e d i me ns io ns o f f o und at io n. B’ = B - 2 e x ; L ’ = L - 2 e y E s t i ma t e e f f e c t i v e a r ea A ’ = L ’ x B’ U s e e f f e c t i v e d i me ns io ns i n shap e f a c t o r and b ea r i n g c ap a c i t y e qu at io n. Bu t us e B an d L f o r c o m putin g d e pt h f a c t o r ( do n o t r e p l a c e B w i t h B ’) D e t e r m i n e u l t i m a t e b ea r i n g c ap a c i t y us i n g e f f e c t i v e d i me ns io n ( B ’ ) T o t al u l t i m a t e lo ad t h a t t h e f o und at io n c an su s t a i n i s Q u lt = q ’ u ( A ’) Filled u p p o rt io n i nd i ca t es th e e f f ec t i v e a r ea du e t o ecce n tr ic lo a d , A ’ e x 2 e x B’ B L 1 - w a y ecc. E cce n tr ic lo a d i n g B’ B 2 - w a y ecc. e y e x L’ L

9. C a se 1 [e L / L ≥ 1 / 6 and e B / B ≥ 1 / 6] E ccen t r ica l l y Loade d Founda t i ons B    B  B  1.5    B 3 e 1 L    L  L  1.5    L 3 e 1 1 1 2 A '  1 B L E f f ec t i v e w i dt h B’ is e qu al t o th e sm aller of B o r L C a se 2 [e L / L < . 5 and e B / B < 1 / 6] A '  1 ( L  L ) B 2 1 2 E f f ec t i v e le n g t h L ’ is th e la r g er of th e L 1 a n d L 2 E f f ec t i v e w i dt h B’ is A ’/ L ’ F r o m e L / L a n d e B / B f i n d L 1 / L a n d L 2 /L H i gh t e r a n d A nd r e r s ( 1985 )

10. C a se 3 [ e L / L < 1 / 6 and < e B / B < . 5] E ccen t r ica l l y Loade d Founda t i ons A '  1 ( B  B ) L 2 1 2 F r om e L / L a n d e B / B f in d t he magn it ud e o f B 1 a n d B 2 f r o m c h a r t H i gh t e r a n d A nd r e r s ( 1985 ) • E f f e c ti v e l e n g th L ’ = L • E f f e c ti v e w id th B ’ is A ’ / L ’

11. C a se 4 [e L / L < 1 / 6 and e B / B < 1 / 6] E ccen t r ica l l y Loade d Founda t i ons A '  L B  1 ( B  B ) ( L  L ) 2 2 2 2 F r om e L / L a n d e B / B f in d t he magn it ud e o f L 2 a n d B 2 f r o m c h a r t H i gh t e r a n d A nd r e r s ( 1985 ) • E f f e c ti v e l e n g th L ’ = L • E f f e c ti v e w id th B ’ is A ’ / L ’

12. U p li ft C apac i ty o f Sha l l ow Founda t i ons F o und at io ns and o t h er s tr u c t u r e s m a y b e sub je c t e d t o up li f t f o r c e s und er sp e c i al c i r c u m s t an c e s. F o r t h o s e f o und at io ns , du r i n g t h e d e s i g n p r o c e ss i t i s d e s i r ab l e t o app l y a su f f i c i ent f a c t o r o f s a f e t y a g a i n s t f a il u r e by up li f t . Q u = w e i g h t o f soil in t h e f a ilu r e z o n e a n d t h e f o und a tion + f r ic tio n a l r e si s t a n ce o f soil a lo n g t h e f a il u r e s u r f a ce u I f the f o und a t i o n i s s ubj ec t e d t o an up li ft l o ad o f Q u , the f ail u r e sur f ace in th e s oil f o r r e l a t i v e l y s m all D f / B v a l u e s w ill m a k e an a ng le α w i t h th e h o r i z o n t a l . The m a g n i tude o f α w ill v a r y w i th the r e l a t i v e d e n s i ty o f c om pa c t i o n i n the c a s e of s and, and w i th the c o n s i s t e n c y i n the c a s e o f c l a y so il s . W h e n the f a il u r e s u r f a c e i n so i l e x t e nds up t o the g r o und s u r f a c e a t u l t i mat e l o ad, i t i s d e f i n e d as a sh all o w f o und a t io n und er up li f t . F o r l a r g e r v a l u e s o f D f / B , f a il u r e t a k e s p l a c e a r o und the f o und a t i o n and the f a il u r e s u r f a c e d oe s n o t e x t e nd t o the g r o und s u r f a ce . Th es e a r e c a ll e d d eep f o und a t io ns und er up li f t . The e m b e d m e n t r a t i o D f / B a t w h i c h a f o und a t i o n c han g e s f r om s ha ll o w t o d ee p c o nd i t i o n i s r e f er r e d t o as the c r i t i c al e mb e dm e n t r a t io ( D f / B ) c r . I n s and the m a g n i tude o f (D f /B ) cr c an v a r y f r om 3 t o ab o ut 11 , and i n s a tu r at e d c l a y i t c an v a r y f r om 3 t o ab o ut 7 . T h e u l t i m a t e up li f t c ap a c i t y , Q

13. U p li ft C apac i ty o f Sha l l ow Founda t i ons T h e u l t i m a t e up li f t c ap a c i t y c an b e e x p r e ss e d i n t h e f o rm o f a n o n d i me ns io nal b r ea k o u t f a c t o r , F q A - A r e a o f f o und a t i on F o und a ti on s in co h e si o n l e s s soil (S a nd, c= 0) T h e b r ea k o u t f a c t o r i s a fun c t io n o f t h e s oi l f r i c t io n an g l e and D f / B . F o r a g i v e n f r i c t io n an g l e, b r ea k o u t f a c t o r i n c r e as e s w i t h D f /B up t o a m a xi mu m v a l u e o f F q = F* q at D f / B = ( D f / B ) c r ( C r i t i c al em b e d me nt r at io ). F o r D f / B > ( D f / B ) c r t h e b r ea k o u t f a c t o r r e ma i ns p r a c t i c a ll y c o n s t a nt ( t h a t i s , F* q ) M e y er hof a n d A d a ms ( 1968 ) , D a s a n d S eel e y ( 1975) f u q A  D Q F   1  2  1  m          K u t a n  A  D f  D f    D f Q u F q  B   B       F o r sha ll ow c i r c u l ar f o und at io ns F o r sha ll ow r e c t an g u l ar f o und at io ns         1             B   B     L      D f  K t a n  1  2 m      1     D f F q  A  D B Q u u f W h e r e, m = a c o e f f i c i ent w h i c h i s a fun c t io n o f φ ; K u = N o m i nal up li f t c o e f f i c i ent

14. U p li ft C apac i ty o f Sha l l ow Founda t i ons F o und a ti on s in co h e si o n l e s s soil (S a nd, c= 0) F q w i th D f / B and φ ’ f or s qu a r e a n d c i r cu lar f oo t i n g s P r o c e du r e : De t e rm i n e D f / B F i nd ( D f / B ) c r us i n g t ab l e ( f o r squ a r e and c i r c u l ar f oo t i n g ) o r e qu at io n ( f o r r e c t an g u l ar f oo t i n g ) If ( D f / B ) ≤ ( D f / B ) c r t h e n i t i s a sha ll ow f o und at io n , h e n c e us e ( D f / B ) f o r e s ti m a ti n g F q , f r o m w h i c h Q u c an b e o b t a i n e d If ( D f / B ) > ( D f / B ) c r t h e n i t i s a d ee p f o und at io n h e n c e us e ( D f / B ) c r f o r e s t i mat i n g F q f r o m w h i c h Q u c an b e o b t a i n e d. T o f i n d ( D f / B ) c r φ ’ K u m + ( D f / B ) cr f o r squ a r e a n d ci r c u lar f oo t i n g Us e t ab l e p r o p ose d b y M e y er h o f and Ada m s (1968 ) f o r r ec t a ngu lar f oo t i n g Das and Jo n e s (1982 ) r e c omme nd e d f o ll o w i ng e qu a t i on  D f   D f    L    D f    B      B    0.13 3  B   0.86 7   1. 4   B     c r  rec t   c r  s qua r e       c r  s qua r e 20 . 856 . 05 2 . 5 25 . 888 . 1 3 30 . 920 . 15 4 40 . 960 . 35 7 45 . 96 . 5 9 + f or s qu a r e a n d c i r cu lar f oo t i n g s

15. U p li ft C apac i ty o f Sha l l ow Founda t i ons F o und a ti on s in co h e si v e soil ( C l a y , φ ’ = 0) P r o c e du r e : If ( D f / B ) ≤ ( D f / B ) c r t h e n i t i s a sha ll ow f o und at io n , If ( D f / B ) > ( D f / B ) c r t h e n i t i s a d ee p f o und at io n  c r  s qua re  D f  c r  rec t  c r  s qua re   D f  D f 0.7 3   1.5 5   B    0.27 B L       B     B                f o r r ec t a ngu lar f oo t i n g Das (1980) f o r squ a r e a n d ci r c u lar f oo t i n g Das (1978) T o f i n d ( D f / B ) c r T h e u l t i m a t e up li f t c ap a c i t y o f a f o und at io n i n a pu r e l y c o h e s i v e s oi l A - A r e a o f f o und a t i o n, m 2 Cu – und r a i n e d c o h es i o n, k P a F c -b r e a k o ut f a c t or Q u  A (  D f  c u F c )  0.10 7 c u  2.5  7   B    cr  s qua r e    D f Q  A (  D  c F *  ' ) u f u c   L   B  F  7.56  1.4 4  c *  cr  D f  D f  B  B   '  *  '  c F c F Q u  A (  D f  c u F c )   L   B  F  F *  7.56  1.4 4  c c

16. Thank You